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Template No (12) Course Specification
University/Academy: Suez canal university
Faculty/Institute: Faculty of Science
Department: Mathematics
1-Course data
Academic year/Level:
Second Level
CourseTitle: Ordinary
Differntial
Equations
Code: MT210
Department/program:
Mathematics, Computer Science,
Statistics, Mathematics
&Computer Science, Statistics
&Computer Science
Credit/ Taught Hours: 3 Theoretical: 2 Practical: 2
1 Apply some of mathematical methods for solving ordinary differential
equations.
2 Develop critical, analytical and personal skills that prepare students to be able to solve some types of ordinary differential equations.
3 Learn the tools and ethics of ordinary differential equations.
4 Develop continuously his knowledge in the specialized field to be qualified
for solving ordinary differential equations.
2- Course aim(s)
3- Intended Learning Outcomes (ILOs):
a1- Describe the importance of mathematics and the relation between
mathematics and other sciences in solving Society problems.
a3-Interpret the theoretical theorems for ordinary differential equations
a4-Illustrate discussion and thought, leading to solution of problems for
ordinary differential equations .
3.A- Knowledge
and
understandings: B1-Conclude the essential facts, concepts, principles and theories relating to
ordinary differential equations.
B2-Analyze the theories of ordinary differential equations.
B4-Apply some mathematical methods in solving problems in ordinary
differential equations. .
3.B- Intellectual
Skills:
C2 - Apply mathematical methods to solve several types of ordinary differential
equations.
C4 - Perform suitable model for different problems through communication
with other branches of basic science.
3.C- Professional
Skills:
D1- Employ recent information and tools effectively in solving some problems
in other fields.
D2- Lead team work effectively for solving problems; appreciating the values
of independent thinking, continuous learning, time management, collaboration,
neatness, property rights, ethics and traditions.
3.D- General
Skills:
Theoretical part content
No. of
Lecture(s)
Week(s)
No.
No. of
Hours
Topic
One 1 2
1- Equations of
order one:
Introduction to
ordinary
differential
equations –
Existence of
solution –
Isoclines and
curves of solution
– Forming
differential
equations.
Three 2,3,4 6
2 Methods of
solutions of first
order ordinary
differential
equations:
Separation of
variables –
Homogeneous
equations, Exact
equations, Linear
equation of first
order
Two 5,6 4
3. Additional
topics on
equations of first
order: Integrating
factor and
methods to
determine an
integrating factor
-Solving an
equation by using
4- Course
content:
(theoretical and
then practical)
substitution
suggested by
equation –
Bernoulli ,Ricatii
and Calauriate
equations
Three 7,8,9 6
4 -Linear
differential
equations of
higher orders:
General form of a
linear equation –
Linearly
independent
solutions - An
existence and
uniqueness
theorem –The
Wroskian
determinant.
General solution
of a
homogeneous
equation –
General solution
of a non-
homogeneous
equation – The
differential
operator and its
fundamental laws
and its properties.
Two 10,11 4
5- Non-
homogeneous
equations:
Solution of a
non-
homogeneous
equation – The
method of
undetermined
coefficients -
Solving by
inspection –
Reduction of
order – Variation
of parameters.
Two 12,13 4
6- Power series:
Linear equation
and power series
– Convergence of
power series –
Ordinary and
singular points –
Solution near an
ordinary point.
One 14 2
7- Numerical
solution of
ordinary
differential
equation: Picard
method Practical part content
Tutorial Practical week(s)
No.
No. of
Hours Topic
One - 1 2
1-solving
problems to
forming the
differential
equations.
Three - 2,3,4 6
2 solving
problems in
ordinary
differential
equations of first
order using:
Separation of
variables –
Homogeneous
equations, Exact
equations, Linear
equation)
three - 5,6,7 6
3. Solving
problems in
ordinary
differential
equations of first
order using::
Integrating factor
and methods to
determine an
integrating factor
-Solving an
equation by using
substitution
suggested by
equation –solving
problems for
Bernoulli, Ricatii
and Caulurit's
equations.
One - 8 2
4- Solving
problems for
homogeneous
linear differential
equations of
higher order with
constant
coefficients.
Three - 9,10,11 6
5 Solving
problems for non-
homogeneous
linear differential
equations of
higher order with
constant
coefficients: The
method of
– Reduction of
order
–undetermined
coefficients
–Variation of
parameters
–simple method.
Two - 12,13 4
6- Solving
problems for
linear ordinary
differential
equations of
second order
using Power
series solutions
for Ordinary and
singular
One - 14 2
7- Solving
problems for
Numerical
solution of
ordinary
differential
equation: Picard
method
5.1- Lectures using whiteboard or occasionally using data
show.
5.2- Problem discussion sessions with students.
5.3- Presentation by student teams of some independent
work relevant to the course. 5.4- Independent search of students about certain results or applications
5- Teaching and
learning methods:
6- Teaching and
learning methods
for limited
capability
students: 7- Students assessment:
4.1- 7.A.1-Assignments, quizzes, and presentations to assess
aaaaa1,a4; b1,b4; c2,d2.
7. A.2- Mid term tests to assess a1-a4; c2.
7. A.3-Oral examination to assess a1-a3; d2,
7. A.4- Final examination to assess a4-a3; b1, b2, b4;
c2;d1.
7.A- Assessment
Methods:
Assessment 1: Four Assignments Week2, 5, 8, 11. Four
quizzes.
