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Differential Equations Topics

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1. Introduction to Differential Equations

1.1

Introduction to differential equations

2. First Order Differential Equations

2.1

Slope fields

2.2

Separable differential equations

2.3

Exact differential equations

2.4

Integrating factor technique

2.5

Bernoulli equations

2.6

Interval of validity

2.7

Modeling with differential equations

2.8

Equilibrium solutions

2.9

Euler's method

3. Second Order Differential Equations

3.1

Homogeneous linear second order differential equations

3.2

Characteristic equation with real distinct roots

3.3

Characteristic equation with complex roots

3.4

Characteristic equation with repeated roots

3.5

Reduction of order

3.6

Wronskian

3.7

Method of undetermined coefficients

3.8

Applications of second order differential equations

4. Laplace Transforms

4.1

Introduction to the laplace transform

4.2

Calculating laplace transforms

4.3

Inverse laplace transforms

4.4

Solving differential equations with the laplace transform

4.5

Step functions

4.6

Solving differential equations with step functions

4.7

Dirac delta function

4.8

Convolution integral

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