Department of Mathematics
University of California, Santa Barbara
Math 4B
Differential Equations
| Video - 11:02 | Introduction to differential equations and the terms order and linear/nonlinear |
| Text | Definitions for order, linear, initial value problem, implicit/explicit solutions |
| Text | Introduction to direction fields, isoclines, and determining long term behavior |
| Interactive | Allows you to enter in function and will plot direction field and solutions |
| Video - 9:01 | Intro to slope fields and examples |
| Interactive | Step by step explanation of slope fields and isoclines |
| Interactive | Interactive applet with example slope fields |
| Interactive | Interactive applet that plots example slope fields and isoclines |
| Video - 12:00 | Examples using separation of variables, one of which has a solution left in implicit form | See second video for more examples |
| Text | Description of separation of variables method and some examples |
| Video - 5:08 | Example using the separation of variables method |
| Video - 5:18 | Second example using the separation of variables metod |
| Video / PDF | Video, course notes, and practice problems on separation of variables |
| Text | Description of integrating factor method and some examples |
| Video - 5:48 | Example using the integrating factor method |
| Video - 3:30 | Second example using the integrating factor method |
| Video / PDF | Introduction to linear ODEs and the superposition principle | Can ignore content on systems |
| Video / PDF | Video lectures, course notes, and practice problems on integrating factor method |
| Text | Supplementary material to 34B CLAS groups on diff eqn |
| Interactive | Gives slope field and sample solutions to growth/decay and logistic equations |
| Video - 8:12 | Introduction to differential equations |
| Video - 8:07 | Introduction to growth and decay differential equations |
| Video - 8:25 | Introduction to Newton's Law of Cooling and examples |
| Text | Introduction and examples for growth/decay |
| Text | In depth explanation of Newton's Law of Cooling |
| Text | Step-by-step proof of the solution to the logistic equation |
| Video - 7:04 | Population growth example requiring the logistic equation |
| Text | Various applications of first order DE's | Most relevant may be the first example on mixing |
| Video - 10:09 | Mixing example |
| Text | Introduction to second order DE's and the principle of superposition in this setting |
| Video - 9:44 | Introduction to second order DE's (linear homogenous case) |
| Video - 4:35 | Brief overview of second order DE's and quickly does 2 real roots example (one distinct, one repeated) | Does not go into why solutions have the form that they do |
| Video / PDF | Lectures and notes on second order ODE's covering all cases (real distinct, real repeated, complex) of roots and connection to harmonic oscillators |
| Text | Examples with real and distinct roots of the characteristic equation |
| Video - 8:28 | Example with two real distinct roots (finds general solution only) |
| Video - 5:59 | Introduces an initial condition to the previous example | See 4th video in sequence for a second example that requires quadratic formula. |
| Text | Examples with complex roots of the characteristic equation |
| Video - 10:27 | Part 1 of 3 videos on complex roots case |
| Video - 3:40 | Example with complex roots |
| Text | Using undetermined coefficients to solve a second order ODE |
| Video - 10:11 | Part 1 of 4 videos on undetermined coefficients |
| Video - 3:55 | Part 1 of 2 videos on an undetermined coefficients example |
| Video / PDF | Course material on undetermined coefficients |
| Text | Using variation of parameters to solve a second order ODE |
| Video - 11:03 | Detailed example using variation of parameters |
| Video - 12:07 | Second example using variation of parameters |
| Interactive | Allows you to enter in mass, damping, spring, and initial conditions, and then graphs position vs. time and position vs. velocity |
| Text | Exampes involving springs |
| Video / PDF | Course material on damped harmonic oscillators |
| Text | Introduction to higher order ODEs |
| Text | Finding solutions to higher order homogenous ODEs |
| Text | Using undetermined coefficients to solve a higher order ODE |
| Text | Introduction to systems of differential equations |
| Video / PDF | Introduction to systems of differential equations and review material |
| Video / PDF | Course material on real, complex, and repeated eigenvalue cases |
| Text | Examples with real eigenvalues |
| Text | Examples with complex eigenvalues |
| Interactive | Graphs direction fields for system of two differential equations |
| Interactive | Java version of Matlab direction field functions | Use pplane for a system of first order ODEs |
| Text | Introduction to sketching phase planes |
| Video / PDF | Course material on phase portraits |
