COURSE NUMBER: MATH 151

COURSE TITLE: Ordinary Differential Equations

COURSE DESCRIPTION: Theory, methods and applications of ordinary differential equations

PREREQUISITE: MATH 38 or MATH 28

SEMESTER OFFERED: First Semester

COURSE CREDIT: 3 units

COURSE OBJECTIVES: Upon completion of the course, the student should be able to solve ordinary differential equations.

OUTLINE

1. Introduction - Definitions and Examples2. Solutions of Ordinary Differential Equations of Order One

2.1. Separable Equations

2.2. Homogeneous Equations

2.3. Exact Equations

2.4. Linear Differential Equations

2.5. Bernoullis Equations

2.6. Equations with Linear Coefficients in 2 Variables

2.7. Substitution as Suggested by the Equation

2.8. Integrating Factors That are Functions of x or y alone

2.9 Integrating Factors Found by Inspection3. Solutions to General Linear Differential Equations

3.1 Definitions and Properties

3.2 Solution to Homogeneous Linear DEs using Auxiliary equations

3.2.1 Roots are real and non-repeated

3.2.2. Roots are real and repeated

3.2.3. Roots are complex conjugates

3.2.4 Roots are repeated complex numbers

3.3. Solution to Non-homogeneous Linear DEs

3.3.1. The Method of Undetermined Coefficients; the Annihilator Concept

3.3.2. Finding Particular Solutions by Inspection

3.3.3. The Use of Reduction of Order

3.3.4 The Method of Variation of Parameters4. Laplace Transforms

4.1. Definitions, Examples, and Other Properties

4.2. Some Special Types of Functions

4.2.1 Sectionally Continuous Functions

4.2.2 Functions of Exponential Order

4.2.3 Functions of Class A

4.3 Transforms of Derivatives

4.4. Derivatives of Transforms

4.5. Inverse Laplace Transforms

4.6. Solution to Initial Value Problems Using Laplace Transforms5. Systems of Differential Equations

5.1. Matrices and Properties

5.2. First-Order System of ODEs

5.2.1. Solutions to homogeneous system

5.2.1.1. Real, non-repeated eigenvalues

5.2.1.2. Complex Eigenvalues

5.2.1.3. Repeated Eigenvalues

5.2.2.. Solutions to Non-homogeneous Systems

5.3. The Use of Laplace Transforms in Solving System of ODEs with given initial conditions

References: Rainville, Bedient, and Bedient, any edition.

Any Ordinary or Elementary Differential Equations books (Bagle and Saff, Betz, etc.)COURSE POLICIES:

1. Course Requirements

4 Long Exams

60 %

Quizzes

20 %

Assignments/Problem Sets10 %

Recitation/Reporting

10 %a. A student who missed a long exam will automatically take the final exam (covering all chapters).

b. A student who missed a long exam gets a 0 for that exam unless he/she has a valid excuse slip (signed by the College Secretary) and in the case of the latter, his/her final exam score shall be used for his/her missed exam.

c. There will be no make-up for any missed quiz, assignment, problem set or reporting.

2. Attendance. The university policy on attendance will be implemented. Accumulated absences of 7 or more will result to either a grade of DRP or a grade of 5.0.

3. Grading Scheme

96-100

1.0

80-83

2.0

60-64

3.0

92-95

1.25

75-79

2.25

55-59

4.0

88-91

1.5

70-74

2.5

0-54

5.0

84-87

1.75

65-69

2.75

4. Exemption:a. A student whose pre-final score is 70% or better will be exempted from taking the final exam and his pre-final score becomes his final score.

b. If a students pre-final score is below 70 %, his final score will be computed as follows:

FINAL SCORE = 70% (pre-final score) + 30% (final exam score). A student who passes the course with perfect attendance and has submitted all requirements gets a bonus grade of 0.25.5. Consultation Hours: TTh1-5 PM (OIL)

M3-5 PM (OIL)