dantuluri narayana raju college (autonomous) · 2019. 5. 2. · ii week 5 distributive lattices...

DANTULURI NARAYANA RAJU COLLEGE (AUTONOMOUS)

(A College with Potential for Excellence)

Bhimavaram, W.G.DIST. A.P.

Teaching Plan for the Academic Year: 2018 – 19.

Department: PG – Mathematics Paper: M105 Discrete Mathematics Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week

Topics to be covered Co-Curricular Activity

Jun – 8 IV Week 8 Graphs, digraphs,network, multi graph, elementary results,

Structure based on connectivity

Group discussion

Jul – 25

I Week 6 Characterization theorems on trees Quiz

II Week 5 Tree distances, Binary trees Assignment

III Week 6 Eulerian graphs, Hamiltonian graphs Seminar

IV Week 8 Spanning trees Group discussion

Aug – 24

I Week 6 Fundamental cycles, Minimal spanning trees Quiz

II Week 5 Kruskal algorithm, Prims algorithm Assignment

III Week 6 Definition of lattices, Two types of definitions, viz ordered

lattices and Algebraic lattices their equivalence

Seminar

IV Week 7 Modular lattices Group discussion

Sep – 21

I Week 5 Distributive lattices Quiz

II Week 4 Distributive lattices continued. Assignment

III Week 5 Basic properties, Seminar

IV Week 7 Boolean polynomials, Group discussion

Oct – 19

I Week 5 Ideals, Assignment

II Week 5 minimal forms of Boolean polynomials Seminar

III Week 0 Holidays

IV Week 9 SEMESTER END EXAMS

Nov - 09 I Week 4 SEMESTER END EXAMS

II Week 5 SEMESTER END EXAMS

Signature of the Lecturer Signature of the HOD Signature of the Principal





Department: Mathematics Paper: M 204 Linear Algebra Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13 III Week 5 Elementary canonical forms: introduction, Characteristic values Group discussion

IV Week 8 Annihilating polynomials, invariance of spaces Quiz

Dec – 23

I Week 6 Simultaneous triangulation, Assignment

II Week 6 simultaneous diagonalization Seminar

III Week 5 Direct sum decompositions, Invariant direct sums Group discussion

IV Week 6 The Primary decomposition theorem, Quiz

Jan – 18

I Week 5 Cyclic subspaces and annihilators Assignment

II Week 4 Cyclic decompositions and rational forms Seminar

III Week 1 The Jordan form - introduction Group discussion

IV Week 8 Computation of invariant factor Quiz

Feb – 21

I Week 6 Semi simple operators Assignment

II Week 4 Semi simple operators continued Seminar

III Week 5 Bilinear forms: Introduction, examples Group discussion

IV Week 6 Symmetric Bilinear forms: Definitions, examples, Results Assignment

Mar – 24

I Week 5 Skew symmetric Bilinear forms: Definitions, examples, Results Seminar

II Week 5 Group preserving Bilinear forms: Theoretical aspects and

problems

Quiz

III Week 6 Revision Assignment

IV Week 8 Revision

Apr – 9 I Week 4 SEMESTER-END EXAMS

II Week 5 SEMESTER - END EXAMS






Department: PG – Mathematics Paper: M105 Discrete Mathematics Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 7 IV Week 7 Graphs, digraphs, network, multi graph, elementary results,


Group discussion

Jul – 25





Aug – 21





Seminar


Sep – 18



III Week 6 Basic properties, Boolean polynomials, Seminar

IV Week 2 Boolean polynomials continued, Group discussion

Oct – 22

I Week 5 Boolean polynomials continue, Ideals, Assignment

II Week 5 minimal forms of Boolean polynomials Seminar

III Week 4 SEMESTER END EXAMS







Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 10

III Week 2 Elementary canonical forms: introduction, Group discussion

IV Week 8 Characteristic values, Annihilating polynomials, invariance of

spaces

Quiz

Dec – 23

I Week 5 Simultaneous triangulation, Assignment

II Week 5 simultaneous diagonalization Seminar

III Week 6 Direct sum decompositions, Invariant direct sums Group discussion

IV Week 7 The Primary decomposition theorem, Quiz

Jan – 17

I Week 5 Cyclic subspaces and annihilators Assignment

II Week 3 Cyclic decompositions and rational forms Seminar

III Week 3 The jordan form - introduction Group discussion

IV Week 6 Computation of invariant factor Quiz

Feb – 22

I Week 6 Semi simple operators Assignment

II Week 4 Semi simple operators continued Seminar

III Week 6 Bilinear forms: Introduction, examples Group discussion

IV Week 6 Symmetric Bilinear forms: Definitions, examples, Results Assignment

Mar – 23

I Week 5 Skew symmetric Bilinear forms: Definitions, examples, Results Seminar

II Week 5 Group preserving Bilinear forms: Theoretical aspects and

problems

Quiz


IV Week 7 Revision Seminar

Apr -10 I Week 5 SEMESTER-END EXAMS


SEMESTER-END EXAMS






Department: Mathematics Paper: M105 Discrete Mathematics Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


June – 8 IV Week 8 Graphs, digraphs, network, multi graph, elementary results,


Group discussion

Jul – 24





Aug – 22





Seminar


Sep – 23



III Week 6 Basic properties, Seminar

IV Week 8 Boolean polynomials, Ideals, Group discussion

Oct – 18

I Week 6 minimal forms of Boolean polynomials Assignment

II Week 0



Nov – 25 I Week 6 SEMESTER END EXAMS








Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec - 5 IV Week 5 Elementary canonical forms: introduction, Characteristic values Group discussion

Jan – 19

I Week 5 Annihilating polynomials, invariance of spaces Quiz

II Week 3 Simultaneous triangulation, Assignment

III Week 3 simultaneous diagonalization Seminar

IV Week 8 Direct sum decompositions, Invariant direct sums Group discussion

Feb – 20

I Week 5 The Primary decomposition theorem, Quiz

II Week 4 Cyclic subspaces and annihilators Assignment

III Week 6 Cyclic decompositions and rational forms Seminar

IV Week 5 The jordan form - introduction Group discussion

Mar – 25

I Week 6 Computation of invariant factor Quiz

II Week 5 Semi simple operators Assignment

III Week 6 Semi simple operators continued Seminar

IV Week 8 Bilinear forms: Introduction, examples Group discussion

Apr – 23 I Week 5 Symmetric Bilinear forms: Definitions, examples, Results Assignment

II Week 5 Skew symmetric Bilinear forms: Definitions, examples, Results Seminar

III Week 6

Group preserving Bilinear forms: Theoretical aspects and

problems

Quiz

IV Week 7 Semester end examinations






Department: Mathematics Paper: M105 Linear Algebra & Discrete Mathematics Class: I MSc. Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Elementary canonical forms: Introduction – Characteristic values,

vectors.

