OOPS - Differential Equations

18.03 Differential Equations, Lecture Videos, Spring 2004 by Prof.Prof. Haynes Miller and Prof. Arthur Mattuck

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The geometrical view of y'=f(x,y): direction fields, integral curves. (220K)

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Euler's numerical method for y'=f(x,y) and its generalizations. (220K)

OOPS SJTU

9-19-2005

50'44''

10-24-05

file

Solving first-order linear ODE's; steady-state and transient solutions.(220K)

yang2liu

2-1-2008

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First-order substitution methods: Bernouilli and homogeneous ODE's. (220K)

Yue

9-27-05

50'11"

Nov 12, 2005

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First-order autonomous ODE's: qualitative methods, applications.(220K)

Complex numbers and complex exponentials. (220K)

First-order linear with constant coefficients: behavior of solutions, use of complex methods. (220K)

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Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models.(220K)

Solving second-order linear ODE's with constant coefficients: the three cases. (220K)

Continuation: complex characteristic roots; undamped and damped oscillations. (220K)

Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians. (220K)

Continuation: general theory for inhomogeneous ODE's. Stability criteria for the constant-coefficient ODE's. (220K)

Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials. (220K)

Interpretation of the exceptional case: resonance. (220K)

Introduction to Fourier series; basic formulas for period 2(pi). (220K)

Continuation: more general periods; even and odd functions; periodic extension. (220K)

Finding particular solutions via Fourier series; resonant terms;hearing musical sounds. (220K)

Introduction to the Laplace transform; basic formulas. (220K)

Derivative formulas; using the Laplace transform to solve linear ODE's. (220K)

Convolution formula: proof, connection with Laplace transform, application to physical problems. (220K)

Using Laplace transform to solve ODE's with discontinuous inputs. (220K)

Use with impulse inputs; Dirac delta function, weight and transfer functions. (220K)

Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system. (220K)

Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case). (220K)

Continuation: repeated real eigenvalues, complex eigenvalues. (220K)

Sketching solutions of 2x2 homogeneous linear system with constant coefficients. (220K)

Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters. (220K)

Matrix exponentials; application to solving systems. (220K)

Decoupling linear systems with constant coefficients. (220K)

Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum. (220K)

Limit cycles: existence and non-existence criteria. (220K)

Relation between non-linear systems and first-order ODE's; structural stability of a system, borderline sketching cases; illustrations using Volterra's equation and principle. (220K)

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