Math 78 Videos
Section Math Sorcerer Professor Williams Alexandra Niedden Professor Maccauley MIT Professor Arthur Mattuck MIT Professor Gilbert Strang Professor Leonard Patrick JMT Khan Academy blackpenredpen
1.1 Section 1.1 Section 1.1 What is a Differential Equation? Overview of Differential Equations Introduction to Differential Equations, Checking Solutions in Differential Equations Basic Idea of What It Means to be a Solution Differential equations introduction
1.2 Section 1.2 Section 1.2 Section 1.2 Initial value problems Introduction to Initial Value Problems
2.1 Section 2.1 Plotting solutions to differential equations Lecture 1, Lecture 5 Introduction to Slope Fields, Applications of Slope Fields, Equilibrium Solutions and Stability of Differential Equations, Stability of Critical Points
2.2 Section 2.2 Section 2.2 Separation of variables Separable Equations Separable Differential Equations, Separable Equations with Initial Values, Applications with Separable Equations Example 1, Example 2, Example 3, Example 4, Example 5 Separable Equations Introduction, Example Example 1, Example 2, Example 3, Example 4, Example 5, Example 6, Example 7
2.3 Section 2.3 Section 2.3 Section 2.3 Solving 1st order inhomogeneous ODEs, Linear differential equations Lecture 3 Introduction to Linear Differential Equations and Integrating Factors, Solving Linear Differential Equations with an Integrating Factor, Domain Restrictions In Differential Equations and Integrating Factors, Special Integration in a Linear Differential Equation Problem, Mixture Problems in Linear Differential Equations First Order Linear Differential Equations, Another Example Integrating Factors 1, Integrating Factors 2 Introduction, Example 1, Example 2, Example 3, Example 4, Example 5, Example 6, Example 7
2.4 Section 2.4 Section 2.4 What are Exact Differential Equations, Solving Exact Differential Equations, Integrating Factor for Exact Differential Equations Exact Differential Equations Intuition 1, Intuition 2, Example 1, Example 2, Example 3 Idea, Check for Exactness, Example 1, Example 2, Example 3, Example 4, Example 5, Example 6, Almost Exact Equation, Almost Exact Equation Example 1, Almost Exact Equation Example 2, Almost Exact Equation Example 3
2.5 Section 2.5 Section 2.5 Section 2.5 Part 1, Section 2.5 Part 2 Lecture 4 Solving Homogeneous First Order Differential Equations, Substitutions for Homogeneous First Order Differential Equations, How to Solve Bernoulli Differential Equations Substitution Example 1, Substitution Example 2, Substitution Example 3, Substitution Example 4, Bernoulli Example 1, Bernoulli Example 2, Bernoulli Example 3 Example 1, Example 2 Substitution Example 1, Substitution Example 2, Substitution Example 3, Substitution Example 4, Substitution Example 5, Substitution Example 6, Bernoulli Example 1, Bernoulli Example 2
2.6 Section 2.6 Euler's method Lecture 2 Basic Idea Euler's Method Example 1, Euler's Method Example 2 Euler's Method Example Euler's Method, Euler's Method Example 1, Euler's Method Example 2
3.1 Section 3.1 Section 3.1 Section 3.1 Basic mixing problems, Advanced mixing problems Lecture 8 Mixing Problems and Separable Differential Equations Newton's Law of Cooling, Applying Newton's Law of Cooling to warm oatmeal Newton's Law of Cooling, Mixing Example 1, Mixing Example 2
3.2 Section 3.2 The logistic equation The Logistic Equation Introduction to Population Models and Logistic Equations Logistic Differential Equation, Analytic Solution, Example Part 1, Example Part 2 Intuition, Example Part 1, Example Part 2 Logistic Differential Equation, Example
3.3 Section 3.3
4.1 Section 4.1 Section 4.1 Section 4.1 Part 1, Section 4.1 Part 2, Section 4.1 Part 3 Second order ODEs Lecture 12 Second Order Equations Second Order Equation Check for Linear Dependence (of 2 functions), Check for Linear Independence (2 functions), Check for Linear Dependence (3 functions, using definition), Check for Linear Independence (3 functions, using definition), Check if 3 functions are LD or LI, Q1a, Check if 3 functions are LD or LI, Q1b, Check if 3 functions are LD or LI, Q1c
4.2 Section 4.2 Second order ODEs Reduction of Order Example Reduction of Order Example
