Syllabus - Math 285 Version B
Ordinary Differential Equations and Linear SystemsText: Elementary Differential Equations with Boundary Value Problems, Edwards and Penny (1996)
Chapter 1: First Order Differential Equations (6 days)
1.1 Differential Equations and Mathematical Models1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves (emphasizing the importance of the existence and uniqueness theorem for the geometric structure of solution families)
1.4 Separable Equations and Applications
1.5 Linear First Order Equations
1.6 Substitution Methods and Exact Equations
Chapter 2: Mathematical Models and Numerical Methods (2 days)
2.1 Population Models2.3 Acceleration-Velocity Models
Chapter 3: Linear Equations of Higher Order (12 days)
3.1 Introduction: Second-Order Linear Equations (1)3.2 General Theory of Linear Equations (including linear independence and Wronskians) (2)
3.3 Homogeneous Equations with Constant Coefficients (including the factorization of constant coefficient operators) (2)
3.4 Mechanical Vibrations (2)
3.5 Nonhomogeneous Equations: Undetermined Coefficients and Variation of Parameters (3)
3.6 Forced Oscillations and Resonance (1)
3.7 Electrical Circuits (1)
Chapter 4: Introduction to Systems of Differential Equations (1 day)
4.1 First Order Systems and ApplicationsChapter 5: Linear Systems of Differential Equations (11 days)
5.1 Matrices and Linear Systems (3)
- Notation, Algebra, Determinants
- Linear Systems, Wronskians, General Theorems
5.2 The Eigenvalue Method for Homogeneous Systems (2)
5.3 Mechanical Applications (a selection of applications) (2)
5.4 Multiple Eigenvalue Solutions (2)
5.? Non-homogeneous Systems (handout from 3rd Edition) (2)
5.5 Matrix Exponentials and Linear Systems (2)
Chapter 9: Fourier Series (6 days)
9.1 Periodic Functions and Trigonometric Series (1)9.2 General Fourier Series and Convergence (2)
9.3 Even-Odd Functions. Termwise Differentiation (1)
9.4 Applications of Fourier Series (2)
Exams: 3 days
Total: 44 days