COURSE SYLLABUS

ACourse Title & NumberDifferential Equations - MTH 205

BPre/Co-requisite(s)MTH 104

CNumber of credits3-0-3

DFaculty NameDr. Ali Saifi

ETerm/ YearFall 2014

FSectionsCRNSecDaysFromToLocationInstructors

2053503M W12:301:45NAB 009Dr Ali Saifi

2053806M W8:009:15NAB 006Dr. Ali Saifi

GInstructor InformationInstructorOfficeTelephoneEmail

Ali SaifiNAB245515 2916sayfy@aus.edu

HCourse Description from CatalogCovers mathematical formulation of ordinary differential equations, methods of solution and applications of first order and second order differential equations, power series solutions, solutions by Laplace transforms and solutions of first order linear systems.

ICourse Learning OutcomesUpon completion of the course, students will be able to:1. Classify a given differential equation as ordinary or partial, and determine its order and whether or not it is linear.2. Solve first-order linear ordinary differential equations.3. Apply reduction of order to find a second linearly independent solution for a homogenous differential equation, given one solution.4. Compute real valued linearly dependent solutions to homogenous ordinary differential equations with constant coefficients.5. Apply variation of parameters and method of undetermined coefficients to find a particular solution.6. Formulate and solve appropriate applied problems involving exponential growth/decay and Newtons law of cooling and series circuits as first order differential equations and solve applied problems from electrical and mechanical engineering as second order differential equations.7. Compute power-series solutions to certain differential equations with variable coefficients.8. Apply the Laplace transform to solve a given Initial-Value problem and solve systems of linear differential equations.

JTextbook and other Instructional Material and Resources Zill D.G., A First Course in Differential Equations with Modeling and Applications, 10th edition, 2012, Brooks/Cole Thomson, U.S.A.

KTeaching and Learning MethodologiesThis is a traditional lecture based course. Students are tested and given feedback throughout the semester via regular homework, quizzes, and exams.

LGrading Scale, Grading Distribution, and Due Dates

Grading Distribution

AssessmentWeightDate

Quizzes and/or homework20%TBA

Exam 122.5%TBA

Exam 222.5%TBA

Final Exam35%TBA

Total100%

Grading ScaleA4.093-100

A-3.789-92

B+3.385-88

B3.081-84

B-2.776-80

C+2.371-75

C2.066-70

C-1.760-65

D1.046-59

F00-45

MExplanation of AssessmentsThere will be in-class quizzes, in addition to two midterm tests, and a comprehensive final exam. Most quizzes will be pre-announced at least one lecture in advance. No make-up quizzes will be given. However the lowest quiz will not be counted toward your final grade. With a valid written excuse and making immediate arrangements with the instructor, a missed exam might be replaced with the grade of the final exam and/or the average grade of all tests (including final) and/or quizzes. The final exam is common and comprehensive. The date and time of the final exam will be scheduled by the registrars office.

NStudent Academic Integrity Code StatementStudent must adhere to the Academic Integrity code stated in the 2014-2015 undergraduate catalog

Please turn off your cellphone before the class!

SCHEDULENote: Tests and other graded assignments due dates are set. No addendum, make-up exams, or extra assignments to improve grades will be given.WEEKCHAPTER

NOTES

First Week1:Introduction to DE1.1Definitions and Terminology 1.2Initial-Value Problems

Second Week 1:Introduction to DE2:First-Order DE1.3Differential Equations as Mathematical Models2.1Solution Curves Without the Solution

Third Week2: 2.2Separable Equations2.3Linear Equations

Fourth Week2:2.4Exact Equations2.5Solutions by Substitutions

Fifth Week 3:Modeling with First-Order DE3.1Linear Models

Sixth Week4:Higher-Order DE4.1Preliminary Theory: Linear Equations1174.2Reduction of Order Midterm 1: March 25, 2015, 5:00-6:30

Seventh Week4:4.3Homogeneous Linear Equations with Constant Coefficients1324.4Undetermined Coefficients Superposition Approach

Spring Break: April 5th April 9th

Eighth Week4:4.6 Variation of Parameters4.7 Cauchy-Euler Equation

Ninth Week5:Modeling with Higher-Order DE5.1 Linear Models: Initial-Value Problems

Tenth Week6:Series Solutions of LDE5.1 Linear Models: Initial-Value Problems6.1 Review of Power Series

Eleventh Week 6:6.2 Solutions about Ordinary Points

Twelfth Week7:The Laplace Transform Midterm 2: May 13, 2015, 5:00-6:30 7.1 Definition of the Laplace Transform7.2 Inverse Transforms and Transforms of Derivatives

Thirteenth Week7:7.3 Operational Properties I7.4 Operational Properties II

Fourteenth Week7:7.5 The Dirac Delta Function7.6 Systems of Linear Equations

Fifteenth WeekReview

Final Exam Common and Comprehensive

Math 205 Suggested ProblemsTEXT: A First Course in Differential Equations with Modeling Application, by D.G. Zill, 10th Edition.SectionPageExercises

1.1101-8, 12, 15, 19, 27, 32

1.2174, 8, 14, 17, 18, 23, 24, 25, 27

1.3281, 5, 13, 14, 17

2.1431, 9, 13, 21, 22, 25, 27, 29

2.2513, 6, 7, 8, 13, 14, 17, 25, 27, 30, 36(a)

2.3615, 9, 12, 13, 17, 23, 24, 25, 28, 29, 31

2.4692, 3, 6, 8, 12, 16, 24, 32, 35, 37

2.5743, 5, 8, 11, 15, 18, 22, 23, 25, 28

3.1901, 3, 6, 7, 14, 15, 23, 26, 27

4.11271, 3, 5, 6, 9, 13, 15, 17, 19, 23, 26, 31, 36, 38, 40

4.21312, 3, 9, 11, 17

4.31373, 5, 11, 15, 16, 22, 23, 24, 31, 33, 43-48, 56, 57, 59

4.41471, 5, 8, 11, 13, 15, 19, 20, 24, 26, 29, 32, 45

4.61611, 3, 9, 15, 19, 25

4.71681, 3, 4, 5, 6, 11, 14, 15, 17, 19, 29, 45

5.12051, 2, 4, 5, 9, 11, 17-20, 21, 23, 29, 31, 45, 47

6.123723, 24, 25, 27, 29, 31,33

6.22461, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21

7.12804, 13, 15, 18, 21, 25, 29, 31,33, 37

7.22882, 3, 7, 9, 11, 15, 19, 24, 33, 34, 36, 39

7.32971, 3, 6, 7, 15, 22, 23, 26, 29, 37, 39, 43, 45, 47, 49, 51, 54, 55, 58 63, 65

7.43091, 5, 7, 8, 11, 23, 25, 27, 29, 37, 39, 41, 45, 49, 51

7.53151, 3, 6, 10

7.63191, 3, 6, 7, 9, 12