This course on Differential Equations aims to teach students the fundamentals of solving various types of differential equations. By the end of the course, learners will be able to understand and apply techniques such as separable equations, linear first-ordered equations, Laplace transforms, and power series solutions. The teaching method involves a combination of theoretical explanations, problem-solving exercises, and real-world applications. This course is intended for students or individuals interested in advanced mathematics, engineering, physics, or any field that requires a deep understanding of differential equations.
Overview
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.
Taught by
Tyler Wallace
