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Differential Equations
Rating: 4.4 out of 5(4 ratings)
23 students

Differential Equations

Differential Equations Crash Course - condensed, intuitive, practical
Created byScott Gong
Last updated 6/2021
English

What you'll learn

  • Differential Equations
  • Engineering mathematics/calculus
  • 1st and 2nd order differential equations
  • First order linear and non-linear systems of differential equations

Course content

1 section9 lectures6h 41m total length
  • What are Differential Equations?59:25
    • Some examples

    • General form of linear first order

    • Direction Fields

    • First Order Differential Equations

      • Modeling common problems

      • Existence and uniqueness

  • First Order Differential Equations50:29
    • Integrating factor

    • Separation of variables (non-linear)

      • Applications to mechanics

    • Numerical methods

  • Second Order Differential Equations (part 1)58:24
    • General solution and particular solution

    • Constant coefficient homogeneous equations

      • Special focus: vibration problem

  • Second Order Differential Equations (part 2)53:38
    • Non-homogeneous equations

    • Repeated Roots and reduction of order

    • Method of Undetermined Coefficients

    • Method of Variation of Parameters

  • Linear Algebra Review and Higher Order Differential Equations50:25
    • Linear Algebra Review

      • Determinants

      • Row reduction and linear independence

      • Eigenpairs

    • Intro to Higher Order Differential Equations

      • Abel’s Theorem

  • First Order Linear Systems (part 1)32:41
    • Calculus of Matrices

    • Intro First Order Linear Systems

      • Converting Higher Order ODE to First Order Linear System

  • First Order Linear Systems (part 2)48:58
    • Eigenvalue Problem for Linear Systems

    • Phase Plane

    • Variation of Parameters for Linear Systems

  • Nonlinear Systems38:46
    • Equilibrium Points and Nullclines

    • Classifying Equilibrium Points

    • Linearization of Nonlinear System

  • Extra lecture: 1st Order Equilibrium Analysis8:51

    Revisit the population logistics model to analyze the equilibrium points of a nonlinear, first order, differential equation.

Requirements

  • Single Variable Calculus
  • Linear Algebra

Description

Differential Equations are commonly used to describe real life phenomenon such as: tank mixing, vibrations, population dynamics, radioactive decay, falling with air resistance, etc. We will study common differential equations and how to solve them.

I find too often that students don’t know why they are learning something or how it relates to future classes or career. Some professors are too focused on getting the material over to you and giving you the test. Sound familiar? I will teach you how to think like an engineer, which means being able to break down complicated problems into simple pieces that you already know how to do! I recognize that students value simplicity and logic over complicated derivations and memorized processes. I will teach you the simplest way that has helped my students become successful for the past 5 years.

By the end of the course, you will know how to approach fundamental problems in each of the major topics and explain why they are relevant in engineering. The course is designed to also be used as a reference when you are taking the full version of the course as well, so don’t be afraid if you don’t pick everything up the first time you see it! My hope is that you have the “ah-ha that’s why Scott approached it that way” moment when you take the real course.

Who this course is for:

  • Sophomores in engineering majors
  • Students who will be taking Differential Equations
  • Students who are currently enrolled in Differential Equations
  • Young professionals who want to brush up on their engineering mathematics