Group discussion

II Week 5 Annihilating polynomials Quiz

III Week 5 Invariant Subspaces Assignment

IV Week 9 Simultaneous Triangulation Seminar

Aug – 22

I Week 6 Simultaneous Diagonalization Group discussion

II Week 5 Direct sum Decompositons, Invariant Direct Sums, Quiz

III Week 5 The Primary Decomposition theorem, Assignment

IV Week 6 Definition of lattices, Examples, theorems Seminar

Sep – 23

I Week 5 Modular lattices Group discussion

II Week 5 distributive lattices Quiz

III Week 5 Boolean Polynomials: Basic properties, Assignment

IV Week 8 Boolean Polynomials, Ideals Seminar

Oct – 19

I Week 5 Ideals continued Group discussion

II Week 5 minimal forms of Boolean polynomials. Assignment






Department: Mathematics Paper: M 205 Graph theory and Advanced Coding theory Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 8 IV Week 8 Graphs, digraphs, network, multi graph, Group discussion

Dec – 24

I Week 6 elementary results, Structure based on connectivity,

Characterization theorems on trees

Quiz

II Week 5 Characterization, trees Assignment

III Week 6 theorems on trees, Tree distances, Seminar

IV Week 7 Binary trees, Eulerian graphs, Group discussion

Jan – 17

I Week 5 Hamiltonian graphs, Spanning trees, Quiz

II Week 1 Fundamental cycles, Assignment

III Week 4 Fundamental cycles continued, Seminar

IV Week 7 Minimal spanning trees, Kruskal algorithm, Prims algorithm Group discussion

Feb – 23

I Week 6 Introduction to coding theory: Introduction, Basic assumptions,

correcting, detecting codes,

Quiz

II Week 5 Information rate, the effects of error detection and correction Assignment

III Week 5 Finding most likely code word transmitted, some basic algebra,

weight and distance

Seminar

IV Week 7 Maximum likelyhood decoding, reliability of M.L.D, error Group discussion

detecting codes, error correcting codes

Mar – 23

I Week 5 Linear codes: Linear codes, two important subspaces,

independence

Assignment

II Week 5 Basis, dimension, matrices, bases for C = and C, generating

matrices and encoding

Seminar

III Week 6 Parity check matrices, equivalent codes, distance of a linear code, Quiz

IV Week 7 cosets, M.L.D for linear codes, reliability of linear codes. Seminar








Department: Mathematics Paper: M105 Linear Algebra & Discrete Mathematics Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Elementary canonical forms: Introduction – Characteristic values,

vectors.

Group discussion

II Week 5 Annihilating polynomials Quiz

III Week 6 Invariant Subspaces Assignment

IV Week 8 Simultaneous Triangulation Seminar

Aug – 21

I Week 6 Simultaneous Diagonalization Group discussion

II Week 4 Direct sum Decompositons, Invariant Direct Sums, Quiz

III Week 4 The Primary Decomposition theorem, Assignment

IV Week 7 Definition of lattices, Examples, theorems Seminar

Sep – 23

I Week 6 Modular lattices Group discussion

II Week 5 distributive lattices Quiz

III Week 6 Boolean Polynomials: Basic properties, Assignment

IV Week 6 Boolean Polynomials, Ideals Seminar

Oct – 19

I Week 1 Ideals continued Group discussion

II Week 5 minimal forms of Boolean polynomials. Assignment






Department: Mathematics Paper: M 205, Graph Theory & Advanced Coding theory Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec – 24

I Week 6 Graphs, digraphs, network, multi graph, Group discussion

II Week 5 elementary results, Structure based on connectivity,

Characterization theorems on trees

Quiz

III Week 6 Characterization, trees Assignment

IV Week 7 theorems on trees, Tree distances, Seminar

Jan – 17

I Week 5 Binary trees, Eulerian graphs, Group discussion

II Week 2 Hamiltonian graphs, Spanning trees, Quiz

III Week 3 Fundamental cycles, Assignment

IV Week 7 Minimal spanning trees, Kruskal algorithm, Prims algorithm Seminar

Feb – 22

I Week 6 Introduction to coding theory: Introduction, Basic assumptions,

correcting, detecting codes,

Group discussion

II Week 5 Information rate, the effects of error detection and correction Quiz

III Week 5 Finding most likely code word transmitted, some basic algebra,

weight and distance

Assignment

IV Week 6 Maximum likelyhood decoding, reliability of M.L.D, error

detecting codes, error correcting codes

Seminar

Mar – 22

I Week 5 Linear codes: Linear codes, two important subspaces,

independence

Group discussion

II Week 5 Basis, dimension, matrices, bases for C = and C, generating

matrices and encoding

Assignment

III Week 5 Parity check matrices, equivalent codes, distance of a linear code, Seminar

IV Week 7 cosets, M.L.D for linear codes, reliability of linear codes. Quiz

Apr - I Week SEMESTER-END EXAMINATIONS

II Week SEMESTER - END EXAMINATIONS






Department: PG – Mathematics Paper: M 101 Algebra – I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 8 IV Week 8 Automorphisms , conjugacy and G-sets Group discussion

