LECTURE NOTES OF WILLIAM CHEN

 

INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS

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.

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Chapter 1 : INTRODUCTION >>

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

Chapter 2 : FIRST ORDER LINEAR EQUATIONS >>

• Homogeneous Equations
• Non-Homogeneous Equations

Chapter 3 : FIRST ORDER LINEAR SYSTEMS >>

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

Chapter 4 : HIGHER ORDER LINEAR EQUATIONS >>

• Homogeneous Equations
• Non-Homogeneous Equations

Chapter 5 : LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS >>

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

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

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

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

• Introduction
• The Singular Case
• The Analytic Case
• An Example

Chapter 8 : EXISTENCE AND UNIQUENESS OF SOLUTIONS >>

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