Differential Equations, Spring 2006

Differential Equations, Spring 2006

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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 of…

Instructors: Prof. Arthur Mattuck Prof. Haynes Miller


    • Aug 5, 2016 LATEST EPISODE
    • infrequent NEW EPISODES
    • 47m AVG DURATION
    • 32 EPISODES


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    Latest episodes from Differential Equations, Spring 2006

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

    Play Episode Listen Later Aug 5, 2016 50:25


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

    Play Episode Listen Later Aug 5, 2016 50:45


    Lecture 28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters

    Play Episode Listen Later Jun 29, 2015 46:53


    Lecture 23: Use with impulse inputs; Dirac delta function, weight and transfer functions

    Play Episode Listen Later Jun 29, 2015 44:55


    Lecture 33: Relation between non-linear systems and first-order ODE's; structural stability of a system

    Play Episode Listen Later Jun 29, 2015 50:09


    Lecture 27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients

    Play Episode Listen Later Jun 29, 2015 50:27


    Lecture 32: Limit cycles: existence and non-existence criteria

    Play Episode Listen Later Jun 29, 2015 45:53


    Lecture 26: Continuation: repeated real eigenvalues, complex eigenvalues

    Play Episode Listen Later Jun 29, 2015 46:37


    Lecture 31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum

    Play Episode Listen Later Jun 29, 2015 47:11


    Lecture 30: Decoupling linear systems with constant coefficients

    Play Episode Listen Later Jun 29, 2015 47:06


    Lecture 29: Matrix exponentials; application to solving systems

    Play Episode Listen Later Jun 29, 2015 48:53


    Lecture 22: Using Laplace transform to solve ODE's with discontinuous inputs

    Play Episode Listen Later Jun 29, 2015 44:09


    Lecture 24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system

    Play Episode Listen Later Jun 29, 2015 47:04


    Lecture 21: Convolution formula: proof, connection with Laplace transform, application to physical problems

    Play Episode Listen Later Jun 29, 2015 44:19


    Lecture 25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case)

    Play Episode Listen Later Jun 29, 2015 49:07


    Lecture 20: Derivative formulas; using the Laplace transform to solve linear ODE's

    Play Episode Listen Later Jun 29, 2015 51:07


    Lecture 19: Introduction to the Laplace transform; basic formulas

    Play Episode Listen Later Jun 29, 2015 47:40


    Lecture 17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds

    Play Episode Listen Later Jun 29, 2015 45:48


    Lecture 16: Continuation: more general periods; even and odd functions; periodic extension

    Play Episode Listen Later Jun 29, 2015 49:29


    Lecture 15: Introduction to Fourier series; basic formulas for period 2(pi)

    Play Episode Listen Later Jun 29, 2015 49:31


    Lecture 14: Interpretation of the exceptional case: resonance

    Play Episode Listen Later Jun 29, 2015 44:26


    Lecture 12: Continuation: general theory for inhomogeneous ODE's

    Play Episode Listen Later Jun 29, 2015 46:26


    Lecture 13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials

    Play Episode Listen Later Jun 29, 2015 47:55


    Lecture 11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians

    Play Episode Listen Later Jun 29, 2015 50:32


    Lecture 10: Continuation: complex characteristic roots; undamped and damped oscillations

    Play Episode Listen Later Jun 29, 2015 46:28


    Lecture 09: Solving second-order linear ODE's with constant coefficients: the three cases

    Play Episode Listen Later Jun 29, 2015 50:00


    Lecture 08: Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models

    Play Episode Listen Later Jun 29, 2015 50:36


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

    Play Episode Listen Later Jun 29, 2015 45:46


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

    Play Episode Listen Later Jun 29, 2015 50:14


    Lecture 06: Complex numbers and complex exponentials

    Play Episode Listen Later Jun 29, 2015 45:28


    Lecture 07: First-order linear with constant coefficients: behavior of solutions, use of complex methods

    Play Episode Listen Later Jun 29, 2015 41:10


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

    Play Episode Listen Later Jun 29, 2015 48:56


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