Copies of the classnotes are on the internet in PDF format as given below.
These notes and supplements have not been classroom tested (and so may have some typographical errors).
They are based on a section of Applied Math 1 (MATH 5610) I taught in fall 1996.
Syllabus for the Class. Course Syllabus
Chapter 1. Systems of Linear Differential Equations.
- Section 1.1. Introduction. Section 1.1 notes
- Section 1.2. Some Elementary Matrix Algebra. Section 1.2 notes
- Section 1.3. The Structure of Solutions of Homogeneous Linear Systems. Section 1.3 notes
- Section 1.4. Matrix Analysis and the Matrix Exponential. Section 1.4 notes
- Section 1.5. The Constant Coefficient Case: Real and Distinct Eigenvalues. Section 1.5 notes
- Section 1.6. The Constant Coefficient Case: Complex and Distinct Eigenvalues. Section 1.6 notes
- Section 1.7. The Constant Coefficient Case: The Putzer Algorithm. Section 1.7 notes
- Section 1.8. General Linear Systems. Section 1.8 notes
- Section 1.9. Some Elementary Stability Considerations.
- Section 1.10. Periodic Coefficients.
- Section 1.11. Scalar Equations.
- Section 1.12. An Application: Coupled Oscillators.
Test 1 (1.1-1.8). Test 1
Chapter 2. Two-Dimensional Autonomous Systems.
- Section 2.1. Introduction. Section 2.1 notes
- Section 2.2. The Phase Plane. Section 2.2 notes
- Section 2.3. Critical Points of some Special Linear Systems. Section 2.3 notes
- Section 2.4. Critical Points of General Two-Dimensional Linear Systems. Section 2.4 notes
- Section 2.5. Behavior of Nonlinear Two-Dimensional Systems Near a Critical Point. Section 2.5 notes
- Section 2.6. Elementary Liapunov Stability Theory.
- Section 2.7. Limit Cycles and the Poincare-Bendixson Theorem.
- Section 2.8. An Example: Lotka-Volterra Competition.
- Section 2.9. An Example: The Simple Pendumlum.
Test 2 (2.1-2.6). Test 2
Chapter 3. Existence Theory.
- Section 3.1. Introduction. Section 3.1 notes
- Section 3.2. Preliminaries. Section 3.2 notes
- Section 3.3. The Contraction Mapping Theorem. Section 3.3 notes
- Section 3.4. The Initial Value Problem for One Scalar Differential Equation. Section 3.4 notes
- Section 3.5. The Initial Value Problem for Systems of Differential Equations.
- Section 3.6. An Existence Theorem for a Boundary Value Problem.
Additional Chapter.
- Chapter 4. Boundary Value Problems.
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