Jul – 25

I Week 6 Normal series solvable groups Quiz

II Week 5 Nilpotent groups Assignment

III Week 6 Structure theorems of groups ;Direct product Seminar

IV Week 8 Finitely generated abelian groups Group discussion

Aug – 24

I Week 6 Invariance of finite abelian group Quiz

II Week 5 Sylow’s theorems Assignment

III Week 6 Groups of orders p^2, pq Seminar

IV Week 7 Ideals and homomorphisms, sum and direct sum of ideals Group discussion

Sep – 21

I Week 5 Maximal and prime ideals Quiz

II Week 4 Nilpotent and Nil ideals, Zorn’s lemma Assignment

III Week 5 Unique factorisation domains Seminar

IV Week 7 Principle ideal domains, Euclidean domains Group discussion

Oct – 19

I Week 5 Polynomial rings over UFD Assignment

II Week 5 Rings of fractions Seminar

III Week 0 Holidays





Department: Mathematics Paper: M 201 Abstract Algebra-II Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13 III Week 5

Algebraic extensions of fields: Irreducible polynomial and

Eisenstein criterion

Group discussion

IV Week 8 Adjunction of roots, algebraic extensions Quiz

Dec – 23

I Week 6 Algebraically closed fields Assignment

II Week 6 Normal and separable extensions : Splitting fields Seminar

III Week 5 Normal extensions, multiple roots Group discussion

IV Week 6 Finite fields ,Separable extensions Quiz

Jan – 18

I Week 5 Galois theory Assignment

II Week 4 Automorphism groups Seminar

III Week 1 Fixed fields Group discussion

IV Week 8 Fundamental theorem of Galois theory Quiz

Feb – 21

I Week 6 Fundamental theorem of algebra Assignment

II Week 4 Applications of Galois theory to classical problems Seminar

III Week 5 Roots of unity Group discussion

IV Week 6 Cyclotonic polynomials Quiz

Mar – 24 I Week 5 Cyclic extensions Assignment

II Week 5 Polynomials solvable for radicals Seminar

III Week 6 Ruler Assignment









Department: PG – Mathematics Paper: M 101 Algebra – I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 7 IV Week 7 Automorphisms , conjugacy and G-sets Group discussion

Jul – 25





Aug – 21





Sep – 18




IV Week 2 Principle ideal domains, Euclidean domains Group discussion

Oct – 22

I Week 5 Polynomial rings over UFD Assignment

II Week 5 Rings of fractions Seminar






Department: Mathematics Paper: M 201 Algebra – II Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week



Algebraic extensions of fields: Irreducible polynomial and


Group discussion

IV Week 8 Adjunction of roots, algebraic extensions Quiz

Dec – 23

I Week 5 Algebraically closed fields Assignment

II Week 5 Normal and separable extensions : Splitting fields Seminar

III Week 6 Normal extensions, multiple roots Group discussion

IV Week 7 Finite fields ,Separable extensions Quiz

Jan – 17

I Week 5 Galois theory Assignment

II Week 3 Automorphism groups Seminar

III Week 3 Fixed fields Group discussion

IV Week 6 Fundamental theorem of Galois theory Quiz

Feb – 22

I Week 6 Fundamental theorem of algebra Assignment

II Week 4 Applications of Galois theory to classical problems Seminar

III Week 6 Roots of unity Group discussion

IV Week 6 Cyclotonic polynomials Quiz

Mar – 23 I Week 5 Cyclic extensions Assignment

II Week 5 Polynomials solvable for radicals Seminar

III Week 6 Ruler Assignment




SEMESTER-END EXAMS






Department: Mathematics Paper: M 101 Algebra – I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


June – 8 IV Week 8 Automorphisms , conjugacy and G-sets Group discussion

Jul – 24





Aug – 22





Sep – 23




IV Week 8 Principle ideal domains, Euclidean domains Assignments

Oct – 18

I Week 6 Polynomial rings over UFD Seminar

II Week 0 Rings of fractions







Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec - 5 IV Week 5 Algebraic extensions of fields: Irreducible polynomial and


Group discussion

Jan – 19

I Week 5 Adjunction of roots, algebraic extensions Quiz

II Week 3 Algebraically closed fields Assignment

III Week 3 Normal and separable extensions : Splitting fields Seminar

IV Week 8 Normal extensions, multiple roots Group discussion

Feb – 20

I Week 5 Finite fields ,Separable extensions Quiz

II Week 4 Galois theory Assignment

III Week 6 Automorphism groups Seminar

IV Week 5 Fixed fields Group discussion

Mar – 25

I Week 6 Fundamental theorem of Galois theory Quiz

II Week 5 Fundamental theorem of algebra Assignment

III Week 6 Applications of Galois theory to classical problems Seminar

IV Week 8 Roots of unity, Cyclotonic polynomials Group discussion

Apr – 23 I Week 5 Cyclic extensions Quiz

II Week 5 Polynomials solvable for radicals Assignment

III Week 6 Ruler Seminar

IV Week 7 Examinations






Department: Mathematics Paper: M 101 Algebra - I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Group Theory: Definition of a group, Some examples of groups,

some preliminary lemmas,

Group discussion

II Week 5 Subgroups, A counting principle, Quiz

III Week 5 Normal subgroups and quotient groups Assignment

IV Week 9 Homomorphisms, Automorphisms Seminar

Aug – 22

I Week 6 Group theory: Cayley’s theorem, permutation group, Group discussion

II Week 5 Another counting principle Quiz

III Week 5 Sylows theorem Assignment

IV Week 6 Direct product, finite abelian groups, Seminar

Sep – 23

I Week 5 Ring Theory: Definition and examples of Rings, Some special

classes of rings

Group discussion

II Week 5 Homomorphisms, Ideals and quotient rings, Quiz

III Week 5 more Ideals and quotient rings, The field of quotients of an

Integral Domain

Assignment

IV Week 8 Ring theory: Euclidean rings, a particular Euclidean ring Seminar

Oct – 19 I Week 5 Polynomial rings Group discussion

II Week 5 Polynomial over the rational field, Quiz

III Week 3 Polynomial rings over the commutative rings. Assignment

IV Week 6 Polynomial rings over the commutative rings. Seminar









Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 8 IV Week 8 Fields: Extension fields, Group discussion

