MIT

MIT Open Course Ware - Differential Equations

Unit I: First Order Differential Equations

Conventions
Basic DE's
Geometric Methods
Numerical Methods
Linear ODE's
Integrating Factors
Complex Arithmetic
Sinusoidal Functions
Constant Coefficients
Exponential Input
Autonomous Equations
Linear vs. Nonlinear

Unit II: Second Order Constant Coefficient Linear Equations

Characteristic Equation
Damped Oscillators
Exponential Response
Gain and Phase Lag
Undetermined Coefficients
Linear Operators
Pure Resonance
Frequency Response
Applications

Unit III: Fourier Series and Laplace Transform

Fourier Series: Basics
Operations
Periodic Input
Step and Delta
Impulse Response
Convolution
Laplace Transform
Partial Fractions
Solving IVP's
Transfer Functions
Poles

Unit IV: First-order Systems

Linear Systems
Matrix Methods
Phase Portraits
Matrix Exponentials
Nonlinear Systems
Linearization
Limit Cycles and Chaos

 

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