Final
1 Introduction
1.1 Definitions and Basic Concepts
- Types of Ordinary Differential Equations
- Systems of ODEs
1.2 Direction Field of First Order ODEs
1.3 The Approaches of Finding Solutions of ODE
- Analytical Approaches
- Numerical Approaches
2. First order ordinary differential equations
2.1 Separable Differential Equations
2.2 Reduction to separable equations.
2.3 Linear Equations
2.4 Exact Differential Equations
2.5 Integrating factor .
2.6 Existence and Uniqueness of Solution
2.7 Application of first order ODEs
- Motion through a resisting medium
- Population growth
- Radioactive decay
- Heating and cooling problems
- Orthogonal trajectories.
- Mixing problems
3. Secocd order ordinary differential equations
3.1 Basic concepts
3.2 Reduction of order
3.3 Homogeneous Equations with Constant Coefficients
- Distinct real roots
- Complex Conjugate Roots
- Repeated Roots . .
3.4 Nonhomogeneous Equations
- Undetermined Coefficients
- Variation of Parameters
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