Dec – 24

I Week 6 the transcendence of e. Quiz

II Week 5 Roots of polynomials Assignment

III Week 6 Construction with straightedge and compass Seminar

IV Week 7 Fields: More about roots Group discussion

Jan – 17

I Week 5 The elements of Galois theory Quiz

II Week 1 The elements of Galois theory Assignment

III Week 4 Solvability by radicals Seminar

IV Week 7 Galois groups over the rational Group discussion

Feb – 23

I Week 6 Finite field: Wedderburn’s theorem on finite division rings Quiz

II Week 5 Wedderburn’s theorem on finite division rings Assignment

III Week 5 Wedderburn’s theorem on finite division rings Seminar

IV Week 7 Wedderburn’s theorem on finite division rings Group discussion

Mar – 23 I Week 5

A theorem of Frobenius: Integral quoternions and the four-square

theorem

Quiz

II Week 5 Integral quoternions and the four-square theorem Assignment

III Week 6 Integral quoternions and the four-square theorem Seminar

IV Week 7 Integral quoternions and the four-square theorem








Department: Mathematics Paper: M101 Algebra - I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Group Theory: Definition of a group, Some examples of groups,

some preliminary lemmas,

Group discussion

II Week 5 Subgroups, A counting principle, Quiz

III Week 6 Normal subgroups and quotient groups Assignment

IV Week 8 Homomorphisms, Automorphisms Seminar

Aug – 21

I Week 6 Group theory: Cayley’s theorem, permutation group, Group discussion

II Week 4 Another counting principle Quiz

III Week 4 Sylows theorem Assignment

IV Week 7 Direct product, finite abelian groups, Seminar

Sep – 23

I Week 6 Ring Theory: Definition and examples of Rings, Some special

classes of rings

Group discussion

II Week 5 Homomorphisms, Ideals and quotient rings, Quiz

III Week 6 more Ideals and quotient rings, The field of quotients of an

Integral Domain

Assignment

IV Week 6 Ring theory: Euclidean rings, a particular Euclidean ring Seminar

Oct – 19 I Week 1 Polynomial rings Group discussion

II Week 5 Polynomial rings Quiz

III Week 6 Polynomial over the rational field, Assignment

IV Week 7 Polynomial rings over the commutative rings. Seminar











Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec – 24

I Week 6 Fields: Extension fields, Group discussion

II Week 5 the transcendence of e. Quiz

III Week 6 Roots of polynomials Assignment

IV Week 7 Construction with straightedge and compass Seminar

Jan – 17

I Week 5 Fields: More about roots Group discussion

II Week 2 The elements of Galois theory Quiz

III Week 3 Solvability by radicals Assignment

IV Week 7 Galois groups over the rational Seminar

Feb – 22

I Week 6 Finite field: Wedderburn’s theorem on finite division rings Group discussion

II Week 5 Wedderburn’s theorem on finite division rings Quiz

III Week 5 Wedderburn’s theorem on finite division rings Assignment

IV Week 6 Wedderburn’s theorem on finite division rings Seminar

Mar – 22

I Week 5 A theorem of Frobenius: Integral quoternions and the four-square

theorem

Group discussion

II Week 5 Integral quoternions and the four-square theorem Quiz

III Week 5 Integral quoternions and the four-square theorem Assignment

IV Week 7 Integral quoternions and the four-square theorem Seminar

Apr - I Week SEMESTER-END EXAMS

II Week SEMESTER - END EXAMS






Department: PG – Mathematics Paper: M 102 Real Analysis – I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 8 IV Week 8 Basic Topology, finite, countable and uncountable sets Group discussion

Jul – 25

I Week 6 Metric spaces, compact sets Quiz

II Week 5 Connected sets, Assignment

III Week 6 Numerical sequences and series, convergent sequences, Seminar

IV Week 8 Sub sequences, Cauchy sequences, upper and lower limit Group discussion

Aug – 24

I Week 6 Some special sequences, series, series of non negative terms,

number

Quiz

II Week 5 The root and ratio tests, Power series Assignment

III Week 6 Summation by parts, absolute convergence Seminar

IV Week 7 Addition and multiplication of series, rearrangements Group discussion

Sep – 21

I Week 5 Continuity: Limits of function, continuous functions. Quiz

II Week 4 Continuity and compactness, continuity and connectedness Assignment

III Week 5 Discontinuities, Monotone functions, Infinite limits and limits at

infinity

Seminar

IV Week 7 Differentiation: The derivate of a real function, Mean value Group discussion

theorems

Oct – 19

I Week 5 The continuity of derivative, L. Hospitals rule, derivatives of

higher order

Assignment

II Week 5 Taylor’s theorem, Differentiation of vector valued functions Seminar

III Week 0 Holidays









Department: Mathematics Paper: M 202 Real Analysis – II Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week



Riemann Stieltjes integral: Definition and existence of the

Riemann Stieltjes integral

Group discussion

IV Week 8 Properties of the integral, Integration and differentiation, Quiz

Dec – 23

I Week 6 The fundamental theorem of calculus – integral of vector –

valued function, rectifiable curves,

Assignment

II Week 6 Sequences and series of the function: Discussion on the main

problem

Seminar

III Week 5 Uniform convergence, uniform convergence and continuity Group discussion

IV Week 6 Uniform convergence and integration, Uniform convergence and

differentiation

Quiz

Jan – 18

I Week 5 Equicontinuous families of function Assignment

II Week 4 The Stone – Weierstrass theorem Seminar

III Week 1 Functions of several variable: Group discussion

IV Week 8 Linear transformation, differentiation Quiz

Feb – 21 I Week 6 The Contraction principle Assignment

II Week 4 The inverse function theorem Seminar

III Week 5 The implicit function theorem Group discussion

IV Week 6 The Rank theorem, Assignment

Mar – 24

I Week 5 Determinates Seminar

II Week 5 Derivatives of higher order Assignment

III Week 6 Differentiation of integrals Seminar

IV Week 8 Revision








Department: PG – Mathematics Paper: M 102 Real Analysis – I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 7 IV Week 7 Basic Topology, finite, countable and uncountable sets Group discussion

