LECTURE NOTES OF WILLIAM CHEN
# INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS

### Chapter 1 : INTRODUCTION >>

### Chapter 2 : FIRST ORDER LINEAR EQUATIONS >>

### Chapter 3 : FIRST ORDER LINEAR SYSTEMS >>

### Chapter 4 : HIGHER ORDER LINEAR EQUATIONS >>

### Chapter 5 : LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS >>

### Chapter 6 : FIRST ORDER LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS >>

### Chapter 7 : SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS >>

### Chapter 8 : EXISTENCE AND UNIQUENESS OF SOLUTIONS >>

This set of notes has been organized in such a way to create a single volume suitable for a very brief introduction to the theory of ordinary differential equations.

To read the notes, click the links below for connection to the appropriate PDF files.

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- A Special Case
- Another Special Case
- The General Case
- A Reduction Argument
- Integral Curves and Direction Field
- The Theorem
- Maximal Interval of Existence

- Homogeneous Equations
- Non-Homogeneous Equations

- Matrix Formulation
- Homogeneous Systems
- The Wronskian
- Non-Homogeneous Systems

- Homogeneous Equations
- Non-Homogeneous Equations

- Homogeneous Equations
- Distinct Roots
- Repeated Roots
- Non-Homogeneous Equations
- Method of Undetermined Coefficients
- Behaviour of Solutions

- Homogeneous Systems
- A Fundamental System of Solutions
- Jordan Normal Form

- Introduction
- The Singular Case
- The Analytic Case
- An Example

- Introduction
- A Metric Space Setting
- A Stronger Version of the Theorem