4.3 Section 4.3 Section 4.3 Section 4.3 2nd order ODEs with constant coefficients Lecture 9 Homogeneous Second Order Linear Differential Equations, Homogeneous Second Order Linear DE - Complex Roots Example Two Unique Roots 1, TUR 2, TUR 2, Repeated Roots 1, RR 2, Copmlex Roots 1, CR 2, CR 3 Second order homogeneous linear differential equations with constant coefficients, Auxiliary equations with repeated roots, Higher order homogeneous linear differential equation
4.4 Section 4.4 Section 4.4 The method of undetermined coefficients Lecture 11 Method of Undetermined Coefficients, An Example of Undetermined Coefficients Method of Undetermined Coefficients/ 2nd Order Linear DE, Method of Undetermined Coefficients - Part 2 Undetermined Coefficients 1, UC 2, UC 3, UC 4 Example 1, Example 2, Example 3, Example 4, Example 5
4.5 Section 4.5
4.6 Section 4.6 Section 4.6 Section 4.6 Variation of parameters Variation of Parameters Variation of Parameters to Solve a Differential Equation (Second Order), Variation of Parameters to Solve a Differential Equation (Second Order) , Ex 2 Introduction and Idea, Example
4.7 Introduction to Cauchy Euler Differential Equations Section 4.7 Cauchy-Euler equations
4.9 Section 4.9 Lecture 24
4.10 Section 4.10
5.1 Section 5.1 Section 5.1 Part 1, Section 5.1 Part 2, Section 5.1 Part 3 Simple harmonic motion, Damped & driven harmonic motion Lecture 10, Lecture 14 Forced Harmonic Motion, Unforced Damped Motion
6.1 Section 6.1 Part 1, Section 6.1 Part 2, Section 6.1 Part 3 Section 6.1 Section 6.1 Part 1, Section 6.1 Part 2 Power Series Solutions Power Series Solutions Example 1, Power Series Solutions Example 2
6.2 Section 6.2 Section 6.2 Section 6.2 Power series solutions
6.3 Section 6.3 The method of Frobenius
7.1 Section 7.1 Part 1, Section 7.1 Part 2 Section 7.1 What is a Laplace transform? Lecture 19 Basic Idea of Laplace Transform, Laplace Transform, Basic Properties, Table of Laplace Transforms, Laplace Transform is a Linear Proof Laplace Transform 1, Laplace Transform 2, Transform of sin(at), Transform of sin(at) 2, Laplace as linear operator, Transform of cos t and polynomials, Transform of t, Transform of t^n Example 1, Example 2, Example 3, Example 4, Example 5, Example 6, Example 7
7.2 Inverse Laplace Transforms - Full Tutorial Section 7.2 Lecture 20 Laplace Transform: First Order Equation Inverse Laplace Transform, Laplace Transform - More Derivatives Laplace of Derivatives, Solving Equations Using Laplace Transform I, Solving Equations Using Laplace Transform II, Laplace Transform Inverse Example 1, Example 2, Example 3, Example 4, Example 5, Example 6, Example 7, Example 8, Example 9, Example 10, Example 11, Example 12, Example 13, Laplace Transform of the first derivative
7.3 The First Translation Theorem for Laplace Transforms, How to Use the First Translation Theorem to Find Laplace Transforms, How to Use the First Translation Theorem to Find Inverse Laplace Transforms, The Second Translation Theorem for Laplace Transforms Section 7.3 Properties & applications of the Laplace transform, Laplace transforms of piecewise functions Lecture 20, Lecture 22 Laplace Transform: Second Order Equation Heaviside Function, Laplace Transform Involving Heaviside Functions, Differential Equation Using Laplace Transform + Heavside Functions Shifting Transform, Using Laplace Transform to Solve Equation, Laplace Transform of Unit Step Function, Laplace/Step Function Differential Equation Laplace Transform: Translation Theorem in s, Inverse laplace transform, translation in s vs translation in t, Laplace transform of f(t-a)u(t-a), the shifted unit step function
7.4 Convlution Playlist Section 7.4 Laplace transforms of periodic functions, Convolution Lecture 21 Laplace Transforms and Convolution Introduction to Convolution, Convolution and Laplace Transform, Use Convolution Theorem to Solve Equation Proof of the Convolution Theorem, aplace transform of sin(t)cos(t) vs laplace transform sin(t)*cos(t), inverse laplace of s/(s^2+1)^2, using convolution theorem
7.5 Introduction to the Dirac Delta Function, Initial Value Problem with Dirac Delta I, Initial Value Problem with Dirac Delta II Section 7.5 Impulse functions Lecture 23 Impulse Response and Step Response Dirac Delta Function, Laplace Transform of Dirac Delta Function
7.6 Section 7.6 Systems of Differential Equations Example 1, Example 2, Example 3