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AMATH 351 A: Introduction to Differential Equations and Applications

Meeting Time: 
MWF 10:30am - 11:20am
MUE 153
Ying-Jen Yang
Ying-Jen Yang

Syllabus Description:

MWF 10:30-11:20 @ MUE 153

Instructor: Ying-Jen Yang


Instructor's office hours: TBD

Teaching Assistant: Yu-Chen Cheng

TA's email:

TA's office hours: TBD


Course Description: 

This course serves as the first course in differential equations after learning Calculus from MATH 124 and 125. In this course, we will learn how to solve Ordinary Differential Equations (ODEs) with examples drawn from physical, chemical, biological sciences and engineering. We motivate most of our theoretical discussions from applications. Most importantly, we aim to illustrate the logic hidden behind different solution methods, not just doing tedious algebra manipulation (although sometimes it is hard to avoid).


Proficiency in manipulation of algebraic equations, evaluation of limits, methods of differentiation & integration at the level of MATH 124 & 125 are assumed. We will introduce and use quite a lot of linear algebra, some complex variable, and power series that are relevant to us. Exposure to linear algebra, complex variable, and Taylor series would be helpful.

Rough Outline:

  1. Introduction to Differential Equations and Dynamical Systems
  2. Solving First order, one dimensional ODE
  3. Autonomous linear system of ODEs and diagonalization
  4. More on linear ODEs: degenerate cases, inhomogeneous
  5. Non-autonomous linear ODEs: series method
  6. A glimpse of nonlinear ODEs

Note: I am deemphasizing Laplace transform in this first ODE course (in my opinion, better learn it after learning contour integral in complex analysis to have a more systematic way to perform inverse Laplace transform, rather than guessing the inverse from a table).  We will emphasize more on solving systems of ODEs (with matrices and a bit linear algebra) since it has many conceptual advantages and connections to later courses in dynamical systems. That said, no need to worry if you haven't taken linear algebra, we will start from the beginning.

Textbook and Reference

No textbook is required. Self-contained typed-up lecture notes would be provided. For textbook
references, the following two books are recommended:

  1. W.E. Boyce, R.C. DiPrima, and D.B. Meade, Elementary Dierential Equations and Boundary Value Problems. 11th ed. (any edition after 9th will do. B&D, Chapter 1- 5 , 7-9 ).
    It is the standard textbook for undergraduate ODE class. We will focus mostly in the material within.
  2. Steven H. Strogatz, Nonlinear Dynamics and Chaos, 2nd ed. (S, Chapter 1, 2, 5, and 6).
    It is an awesome textbook that is used in almost all undergraduate Dynamical Systems class around the world! We will only touch a little bit of it. You can take Amath 402/502 for a thorough introduction of the book and the subject.


Weekly homework. Details TBD.

Exam and Grade

One in-class midterm, detail TBD.

In-class final exam on Jun 8 (Mon) 8:30-10:20

Catalog Description: 
Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and. Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering. Prerequisite: MATH 125 or MATH 135. Offered: AWSpS.
GE Requirements: 
Natural World (NW)
Last updated: 
January 16, 2020 - 11:20pm