Assessment 2: Two mid term tests, first Week7, second
Week 12.
Assessment 3: Oral examination Week14.
Assessment 4: Final Examination Week15.
7.B- Assessment
schedule
Mid-term examination % 20% Final-term examination % 60%
Oral examination % 10% Semester work % 10% Total 100%
7.C- Assessments
Weights
8- List of Books and references
Not applicable.
8.A- Notes:
1- Braun, M. V., Differential Equations and Their Applications, 4th
Edition Springer Verlag, 1993.
2- Boyce, W. E. and DiPrima, R.C., Elementary Differential Equations
and Boundary Value Problems, Sixth Edition, John Wiley and Sons,
1997.
3- E. D. Rainville, P. E. Bedient, R. E. Bedient, Elementary Differential
Equations ( 8th Edition, Prentice Hall Inc., 1996.
4- Simmons, G. F., Differential Equations with Applications and
Historical Notes, Second Edition, McGraw-Hill, Inc., 1991.
8.B- Essential
books:
None
8.C- Recommended
books:
Course coordinator: Head of Department:
Dr. Zinab Abdel-Hady Dr. Abd ElGawad abou El-fadel
None 8.D- Scientific
periodicals, websites
….etc
Suez Canal University: Course code:MT210
Faculty of Science: Course title: Ordinary differential equation
Matrix of intended knowledge and skills of the course
1- Intended Learning Outcomes (ILOs):
A- Knowledge and understandings:
a3-Interpret the theoretical theorems for ordinary differential equations
a4-Illustrate discussion and thought, leading to solution of problems for ordinary differential equations
B- Intellectual Skills: B1-Conclude the essential facts, concepts, principles and theories relating to ordinary differential equations.
B2-Analyze the theories of ordinary differential equations.
B4-Apply some mathematical methods in solving problems in ordinary differential equations. .
C- Professional Skills: C2 - Apply mathematical methods to solve several types of ordinary differential equations.
C4 - Perform suitable model for different problems through communication with other branches of basic science.
D- General Skills: D1- Employ recent information and tools effectively in solving some problems in other fields.
D2- Lead team work effectively for solving problems; appreciating the values of independent thinking, continuous
learning, time management, collaboration, neatness, property rights, ethics and traditions.
a1-Describe the importance of mathematics and the relation between mathematics and other sciences in solving Society
problems.
2- Course matrix table:
Course content for theoretical part
Week (s)
No.
A knowledge and
Understanding Skills
Intellectual Skills
Professional
and Practical Skills
General
Skills
1- Equations of order
one:
Introduction to ordinary
differential equations
Existence of solution
Isoclines and curves
of solution
1 a1 b1
2- Methods of solutions
of ordinary differential
equations of first order:
Separation of variables –
Homogeneous equations,
Exact equations, Linear
equation of first order
2,3,4 a3,a4 b2,b4 c2 d1
3. Additional topics on
equations of first order:
Integrating factor and
methods to determine an
integrating factor -
Solving an equation by
using substitution
suggested by equation –
Bernoulli, Ricatii
&Cauliourat equations.
5,6
a3,a4 b2,b4 c2 d1
4 -Linear differential
equations: General forms
of a linear equation of
higher order– Linearly
independent solutions -
An existence and
7,8,9 a3,a4 b1,b4 c2 d1
uniqueness theorem –The
Wroskian determinants-
General solution of a
linear
Homogeneous equation
with constants
coefficients– The
differential operator and
its fundamental laws and
properties.
5- Non-homogeneous
equations: Solution of a
non-homogeneous
equation – The method of
undetermined
coefficients - Solving by
inspection – Reduction of
order – Variation of
parameters-Simple
method.
10,11 a3,a4 b1,b4 c2 d1
6- Power series: Linear
equation and power
series – Convergence of
power series – Ordinary
and singular points –
Solution near an ordinary
point.
12,13 a3,a4 b1,b4 c2,c4 d1,d2
7- Numerical solution of
ordinary differential
equation: Picard's method
14 a4 b4 c2 d1
Course content for practical part
Week (s)
No.
A knowledge and
Understanding Skills
Intellectual Skills
Professional
and Practical Skills
General
Skills
1-solving problems to
forming the differential
equations. 1
2 solving problems in
ordinary differential
equations of first order
using: Separation of
variables –
Homogeneous equations,
Exact equations, Linear
equation)
2,3,4 c2 d1
3. Solving problems in
ordinary differential
equations of first order
using:: Integrating factor
and methods to
determine an integrating
factor -Solving an
equation by using
substitution suggested by
equation –solving
problems for Bernoulli,
Ricatii and Caulurit's
equations.
5,6
c2 d1
4- Solving problems for
homogeneous linear
differential equations of
higher order with
constant coefficients.
7,8,9 c2 d1
Course coordinator: Head of Department:
Dr. Zinab Abdel-Hady Dr. Abd ElGawad abou El-fadel
5 Solving problems for
non-homogeneous linear
differential equations of
higher order with
constant coefficients: The
method of
– Reduction of order
–undetermined
coefficients
–Variation of parameters
–simple method.
10,11 c2 d1
6- Solving problems for
linear ordinary
differential equations of
second order using
Power series solutions
for Ordinary and singular
12,13 c2,c4 d1,d2
7- Solving problems for
Numerical solution of
ordinary differential
equation: Picard method
14 c2 d1