MATH3270B - Ordinary Differential Equations - 2014/15

Course Name: 
Ordinary Differential Equations
Teacher: 
Dr. Qin LI
Course Year: 
2014/15
Term: 
S

Announcement

  • The homework assignment is based on the tenth edition of the textbook.
  • The classroom for both lectures and tutorial will be moved to Science Center L1, from May 18 to June 29. Except that on June 24, the classroom is Science Center L2.
  • The midterm is scheduled in the lecture on June 3rd.
  • The final exam is scheduled on June 29th, in the last lecture.

General Information

Lecturer

  • Dr. Qin LI
    • Office: LSB 228
    • Tel: 3943 7955
    • Email:

Teaching Assistant

  • Mr. Yuan YUAN
    • Office: AB1 614
    • Tel: 3943 4109
    • Email:
  • Ms. Rong ZHANG
    • Office: AB1 614
    • Tel: 3943 4109
    • Email:

Time and Venue

  • Lecture: Mo 2:30PM - 5:15PM, SC_L1; We 2:30PM - 5:15PM, SC_L1
  • Tutorial: Mo 5:30PM - 6:15PM, SC_L1; We 5:30PM - 6:15PM, SC_L1

Course Description

Objectives: To acquaint with basic concepts in ordinary differential equations; (2) To learn standard techniques in solving linear or nonlinear ordinary differential equations; (3) To understand the basic theory of linear ODES and the stability theory of nonlinear ODES; (4) To solve basic boundary value problems.

Course Topics:

Part 1: Introduction (Chapter 1.1 - 1.3)

¡V Some Basic Mathematical Models; Direction Fields

¡V Solutions of Some Differential Equations

¡V Classification of Differential Equations

Part 2: First Order Differential Equations (Chapter 2.1 - 2.7)

¡V Linear Equations; Method of Integrating Factors

¡V Separable Equations

¡V The Existence and Uniqueness Theorem

¡V Autonomous Equations and Population Dynamics

¡V Exact Equations and Integrating Factors

Part 3: Second Order Linear Equations (Chapter 3.1 - 3.7)

¡V Homogeneous Equations with Constant Coefficients

¡V Solutions of Linear Homogeneous Equations; the Wronskian

¡V Complex Roots of the Characteristic Equation

¡V Repeated Roots; Reduction of Order

¡V Nonhomogeneous Equations; Method of Undetermined Coefficients

¡V Variation of Parameters

Part 4: Higher Order Linear Equations (Chapter 4.1 - 4.4)

¡V General Theory of nth Order Linear Equations

¡V Homogeneous Equations with Constant Coefficients

¡V The Method of Undetermined Coefficients

¡V The Method of Variation of Parameters

Part 5: Systems of First Order Linear Equations (Chapter 7.1 - 7.9)

¡V Introduction

¡V Review of Matrices

¡V Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors

¡V Basic Theory of Systems of First Order Linear Equations

¡V Homogeneous Linear Systems with Constant Coefficients

¡V Complex Eigenvalues

¡V Fundamental Matrices

¡V Repeated Eigenvalues

¡V Nonhomogeneous Linear Systems

Part 6: Nonlinear Differential Equations and Stability (Chapter 9.1 - 9.8)

¡V The Phase Plane: Linear Systems

¡V Autonomous System and Stability

¡V Locally Linear Systems

¡V Competing Species

¡V Predator-Prey Equations

¡V Liapunov¡¦s Second Method

¡V Periodic Solutions and Limit Cycles


Textbooks

  • Boyce and DiPrima, "Elementary Differential Equations and Boundary Value Problems", 10th ed., J. Wiley and Sons, Singapore.

Lecture Notes


Tutorial Notes


Assignments


Solutions


Assessment Scheme

Final Examination  60%
Midterm Examination  30%
Homework 10%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.

Last updated: June 22, 2015 19:37:43