 32 episodes

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams. # Differential Equations, Spring 2006 MIT

• Education

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

• video
Lecture 01: The geometrical view of y'=f(x,y): direction fields, integral curves

## Lecture 01: The geometrical view of y'=f(x,y): direction fields, integral curves

• 48 min
• video
Lecture 02: Euler's numerical method for y'=f(x,y) and its generalizations

## Lecture 02: Euler's numerical method for y'=f(x,y) and its generalizations

• 50 min
• video
Lecture 03: Solving first-order linear ODE's; steady-state and transient solutions

## Lecture 03: Solving first-order linear ODE's; steady-state and transient solutions

• 50 min
• video
Lecture 04: First-order substitution methods: Bernouilli and homogeneous ODE's

## Lecture 04: First-order substitution methods: Bernouilli and homogeneous ODE's

• 50 min
• video
Lecture 05: First-order autonomous ODE's: qualitative methods, applications

## Lecture 05: First-order autonomous ODE's: qualitative methods, applications

• 45 min
• video
Lecture 06: Complex numbers and complex exponentials

• 45 min