Jul – 25





Aug – 21


number

Quiz




Sep – 18

I Week 5 Continuity: Limits of function, continuous functions Quiz



infinity, Differentiation: The derivate of a real function,

Seminar

IV Week 2 Mean value theorems Group discussion

Oct – 22


higher order

Assignment





II Week 5 SEMESTER END EXAMS Exam 23 - 10







Month &

No. of

working

Days

Week

No. of

periods

per

Week



Riemann Stieltjes integral: Definition and existence of the


Group discussion

IV Week 8 Properties of the integral, Integration and differentiation, Quiz

Dec – 23

I Week 5 The fundamental theorem of calculus – integral of vector –


Assignment

II Week 5 Sequences and series of the function: Discussion on the main

problem

Seminar

III Week 6 Uniform convergence, uniform convergence and continuity Group discussion

IV Week 7 Uniform convergence and integration, Uniform convergence and

differentiation

Quiz

Jan – 17

I Week 5 Equicontinuous families of function Assignment

II Week 3 The Stone – Weierstrass theorem Seminar

III Week 3 Functions of several variable: Group discussion

IV Week 6 Linear transformation, differentiation Quiz

Feb – 22 I Week 6 The Contraction principle Assignment

II Week 4 The inverse function theorem Seminar

III Week 6 The implicit function theorem Group discussion

IV Week 6 The Rank theorem, Assignment

Mar – 23

I Week 5 Determinates Seminar



IV Week 7 Revision



SEMESTER-END EXAMS






Department: Mathematics Paper: M102 Real Analysis – I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


June – 8 IV Week 8 Basic Topology, finite, countable and uncountable sets Group discussion

Jul – 24





Aug – 22


number

Quiz




Sep – 23

I Week 5 Continuity: Limits of function, continuous functions. Quiz



infinity

Seminar

IV Week 8 Differentiation: The derivate of a real function, Mean value Group discussion

theorems

Oct – 18


higher order

Assignment


III Week 5 Holidays


Nov – 25 I Week 6 SEMESTER END EXAMS Second sem class work







Department: Mathematics Paper: M 202 Real Analysis - II Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec - 5 IV Week 5 Riemann Stieltjes integral: Definition and existence of the


Group discussion

Jan – 19

I Week 5 Properties of the integral, Integration and differentiation, Quiz

II Week 3 The fundamental theorem of calculus – integral of vector –


Assignment

III Week 3 Sequences and series of the function: Discussion on the main

problem

Seminar

IV Week 8 Uniform convergence, uniform convergence and continuity Group discussion

Feb – 20

I Week 5 Uniform convergence and integration, Uniform convergence and

differentiation

Quiz

II Week 4 Equicontinuous families of function Assignment

III Week 6 The Stone – Weierstrass theorem Seminar

IV Week 5 Functions of several variable: Group discussion

Mar – 25 I Week 6 Linear transformation, differentiation Quiz

II Week 5 The Contraction principle Assignment

III Week 6 The inverse function theorem Seminar

IV Week 8 The implicit function theorem, The Rank theorem, Group discussion

Apr – 23 I Week 5 Determinates, Derivatives of higher order Assignment

II Week 5 Differentiation of integrals Seminar

III Week 6 Examinations







Department: Mathematics Paper: M102 Real Analysis - I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Basic Topology, finite, countable and uncountable sets Group discussion

II Week 5 Metric spaces, compact sets Quiz

III Week 5 Connected sets, Assignment

IV Week 9 Numerical sequences and series, convergent sequences, Seminar

Aug – 22

I Week 6 Sub sequences, Cauchy sequences, upper and lower limit Group discussion

II Week 5 Some special sequences, series, series of non negative terms,

number

Quiz

III Week 5 The root and ratio tests, Power series Assignment

IV Week 6 Summation by parts, absolute convergence Seminar

Sep – 23

I Week 5 Addition and multiplication of series, rearrangements Group discussion

II Week 5 Continuity: Limits of function, continuous functions. Quiz

III Week 5 Continuity and compactness, continuity and connectedness Assignment

IV Week 8

Discontinuities, Monotone functions, Infinite limits and limits at

infinity, Differentiation: The derivate of a real function, Mean

value theorems

Seminar

Oct – 19


higher order,

Group discussion

II Week 5 Taylor’s theorem, Differentiation of vector valued functions Assignment

III Week 3 SEMESTER END EXAMS Seminar




III Week SEMESTER END EXAMS







Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 8 IV Week 8 Riemann Stieltjes integral: Definition and existence of the


Group discussion

Dec – 24

I Week 6 Properties of the integral, Integration and differentiation, Quiz

II Week 5 The fundamental theorem of calculus – integral of vector –


Assignment

III Week 6 Sequences and series of the function: Discussion on the main

problem

Seminar

IV Week 7 Uniform convergence, uniform convergence and continuity Group discussion

Jan – 17

I Week 5 Uniform convergence and integration, Uniform convergence and

differentiation

Quiz

II Week 1 Equicontinuous families of function Assignment

III Week 4 The Stone – Weierstrass theorem Seminar

IV Week 7 Functions of several variable: Group discussion

Feb – 23 I Week 6 Linear transformation, differentiation Quiz

II Week 5 The Contraction principle Assignment

III Week 5 The inverse function theorem Seminar

IV Week 7 The implicit function theorem Group discussion

Mar – 23

I Week 5 The Rank theorem, Assignment

II Week 5 Determinates Seminar

III Week 6 Derivatives of higher order Quiz

IV Week 7 Differentiation of integrals Assignments

Apr – 8 I Week 5 Examinations







Department: Mathematics Paper: M 102: Real Analysis – 1 Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Basic Topology, finite, countable and uncountable sets Group discussion

