A

Course Title
& Number

Differential Equations - MTH 205

B

Pre/Co-requisite(s)

MTH 104

C

Number of credits

3-0-3

D

Faculty Name

Dr. Amjad Tuffaha

E

Term/ Year

Fall 2015

F

Sections

G

Instructor Information

Office Hours: Sunday, Tuesday, Thursday: 10:00-11:30 am

H

Course Description from Catalog

Covers 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.

I

Course Learning Outcomes

Upon completion of the course, students will be able to:

(1)Explain basic definitions, concepts, vocabulary, and mathematical notation of differential equations.

(2)Demonstrate the necessary manipulative skills required to solve equations of first order and higher-order constant-coefficient linear differential equations.

(3)Demonstrate the necessary manipulative skills required to find particular solutions of second order differential equations.

(4)Apply Laplace transform to solve IVPs and systems of linear differential equations.

(5)Understand the fundamental properties of power series, and how to use them to solve linear differential equations with variable coefficients.

(6)Formulate and solve applied physical problems arising in science and engineering.

J

Textbook and other Instructional Material and Resources

Zill D.G., A First Course in Differential Equations with Modeling and Applications, 10^th edition, 2012, Brooks/Cole – Thomson, U.S.A.

K

Teaching and Learning Methodologies

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

L

Grading Scale, Grading Distribution, and Due Dates

Grading Distribution

M

Explanation of Assessments

There 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 registrar’s office.

N

Student Academic Integrity Code Statement

Student must adhere to the Academic Integrity code stated in the 2014-2015 undergraduate catalog

WEEK

CHAPTER

NOTES

1 Sept 6-10

1: Introduction to DE

1.1 Definitions and Terminology

1.2 Initial-Value Problems

2 Sept 13-17

1: Continue

2: First-Order DE

1.3 Differential Equations as Mathematical Models

2.1 Solution Curves Without the Solution

Sept 20-24

Eid Aladha Break

3 Sept 27-Oct 1

2: Continue

2.2 Separable Equations

2.3 Linear Equations

4 Oct 4-8

2: Continue

2.4 Exact Equations

2.5 Solutions by Substitutions

5 Oct 11-15

3: Modeling with First-Order DE

3.1 Linear Models

6 Oct 18-22

4: Higher-Order DE

Midterm 1: Monday, October 19, 2015, 5:30-7:00, Testing Center

Sections: 1.1-1.3, 2.1-2.5, 3.1

4.1 Preliminary Theory: Linear Equations

7 Oct 25-29

4: Continue

4.2 Reduction of Order

4.3 Homogeneous Linear Equations with Constant Coefficients

8 Oct 1-5

4: Continue

4.4 Undetermined Coefficients – Superposition Approach

4.6 Variation of Parameters

9 Nov 8-12

4: Continue

5: Modeling with higher-

Order DE

4.7 Cauchy-Euler Equation

5.1 Linear Models: Initial-Value Problems

10 Nov 15-19

5: Continue

6: Series Solutions of LDE

5.1 Spring/Mass System and Series Cicuit

6.1 Review of Power Series

11 Nov 22-26

6: Continue

7: The Laplace Transform

6.2 Solutions about Ordinary Points

7.1 Definition of the Laplace Transform

12 Nov 29-Dec 3

7: Continue

7.2 Inverse Transforms and Transforms of Derivative

13 Dec 6-10

7: Continue

7.3 Translations on the s-Axis and the t-Axis

Midterm 2: Thursday, Dec 10, 2015, 5:30-7:00, Testing Center

Sections: 4.1-4.4, 4.6-4.7, 5.1, 6.1-6.2, 7.1-7.2

14 Dec 13-17

7: Continue

7: Continue

7.4 Derivatives of Transform, Transforms of integrals and Periodic Functions

7.5 The Dirac Delta Function

Dec 20-Jan 2

Fall Break

15 Jan 3-7

7: Continue

7.6 Systems of Linear Equations

16 Jan 10-17

Final Exam (Comprehensive and common)

Section

Page

Exercises

1.1

10

1-8, 12, 15, 19, 27, 32

1.2

17

4, 8, 14, 17, 18, 23, 24, 25, 27

1.3

28

1, 5, 13, 14, 17

2.1

43

1, 9, 13, 21, 22, 25, 27, 29

2.2

51

3, 6, 7, 8, 13, 14, 17, 25, 27, 30, 36(a)

2.3

61

5, 9, 12, 13, 17, 23, 24, 25, 28, 29, 31

2.4

69

2, 3, 6, 8, 12, 16, 24, 32, 35, 37

2.5

74

3, 5, 8, 11, 15, 18, 22, 23, 25, 28

3.1

90

1, 3, 6, 7, 14, 15, 23, 26, 27

4.1

127

1, 3, 5, 6, 9, 13, 15, 17, 19, 23, 26, 31, 36, 38, 40

4.2

131

2, 3, 9, 11, 17

4.3

137

3, 5, 11, 15, 16, 22, 23, 24, 31, 33, 43-48, 56, 57, 59

4.4

147

1, 5, 8, 11, 13, 15, 19, 20, 24, 26, 29, 32, 45

4.6

161

1, 3, 9, 15, 19, 25

4.7

168

1, 3, 4, 5, 6, 11, 14, 15, 17, 19, 29, 45

5.1

205

1, 2, 4, 5, 9, 11, 17-20, 21, 23, 29, 31, 45, 47

6.1

237

23, 24, 25, 27, 29, 31,33

6.2

246

1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21

7.1

280

4, 13, 15, 18, 21, 25, 29, 31,33, 37

7.2

288

2, 3, 7, 9, 11, 15, 19, 24, 33, 34, 36, 39

7.3

297

1, 3, 6, 7, 15, 22, 23, 26, 29, 37, 39, 43, 45, 47, 49, 51, 54, 55, 58 63, 65

7.4

309

1, 5, 7, 8, 11, 23, 25, 27, 29, 37, 39, 41, 45, 49, 51

7.5

315

1, 3, 6, 10

7.6

319

1, 3, 6, 7, 9, 12