Table of Contents
Soft Introduction to Differential Equations
Lesson 0.1 - Review of Partial Fraction Decomposition
Lesson 1 - What Are Differential Equations? What Should I Know Before Beginning?
Lesson 2 - Existence and Uniqueness Theorem
Lesson 3 - Direction Fields
Lesson 4 - Euler's Method
Methods for Solving Differential Equations
Lesson 5 - Separable Equations
Lesson 6 - Linear First-Order Equations
Lesson 7 - Exact Equations
Lesson 8 - Substitutions and Transformations for First Order Equations
Lesson 9 - Homogeneous Second Order Linear Equations
Lesson 10 - Method of Undetermined Coefficients
Lesson 11 - Variations of Parameters
Lesson 12 - Theory of Linear Differential Equations (Theorem 1)
Lesson 12.1 - The Differential Operator
Lesson 12.2 - The Wronskian for nth-Order Differential Equations
Lesson 12.3 - Another Theory of Linear Differential Equations (Theorem 2)
Lesson 13 - Mass Spring Systems
Lesson 13.1 Mass Spring Systems Damping and Worked Examples
Series
Lesson 14 - Infinite Series
Lesson 15 - Geometric Series and Ratio Test
Lesson 16 - Alternating Series and Alternating Series Test
Lesson 17 - Power Series
Lesson 18 - Taylor Series
Lesson 19 - Taylor Polynomial, Power Series and Shifting Index
Lesson 20 - Power Series Solutions
Laplace Transforms, Heaviside Functions and Dirac Delta
Lesson 21 - Definition of Laplace Transforms
Lesson 21.1 - Table of Laplace Transforms
Lesson 22 - Inverse Laplace Transforms
Lesson 23 - Solving IVPs using Laplace Transforms
Lesson 24 - Introduction to Discontinuous Functions (Heaviside Functions)
Lesson 25 - Transforms of Heaviside Functions
Lesson 26 - Convolution
Lesson 27 - The Dirac Delta Function
Lesson 27.1 - Extra Practice Solving IVPs Containing Dirac Delta Functions
Lesson 28 - Solving Linear Systems with Laplace Transforms
Additional Material
Lesson 29 - Quick Lesson on Matrices
Lesson 30 - Matrix Methods for Linear Homogeneous Systems