Differential Equations, Spring 2006
Lecture 03: Solving first-order linear ODE's; steady-state and transient solutions
Lecture 02: Euler's numerical method for y'=f(x,y) and its generalizations
Lecture 28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters
Lecture 23: Use with impulse inputs; Dirac delta function, weight and transfer functions
Lecture 33: Relation between non-linear systems and first-order ODE's; structural stability of a system
Lecture 27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients
Lecture 32: Limit cycles: existence and non-existence criteria
Lecture 26: Continuation: repeated real eigenvalues, complex eigenvalues
Lecture 31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum
Lecture 30: Decoupling linear systems with constant coefficients
Lecture 29: Matrix exponentials; application to solving systems
Lecture 22: Using Laplace transform to solve ODE's with discontinuous inputs
Lecture 24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system
Lecture 21: Convolution formula: proof, connection with Laplace transform, application to physical problems
Lecture 25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case)
Lecture 20: Derivative formulas; using the Laplace transform to solve linear ODE's
Lecture 19: Introduction to the Laplace transform; basic formulas
Lecture 17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds
Lecture 16: Continuation: more general periods; even and odd functions; periodic extension
Lecture 15: Introduction to Fourier series; basic formulas for period 2(pi)
Lecture 14: Interpretation of the exceptional case: resonance
Lecture 12: Continuation: general theory for inhomogeneous ODE's
Lecture 13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials
Lecture 11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians
Lecture 10: Continuation: complex characteristic roots; undamped and damped oscillations
More from Instructors: Prof. Arthur Mattuck Prof. Haynes Miller
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