Differential Equations

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Differential Equations by Mind Map: Differential Equations

1. Basic Concepts

1.1. Notation for D.E.

1.2. Ordinary vs. Partial D.E.

1.3. Order of the Differential Equation

1.4. Initial-Value Problem

1.5. Verifying a Solution

1.6. Solutions on an Interval

1.7. Direction Fields

2. Numerical Solution of Differential Equations

2.1. Euler's Method

2.2. Runge Kutta 4th Order Method

2.3. Mathematica Numerical Solution

3. First Order Differential Equations

3.1. Directly Integrable Equations

3.2. Separable D.E.

3.2.1. Radioactive Decay

3.2.2. Carbon Dating

3.2.3. Exponential Growth

3.2.4. Logistic Growth

3.3. Exact D.E.

3.4. Linear 1st Order D.E.

3.5. Series Solutions

4. Second Order Differential Equations

4.1. Linear 2nd Order D.E.

4.1.1. Homogeneous

4.1.2. Nonhomogeneous

4.2. Second

4.2.1. Real Distinct Roots

4.2.2. Repeated Roots

4.2.3. Complex Roots

4.3. Wronskian

4.4. Variation of Parameters

4.5. Simple Harmonic Oscillator

5. Laplace Transform

5.1. Definition of Laplace Transform

5.2. Finding the Laplace Transform for Basic Functions

6. Special Functions

6.1. Step Function

6.2. Delta Function

7. Systems of Differential Equations

7.1. Basic Terminology and Notions

7.2. Converting Higher Order Linear D.E. into a system of 1st Order D.E.

7.3. Mixing problems

7.4. Laplace Transform for Systems of Differential Equations

8. Mathematica Methods

9. Review of Calculus

9.1. Functions

9.2. Limits

9.3. Derivatives

9.4. Integrals