II Week 5 Metric spaces, compact sets Quiz

III Week 6 Connected sets, Assignment

IV Week 8 Numerical sequences and series, convergent sequences, Sub

sequences, Cauchy sequences, upper and lower limit

Seminar

Aug – 21


number

Group discussion

II Week 4 The root and ratio tests, Power series Quiz

III Week 4 Summation by parts, absolute convergence Assignment

IV Week 7 Addition and multiplication of series, rearrangements Seminar

Sep – 23

I Week 6 Continuity: Limits of function, continuous functions. Group discussion

II Week 5 Continuity and compactness, continuity and connectedness Quiz


infinity, Differentiation: The derivate of a real function,

Assignment

IV Week 6 Mean value theorems, The continuity of derivative, L. Hospitals Seminar

rule,

Oct – 19

I Week 1 Derivatives of higher order Group discussion

II Week 5 Taylor’s theorem, Differentiation of vector valued functions Assignment













Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec – 24

I Week 6 Riemann Stieltjes integral: Definition and existence of the


Group discussion

II Week 5 Properties of the integral, Integration and differentiation, Quiz

III Week 6 The fundamental theorem of calculus – integral of vector –


Assignment

IV Week 7 Sequences and series of the function: Discussion on the main

problem

Seminar

Jan – 17

I Week 5 Uniform convergence, uniform convergence and continuity Group discussion

II Week 2 Uniform convergence and integration, Uniform convergence and

differentiation

Quiz

III Week 3 Equicontinuous families of function Assignment

IV Week 7 The Stone – Weierstrass theorem Seminar

Feb – 22

I Week 6 Functions of several variable: Group discussion

II Week 5 Linear transformation, differentiation Quiz

III Week 5 The Contraction principle, The inverse function theorem Assignment

IV Week 6 The implicit function theorem Seminar

Mar – 22

I Week 5 The Rank theorem, Determinates Group discussion



IV Week 7 Revision

Apr - I Week

II Week






Department: PG – Mathematics Paper: M 104 Topology Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 8 IV Week 8 Sets and set inclusion, The Algebra of sets, Functions, Products

of sets, Partition and equivalence relations

Group discussion

Jul – 25

I Week 6 countable sets, Uncountable sets, Quiz

II Week 5 Partially ordered sets and lattices Assignment

III Week 6 Metric spaces, The definition and some examples, Seminar

IV Week 8 open sets, closed sets. Group discussion

Aug – 24

I Week 6 Convergence, completeness and Baire’s theorem. Quiz

II Week 5 Continuous mappings. Assignment

III Week 6 Spaces of continuous functions, Euclidean and Unitary spaces. Seminar

IV Week 7 Topological Spaces-The definition and some examples,

elementary concepts,

Group discussion

Sep – 21

I Week 5 open bases and open subbases. Week topologies, Quiz

II Week 4 The function algebras C(X, R) and C(X, C). Assignment

III Week 5 Compact spaces.. Seminar

IV Week 7 product of spaces – Techonoff’s theorem and locally compact

spaces

Group discussion

Oct – 19

I Week 5 Compactness for metric spaces Assignment

II Week 5 Compactness for metric spaces – Ascoli’s theorem Seminar

III Week 0 Holidays





Department: Mathematics Paper: M 205 Probability Theory & Statistics Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13 III Week 5 Sample spaces and events Group discussion

IV Week 8 The axiom of probability, some theorems on probability, Quiz

Dec – 23

I Week 6 Boole’s inequality, Conditional probability, Assignment

II Week 6 Multiplication theorem on probability, Independent events,

Multiplication theorem on probability for Independent events

Seminar

III Week 5 Extension of Multiplication theorem on probability to n events,

Pairwise Independent events, Baye’s Theorem

Group discussion

IV Week 6

Discrete function, Discrete Random variable, Continuous

Random variables, Mathematical expectation, Expected value of

function of a random variable

Quiz

Jan – 18

I Week 5 Properties of expectation, Properties of variance, covariance, Assignment

II Week 4 Moment generating functions, characteristic function Seminar

III Week 1 characteristic function continued Group discussion

IV Week 8 Binomial distribution, Poisson distribution, Quiz

Feb – 21

I Week 6 Normal distribution and Uniform Distributions, Assignment

II Week 4 Correlation: Introduction, meaning of correlation, scatter diagram Seminar

III Week 5 Pearson’s Coefficient of correlation, Rank correlation Group discussion

IV Week 6 Linear and Curvilinear Regression, Introduction, linear

regression, curvilinear regression

Quiz

Mar – 24

I Week 5 Large sampling theory: Introduction, types of sampling Assignment

II Week 5 parameters and statistic Seminar

III Week 6 tests of significance, procedure for testing of hypothesis Assignment

IV Week 8 tests of significance for large samples. Seminar








Department: PG – Mathematics Paper: M 104 Topology Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 7 IV Week 7 Sets and set inclusion, The Algebra of sets, Functions, Products

of sets, Partition and equivalence relations.

Group discussion

Jul – 25

I Week 6 Countable sets, Uncountable sets, Quiz

II Week 5 Partially ordered sets and lattices. Assignment


IV Week 8 Open sets, closed sets. Convergence, completeness. Group discussion

Aug – 21

I Week 4 Baire’s theorem. Quiz

II Week 4 Continuous mappings. Assignment

III Week 5 Spaces of continuous functions, Euclidean and Unitary spaces. Seminar


elementary concepts, open bases and open subbases.

