Differential Equations

This course develops methods for solving ordinary differential equations, covering first- and second-order equations, systems, Laplace transforms, power-series solutions, and applications to population models, motion, vibrations, and RLC circuits.

Syllabus

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.