Differential Equations

Explore the fundamental concepts and applications of differential equations in this comprehensive 10-hour course. Learn to solve various types of differential equations, including first-order, second-order, and systems of equations. Master techniques such as separation of variables, integrating factors, and variation of parameters. Investigate real-world applications in population models, mechanical vibrations, and RCL circuits. Delve into advanced topics like Laplace transforms and power series solutions. Develop problem-solving skills through slope fields, homogeneous and nonhomogeneous equations, and both ordinary and singular points in differential equations.

1.1 Differential Equations.
1.2 - 1.3 Integrals as Solutions and Slope Fields.
1.4 Separable Equations.
1.5 Linear First-Ordered Equations.
1.6a Homogeneous Equations.
1.6b Bernoulli Equations.
1.6c Exact Equations.
3.1 Second Ordered Linear Equations.
3.2 General Solutions of Linear Equations.
3.3 Homogeneous Equations with Constant Coefficients.
3.5b Variation of Parameters.
2.1 Population Models.
2.3 Acceleration Velocity Models.
3.5a Nonhomogeneous Equations and Undetermined Coefficients.
3.4a Mechanical Vibrations Free Undamped Motion.
3.4b Mechanical Vibrations Free Damped Motion.
3.6 & 3.7 Forced Oscillations and RCL Circuits.
4.2a Homogeneous Systems of Differential Equations.
4.2b Nonhomogeneous Systems of Differential Equations.
7.1 Laplace Transforms.
7.3 Partial Fractions and Laplace Transforms.
7.2 Solving Differential Equations with Laplace Transforms.
8.1 Power Series as a Solution to Differential Equations.
8.2 Ordinary Points.
8.3 Singular Points.