Group discussion

Sep – 18

I Week 5 Week topologies, The function algebras C(X, R) and C(X, C). Quiz

II Week 5 Compact spaces Assignment

III Week 6 product of spaces – Techonoff’s theorem and locally compact Seminar

spaces

IV Week 2 Compactness for metric spaces Group discussion

Oct – 22

I Week 5 Compactness for metric spaces Assignment

II Week 5 Ascoli’s theorem Seminar











Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 10 III Week 2 Sample spaces and events Group discussion

IV Week 8 The axiom of probability, some theorems on probability, Quiz

Dec – 23

I Week 5 Boole’s inequality, Conditional probability, Assignment

II Week 5 Multiplication theorem on probability, Independent events,


Seminar

III Week 6 Extension of Multiplication theorem on probability to n events,


Group discussion

IV Week 7




Quiz

Jan – 17

I Week 5 Properties of expectation, Properties of variance, covariance, Assignment

II Week 3 Moment generating functions, characteristic function Seminar

III Week 3 continued Group discussion

IV Week 6 Binomial distribution, Poisson distribution, Quiz

Feb – 22

I Week 6 Normal distribution and Uniform Distributions, Assignment

II Week 4 Correlation: Introduction, meaning of correlation, scatter diagram Seminar

III Week 6 Pearson’s Coefficient of correlation, Rank correlation Group discussion

IV Week 6 Linear and Curvilinear Regression, Introduction, linear

regression, curvilinear regression

Quiz

Mar – 23

I Week 5 Large sampling theory: Introduction, types of sampling Assignment

II Week 5 parameters and statistic Seminar

III Week 6 tests of significance, procedure for testing of hypothesis Assignment

IV Week 7 tests of significance for large samples. Seminar



SEMESTER-END EXAMS






Department: Mathematics Paper: M 104 Topology Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


June – 8 IV Week 8 Sets and set inclusion, The Algebra of sets, Functions, Products


Group discussion

Jul – 24

I Week 5 Countable sets, Uncountable sets, Quiz

II Week 5 Partially ordered sets and lattices. Assignment


IV Week 8 Open sets, closed sets. Convergence, completeness, Baire’s

theorem.

Group discussion

Aug – 22

I Week 6 Continuous mappings. Quiz

II Week 4 Spaces of continuous functions, Euclidean and Unitary spaces. Assignment

III Week 4 Topological Spaces-The definition and some examples, Seminar

IV Week 8 Elementary concepts, open bases and open subbases, Week

topologies,

Group discussion

Sep – 23 I Week 5 The function algebras C(X, R) and C(X, C). Quiz

II Week 4 Compact spaces Assignment

III Week 6 product of spaces – Techonoff’s theorem and locally compact

spaces.

Seminar

IV Week 8 Compactness for metric spaces. Assignments

Oct – 18

I Week 6 Ascoli’s theorem. Seminar

II Week 0



Nov – 25 I Week 6 SEMESTER END EXAMS Second sem class work








Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec - 5 IV Week 5 Sample spaces and events Group discussion

Jan – 19

I Week 5 The axiom of probability, some theorems on probability, Quiz

II Week 3 Boole’s inequality, Conditional probability, Assignment

III Week 3 Multiplication theorem on probability, Independent events,


Seminar

IV Week 8 Extension of Multiplication theorem on probability to n events,


Group discussion

Feb – 20

I Week 5




Quiz

II Week 4 Properties of expectation, Properties of variance, covariance, Assignment

III Week 6 Moment generating functions, characteristic function Seminar

IV Week 5 continued Group discussion

Mar – 25 I Week 6 Binomial distribution, Poisson distribution, Quiz

II Week 5 Normal distribution and Uniform Distributions, Assignment

III Week 6 Correlation: Introduction, meaning of correlation, scatter

diagram, Pearson’s Coefficient of correlation

Seminar

IV Week 8 Rank correlation, Linear and Curvilinear Regression,

Introduction, linear regression, curvilinear regression

Group discussion

Apr – 23 I Week 5

Large sampling theory: Introduction, types of sampling,

parameters and statistic

Quiz

II Week 5 tests of significance, procedure for testing of hypothesis Assignment

III Week 6 tests of significance for large samples Seminar

IV Week 7

.






Department: Mathematics Paper: M104 Topology - I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Sets and set inclusion, The Algebra of sets, Functions, Products


II Week 5 Countable sets, Uncountable sets,

III Week 5 Partially ordered sets and lattices.

IV Week 9 Metric spaces, The definition and some examples,

Aug – 22

I Week 6 Open sets, closed sets. Convergence, completeness, Baire’s

theorem.

II Week 5 Continuous mappings.

III Week 5 Spaces of continuous functions, Euclidean and Unitary spaces.


Sep – 23

I Week 5 Elementary concepts, open bases and open subbases, Week

topologies,

II Week 5 The function algebras C(X, R) and C(X, C).

III Week 5 Compact spaces


spaces.

Oct – 19

I Week 5 Compactness for metric spaces.

II Week 5 Ascoli’s theorem.










Department: Mathematics Paper: M 203 Topology – II Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 8 IV Week 8 T1 spaces and Hausdorff spaces.

Dec – 24

I Week 6 Completely regular spaces and normal spaces,

II Week 5 Urysohn’s lemma and the Tietze extension theorem.

III Week 6 The Urysohn imbedding theorem, The Stone – cech compactness.

IV Week 7 Connected spaces.

Jan – 17

I Week 5 The components of a space.

II Week 1 The components of a space.

III Week 4 Totally disconnected spaces.

IV Week 7 Locally connected spaces.

Feb – 23

I Week 6 The Weierstrass approximation theorem.

II Week 5 The Stone – Weierstrass theorems.

III Week 5 Locally compact Hausdorff spaces,

IV Week 7 The extended Stone – Weiersatrass theorems.

Mar – 23

I Week 5 Neighbourhoods of a point in topological group.

II Week 5 Isomorpism and local isomorphisms.

III Week 6 Subgroups – Quotient groups.

IV Week 7 Homomorphisms.








Department: Mathematics Paper: M104 Topology - I Class: I MSc Semester: I

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jul – 25

I Week 6 Sets and set inclusion, The Algebra of sets, Functions, Products


II Week 5 Countable sets, Uncountable sets,

III Week 6 Partially ordered sets and lattices.

IV Week 8 Metric spaces, The definition and some examples,

Aug – 21

I Week 6 Open sets, closed sets. Convergence, completeness, Baire’s

theorem.

II Week 4 Continuous mappings.

III Week 4 Spaces of continuous functions, Euclidean and Unitary spaces.


Sep – 23

I Week 6 Elementary concepts, open bases and open subbases, Week

topologies,

II Week 5 The function algebras C(X, R) and C(X, C).

III Week 6 Compact spaces


spaces.

Oct – 19

I Week 1 Compactness for metric spaces.

II Week 5 Ascoli’s theorem.










