Differential Equations – Freedom Academy (Under Construction)

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A step-by-step video course in Differential Equations. You need this material to analyze more complex circuits with capacitors and inductors.

Course Content

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Introduction to Differential Equations

Lesson 1: Introduction to Differential Equations 11 Topics

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Introduction to Differential Equations – Part 1

Linearity of Solutions

Verification of Solution to Differential Equations – Examples

Verification of Solution to Differential Equations – More Examples – Implicit Solution

Family of Solutions

Example of Piecewise-Defined Solution

Initial Value Problem

Initial Value Problem – Example

Initial Value Solution with Several Solutions

Second Order Initial Value Problem

Existence and Uniqueness of a Solution

First-Order Differential Equations

Lesson 2: First-Order Differential Equations 12 Topics

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Autonomous First-Order Equations

Solution Curves of an Autonomous Differential Equations

Attractors and Repellers

First-Order Differential Equation Solution Curves Without A Solution

First-Order Differential Equation with Several Variables – Example 1

First-Order Differential Equation with Several Variables – Example 2

First-Order Differential Equation Using Separation of Variables

First-Order Differential Linear Equations

First-Order Differential Linear Equations – Variation of Parameters

Solving a Linear First-Order Equation

Solving a Linear First Order Equation Examples

Solving a Linear First-Order Equation – More Examples

Modeling with First-Order Differential Equations

Lesson 3: Modeling with First-Order Differential Equations 7 Topics

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Modeling Using Linear First-Order Equations

Modeling Using Linear First-Order Equations – Example – Half-Life of Plutonium

Modeling Using Linear First-Order Equations – Example – Carbon Dating

Modeling Using Linear First-Order Equations – Example – Newton’s Law of Cooling or Warming

Modeling Using Linear First-Order Equations – Example – Mixtures

Modeling Using Linear First-Order Equations – Example – Series Circuits – Part 1

Modeling Using Linear First-Order Equations – Example – Series Circuits – Part 2

Solutions of Ordinary Differential Equations

Lesson 4: Solutions of Ordinary Differential Equations 21 Topics

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Solutions of Ordinary Differential Equations

Solutions of Ordinary Differential Equations – Boundary Value Problems

Homogeneous Equations

Superposition Principle

General Solution of Homogeneous Differential Equation

General Solution of Non-Homogenous Differential Equation and Superposition

Homogeneous Linear Equations with Constant Coefficients

Homogeneous Linear Higher Order Differential Equations

Euler’s Formula and Second-Order Differential Equations

Finding Solution to Second-Order Homogeneous Differential Equations

Second-Order Differential Equations and Damping

Method of Undertermined Coefficients to Find Solution of Higher Order DE

Homogeneous 4th Order Differential Equations

Method of Undermined Coefficients and Superpostion Principle

Method of Underdetermined Coefficients for 2nd Order Differential Equations

Method of Undetermined Coefficients for Non Homogeneous Differential Equations

Method of Undetermined Coefficients – Case 1

Method of Undetermined Coefficients – Case 2

Initial Value Problem – Multiplication Rule for Case II

Particular Solution and the Multiplication Rule for Case II

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Modeling with Higher-Order Differential Equations

Lesson 5: Modeling with Higher-Order Differential Equations 8 Topics

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Modeling With Higher Order Differential Equations

Spring Mass Systems for Free Undamped Motion and Hooke’s Law

Spring Mass Systems for Free Undamped Moton

Spring Mass Systems for Free Undamped Moton – Alternative Form

Spring Mass Systems for Damped Motion

Critically Damped Motion for Spring Mass System

Force Driven Spring-Mass Motion

Transient and Steady-State Motion

LaPlace Transforms

Lesson 6: Laplace Transforms 19 Topics

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Definition of Laplace Transform

Laplace Transform Examples Exponential

Laplace Transform of Sinusoidal Functions

Linearity of Laplace Transform and Transform of Some Basic Functions

Inverse Laplace Transform

Laplace Transform Using Partial Fraction Expansion

Laplace Transform Using Partial Fraction Expansion – Another Example

Transform of Derivatives

Solving Linear Differential Equations Using The Laplace Transform

Solving Initial Value Problem with the Laplace Transform

Operational Properties of the Laplace Transform

Inverse Laplace Transform Using Partial Fraction Expansion

Initial Value Problem Using Laplace Transform – Another Example

Initial Value Problem Usng Laplace Transform – One More Example

Translation Property in the Time Domain and Laplace Transform

Application of Translation Time Property to Find Laplace Transform

Alternative Form of Translation Time Property to Find Laplace Transform

Another Example of Translation Time Property to Find Laplace Transform

Using Matlab to Find the Partial Fraction Expansion and Inverse Lapace Transform