SHAW UNIVERSITY
COURSE OUTLINE
MAT 411 DIFFERENTIAL EQUATIONS SPRING 2008

Instructor: Dr. S. Ugwuoke

Phone:      546-8543

Office:     Graphics Bldg. Room 4

E-mail:     sugwuoke@shawu.edu

Office Hours: M,W,Th,F 11:00 AM – 1:00 PM  

                                 T        12:00 N  - 2:00 PM

Required Text
Edwards, C. Henry and Penny, David E. Differential Equations and Boundary Value Problems; 3rd Edition; Copyright © 2004 by Pearson Education, Inc.

Supplementary Texts:

  1. Blanchard, Paul, Devaney, Robert L., & Hall, Glen R. Differential Equations; 2nd Ed. Copyright © 2002 the Wadsworth Group.
  2. Differential Equations with Applications & Historical Notes by George F. Simmons. Copyright © 1992 by McGraw-Hill, Inc.
  3. Theory and Problems of Modern Introductory Differential Equations (Schaum's Outline Series) by Richard Bronson; McGraw-Hill Book Co.

Technology Used in This Course

1. Blackboard and Quizlab (websites)
2. Maple V Release 5 (Computer Lab)
3. Graphing Calculator (TI-92); 4. PcCalculator


General Description
This is a study of ordinary differential equations of different orders and degrees, their solutions, meanings and methods of solutions, trajectories, numerical techniques, Laplace transforms, power series methods, systems of equations, and applications to other disciplines and real-life problems.

Student Learning Outcomes
After completing this course, students should be able to:
· demonstrate an understanding of basic concepts of ODE such

  as order and degree of ODE, linear DE., notations;

· distinguish between a solution, a particular solution, and a

  general solution of ODE;
· classify first order differential equations;
· solve separable first-order differential equations, including initial-value   problems;
· solve homogeneous first-order DE
; · solve exact first-order DE;
· find solution of DE by using integrating factors;
· solve linear first-order DE; · apply first-order DE to real-life situations;
· identify and solve linear differential equations;
· solve second-order linear homogeneous equations with

constant coefficients by using characteristic equations;
· solve nth order linear homogeneous equations with constant

coefficients by using characteristic equations;
· solve ODE using the method of undetermined coefficients;
· solve initial-value problems;
· apply second-order linear DE with constant coefficients;
· solve problems involving Laplace transforms;
· apply Laplace transforms and its inverse in solving DE;
· solve systems of linear differential equations;
· apply systems of linear DE to real-life situations;
· apply numerical methods, e.g. Euler method, in solving DE.
· demonstrate an understanding of power series solution of D.E.
· demonstrate an understanding of analytical, qualitative,

and numerical techniques of making predictions.

Topic Outline
Chapter:

  1. First-Order Differential Equations
    1. Differential Equations and Mathematical Models
    2. Integrals as General and Particular Solutions
    3. Slope Fields and Solution Curves
    4. Separable Equations and Applications
    5. Linear First-Order Equations
    6. Substitution Methods and Exact Equations

2.Mathematical Models and Numerical Methods

2.1 Population Models

2.2 Equilibrium Solutions and Stability

2.3 Acceleration-Velocity Models

2.4 Numerical Approximation: Euler's Method

2.5 A closer look at the Euler's Methods

2.6 The Runge Kutta Method

3.Lnear Equations of Higher Order

3.1 Introduction: Second-Order Equations

3.2 General Solutions of Linear Equations

3.3 Homogeneous Equations with Constant Coefficients

3.4 Mechanical Vibrations

3.5 Non-homogeneous Equations and Undetermined Coefficients
3.6 Forced Oscillations and Resonance

3.7 Electrical Circuits

4.Introduction to Systems of Differential Equations;

4.1 First-Order Systems and Applications

4.2 The Method of Elimination

4.3 Numerical Methods for Systems

5.Linear Systems of Differential Equations

5.1 Matrices and Linear Systems

5.2 The Eigenvalue Method for Homogeneous Systems

5.3 Second–Order Systems and Mechanical Applications

5.4 Multiple Eigenvalue Solutions

5.5 Matrix Exponentials and Linear Systems

5.6 Non-homogeneous Linear Systems

6.Nonlinear Systems and Phenomena

6.1 Stability and the Phase Plane

6.2 Linear and Almost Linear Systems

6.3 Ecological Models: Predators and Competitors

6.4 Nonlinear Mechanical Systems

6.5 Chaos in Dynamical Systems

7.Laplace Transform Methods

7.1 Laplace Transforms and Inverse Transforms

7.2 Transformation of Initial-Value Problems

7.3 Translation and Partial Fractions

7.4 Derivatives, Integrals, and Products of Transforms

7.5 Periodic and Piecewise Continuos Input Functions

7.6 Impulses and Delta Functions

8.Power Series Methods

8.1 Power Series Methods

8.2 Series Solutions Near Original Points

8.3 Regular Singular Points

8.4 Methods of Frobenius: The Exceptional Cases

8.5 Bessel’s Equation

8.6 Applications of Bessel Functions

9. Fourier Series Methods

9.1 Periodic Functions and Trigonometric Series

9.2 General Fourier Series and Convergence

9.3 Fourier Sine and Cosine Series

9.4 Applications of Fourier Series

9.5 Heat Conduction and Separation of Variables

9.6 Vibrating Strings and One-Dimensional Wave Equation

9.7 Steady-State Temperature and Laplace’s Equation

10.Eigenvalues and Boundary-Value Problems

10.1 Sturm-Liouville Problems and Eigenfunction Expansions

10.2 Applications of Eigenfunction Series

10.3 Steady Oeriodic Solutions and Natural Frequences

10.4 Cylindrical Coordinate Problems

 

Alignment With Standards

NCDPI 3.1, 3.4, 3.5

Grading System
Attendance, Quizzes, Assigments, and Projects 30%
Hourly Tests 40%
Final Exam 30%

Attendance Policy:
Students who miss classes are responsible for subject matter covered, any announcements made during their absence, regarding quiz, test, or any other relevant matter. The University policy on this course is that more than three unexcused absences
may result in failure in the course.

Student Classroom Decorum Expectations

To enhance the learning atmosphere of the classroom, students are expected to dress and behave in a fashion conducive to learning in the classroom. More specifically, students will refrain from disruptive classroom behavior (i. e., talking to classmates, disrespectful responses to teacher instructions; swearing; wearing clothes that impede academic learning such as but not limited to, wearing body-revealing clothing and excessively baggy pants; hats/caps, and/or headdress). Students will turn off telephones prior to entering the classroom.

Students who exhibit the behaviors described above, or similar behaviors will be immediately dismissed from class at the third documented offense. The student will be readmitted to class only following a decision by the department chair. The student may appeal the decision of the department chair to the Dean of the College offering the course, and, subsequently, to the Office of the Vice President for Academic Affairs, and then to the President of Shaw University. The decision of the President will be final.

Failure to follow the procedures herein outlined will result in termination of the appeal, and revert to the decision of the department chair.

Each behavior construed by the teacher/professor as noncontributive to learning will be recorded, properly documented, and appropriately reported to the student and to the chair of the academic department offering the course. The report will be in written form with a copy provided to both the student and the department chair. The faculty member should retain a copy for his/her own records.

Additional student behavior codes may be found in Student Affairs.