Math 391 Videos, Summaries, Problem Sets

1.1 Basic Mathematical Models; Direction Fields

The Geomtetrical View of y' = f(x,y)

Direction Fields (Recitation Problem)

Introduction and Modeling

Sketching Slope Fields

Reasoning Using Slope Fields

Graphical Notes

1.2 Solutions of Differential Equations

Finding General Solutions Using Separation of Variables

Finding Particular Solutions Using Separation of Variables

2.1 Linear Differential Equations; Methods of Integrating Factors

Arthur Mattuck: Solving First-order Linear ODEs

First Order Linear (Recitation Problem)

Linear Equations (Recitation Problems)

2.2 Separable Differential Equations

Separable Equation (Recitation Problem)

Separable Differential Equations

Initial Value Problem

2.3 Modeling

Modeling by First Order ODE (notes)

3.1 and 3.2 Linear Homogeneous Second Order Linear ODE

Theory of General Second Order Linear Homogeneous ODE

Normalized Solutions (notes)

Operators and Exponential Response (notes)

3.3 Complex Roots Characteristic Equation

Complex Numbers (notes)

Complex Numbers and Complex Exponential (Mattuck Lecture)

Complex Numbers and Euler's Formula (Recitation Problems)

Applications to Temperature, Mixing, RC-circuit, Growth and Decay (Mattuck Lecture)

Sinusoidal Functions (Recitation Problems)

3.4 Repeated Roots

Second Order Linear Constant Coefficient (Lecture Mattuck)

Complex Characteristic Roots; Undamped and Damped Oscillations (Lecture Mattuck)

Exploration of Damped Vibrations (Applet)

Damped Harmonic Oscillator (Recitation)

3.5 Non Homogeneous Equations; Methods of Undetermined Coefficients

First Order Input-Response model of Inhomogeous Equation (notes)

First Order Inhomogeneous (notes)

First Order Inhomogeneous Sinusoidal Inputs (notes)

First Order Constant Coefficient Non Homogeneous (Lecture Mattuck)

First Order Constant Coefficient Non Homogeneous (Recitation Problems)

First Order Constant Coefficient Non Homogeneous Sinusoidal Inputs (Recitation Problems)

Second Order Constant Coefficient Non Homogeneous (Lecture Mattuck)

Finding Particular Solutions to Inhomogeneous ODEs (Lecture Mattuck)

Finding Particular Solutions to Inhomogeneous ODEs (Recitation Problems)

Finding Particular Solutions to Inhomogeneous ODEs (Recitation Problems Part 2)

Linear Differential Operators (notes)

Undetermined Coefficients (notes)

Undetermined Coefficients (Recitation Problems)

Undetermined Coefficients (notes 2)

3.7 Mechanical and Electrical Vibrations

Amplitude and Phase 1st Order Applet

Explorations of Damped Oscillations Applet

Damped Harmonic Oscillator (recitation)

3.8 Forced Vibrations

Resonance and the Exponential Shift Rule (notes)

Pure Resonance (recitation)

Amplitude and Phase Second Order I Applet

Frequency Response (recitation)

Chapter 6 Laplace Transformation

Introduction to Laplace Transform

Derivative Formulas

Convolution Formula

Using Laplace Transforms to Solve ODE with discontinuous Inputs

Laplace Transform with Inputs

Lapleace Transform (recitation vicdeo)

Inverse Laplace Transform and Partial Fractions (recitation video)

Chapter 10 Fourier Series and Heat Equation

Linear ODEs with Periodic Input (recitation video)

Manipulating Fourier Series (recitation video)

Introduction to Fourier Series (lecture Mattuck)

Continuation: More General Periods (lecture Mattuck)

Finding Particular Solutions via Fourier Series (lecture Mattuck)