Department: Mathematics Paper: M 203 Topology – II Class: I MSc Semester: II

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Dec – 24

I Week 6 T1 spaces and Hausdorff spaces.

II Week 5 Completely regular spaces and normal spaces,

III Week 6 Urysohn’s lemma and the Tietze extension theorem.

IV Week 7 The Urysohn imbedding theorem, The Stone – cech compactness.

Jan – 17

I Week 5 Connected spaces.

II Week 2 The components of a space.

III Week 3 The components of a space.

IV Week 7 Totally disconnected spaces.

Feb – 22

I Week 6 Locally connected spaces.

II Week 5 The Weierstrass approximation theorem.

III Week 5 The Stone – Weierstrass theorems.

IV Week 6 Locally compact Hausdorff spaces, The extended Stone –

Weiersatrass theorems.

Mar – 22

I Week 5 Neighbourhoods of a point in topological group.

II Week 5 Isomorpism and local isomorphisms.

III Week 5 Subgroups – Quotient groups.

IV Week 7 Homomorphisms.

Apr - I Week SEMESTER-END EXAMINATIONS

II Week SEMESTER - END EXAMINATIONS






Department: PG – Mathematics Paper: M 304 Partial Differential Equations Class: II MSc Semester: III

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 22

I Week 4 Introduction, Methods of Solution of R

dz

Q

dy

P

dx

Group discussion

II Week 5 Orthogonal trajectories of a system of curves on a surface Quiz

III Week 5 Pfaffian Differential forms and equations, Solutions of Pfaffian

differential equations in three variables

Assignment

IV Week 8 Cauchy’s problem for first order partial differential differential

equations

Seminar

Jul – 25

I Week 6 Linear Equations of the first order, Integral surfaces, Orthogonal

surfaces,

Group discussion

II Week 5 Non-linear partial differential equations of the first order Quiz

III Week 6 Cauchy’s method of characteristics, Compatible system of first

order equations,

Assignment

IV Week 8 Charpits method, Special types of first order equations, Jacobi’s

method

Seminar

Aug – 24 I Week 6 Partial Differential equations of the second order, Their orgin, Group discussion

II Week 5 Linear partial differential equations with constant and variable

coefficients,

Quiz

III Week 6 Solutions of linear hyperbolic equations Assignment

IV Week 7 Method of equation of variables, Monger’s method. Seminar

Sep – 21

I Week 5 Laplace equations, elementary solutions Group discussion

II Week 4 Families of equipotential surfaces Quiz

III Week 5 Boundary value problems Assignment

IV Week 7 Methods of separation of variables of solving Laplace equations,

problems with axial symmetry,

Seminar

Oct – 19

I Week 5 Kelvin’s inversion theorem, the wave equation Assignment

II Week 5 Elementary solution in one dimential form, Riemann – Volterra

solution of one dimentional wave equation

Seminar

III Week 0


Nov - 09 I Week 4 Examinations

II Week 5 Examinations






Department: PG – Mathematics Paper: M 405 Discrete Dynamical Systems Class: II MSc. Semester: IV

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Nov – 13 III Week 5 Phase Portraits Group discussion

IV Week 8 Periodic Points and Stable Sets Quiz

Dec – 23

I Week 6 Stable Sets continued, Sarkovskii’s theorem Assignment

II Week 6 Differentiability and its implications (hyperbolic, attractive and

repelling periodic points)

Seminar

III Week 5 Parameterized Families of Functions Group discussion

IV Week 6 Bifurcations Quiz

Jan – 18

I Week 5 The Logistic Function Part I [Cantor Sets] Assignment

II Week 4 Symbolic Dynamics and Chaos. Seminar

III Week 1 Symbolic Dynamics and Chaos. Group discussion

IV Week 8 The Logistic Function Part II Topological Conjugacy, Quiz

Feb – 21

I Week 6 The Logistic Function Part III [Period Doubling Cascade], Assignment

II Week 4 Newton’s Method Seminar

III Week 5 Numerical solutions of Differential Equations, Group discussion

IV Week 6 The Dynamics of Complex functions [Newton’s Method in Quiz

Complex Plane],

Mar – 24

I Week 5 the Quadratic Family Assignment

II Week 5 Mandelbrot Set Seminar



Apr – 8 I Week 5 SEMESTER - END EXAMINATIONS

II Week 3 SEMESTER - END EXAMINATIONS




Bhimavaram, W.G.DIST. A. P.


Department: PG – Mathematics Paper: M 302 Partial Differential Equations Class: II MSc Semester: III

Month &

No. of

working

Days

Week

No. of

periods

per

Week


Jun – 24

I Week 6 Introduction, Methods of Solution of R

dz

Q

dy

P

dx

Group discussion

II Week 5 Orthogonal trajectories of a system of curves on a surface Quiz

III Week 6 Pfaffian Differential forms and equations, Solutions of Pfaffian

differential equations in three variables

Assignment

IV Week 7 Cauchy’s problem for first order partial differential differential

equations

Seminar

Jul – 25

I Week 6 Linear Equations of the first order, Integral surfaces, Orthogonal

surfaces,

Group discussion

II Week 5 Non-linear partial differential equations of the first order Quiz

III Week 6 Cauchy’s method of characteristics, Compatible system of first

order equations,

Assignment

IV Week 8 Charpits method, Special types of first order equations, Jacobi’s

method

Seminar

Aug – 21 I Week 4 Partial Differential equations of the second order, Their orgin, Group discussion

II Week 4 Linear partial differential equations with constant and variable

coefficients,

Quiz

III Week 5 Solutions of linear hyperbolic equations Assignment

IV Week 8 Method of equation of variables, Monger’s method. Seminar

Sep – 18

I Week 5 Laplace equations, elementary solutions Group discussion

II Week 5 Families of equipotential surfaces Quiz

III Week 6 Boundary value problems Assignment

IV Week 2 Methods of separation of variables of solving Laplace equations,

problems with axial symmetry,

Seminar

Oct – 22

I Week 5 Kelvin’s inversion theorem, the wave equation Assignment

II W

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