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General Course Description
The behavior of many physical systems can be mathematically modeled by ordinary differential equations (ODEs). Mathematical models based on ODEs occur frequently in science and engineering. Examples include Newton's second law, chemical kinetics, and control theory. ODEs are also important for solving more complex mathematical models described by partial differential equations (PDEs). In this course, we will study the theory and computation of ODEs. Numerical methods are often needed when deriving explicit formulas for solutions is not possible. In such cases, we employ numerical methods to compute approximate solutions of ODEs.
Student Learning Outcomes (SLOs) and Rubric for Math 316
Textbook
William E. Boyce and Richard C. DiPrima, Elementary Differential Equations, 10th edition, Wiley (Required).
9th Edition will also work.
Course Material
(by Dr. Mohammad Motamed)
It is not guaranteed that the posted lecture notes are free of errors. Please contact and notify the instructor immediately or as soon as possible should any errors be discovered.
Chapter 1. Notes, Code 1, Code 2, Code 3, Example on Linearity, Derivative of ln
Chapter 2. Notes, Code for Ex. 4, Code for Ex. 6, Code for Ex. 7, Example on Integrating Factor
Chapter 3. Notes 1, MATLAB Code for Solution Families, Method of Undetermined Coefficients, Method of Variation of Parameters, Example on Nonhomogeneous ODEs, Notes 2
Chapter 6. Lectures Notes, Laplace Transforms
Chapter 7. Notes 1, Notes 2, Code for System 1, Code for System 2, Code for System 3, Code for System 4
Chapter 8. Lecture Notes, Code for Ex. 1, Code for Ex. 2, Code for Ex. 3, Code for Ex. 4, Code for Ex. 5, 6, 7
Chapter 9. Lecture Notes, MATLAB Ex. 1, MATLAB Ex. 3
Homework
With the exception of Homework 6, do not include your MATLAB codes in your report. It is not necessary to see your codes. Only include the plots.
Homework 1 (on Chapter 1)
Homework 2 (on Chapter 2)
Homework 3 (on Chapter 3)
Homework 4 (on Chapter 7)
Homework 5 (on Chapter 7)
Homework 6 (on Chapter 8)
Exams
Midterm Exam: Study Questions for Midterm (Chapters 1 - 3)
Euler's Method (Question 7) will not be covered on the midterm exam. However, the review session will allow an opportunity for the instructor to introduce students to numerical methods for solving ODEs (as a "preview" of things to come) before plunging into more depth on this topic in chapter 8.
Final Exam: Study Questions for Final (Chapters 7 - 9)
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