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 linear first order transient steady state

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

Play Episode Listen Later Aug 5, 2016 50:45

method lecture generalization numerical

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

Play Episode Listen Later Jun 29, 2015 46:53

matrix methods lecture fundamental variation parameters systems theory

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

Play Episode Listen Later Jun 29, 2015 44:55

weight delta lecture impulse functions inputs dirac

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

system lecture stability relation structural first order nonlinear

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

Play Episode Listen Later Jun 29, 2015 50:27

system lecture constant linear sketching homogeneous

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

Play Episode Listen Later Jun 29, 2015 45:53

limit lecture cycles existence criteria

Lecture 26: Continuation: repeated real eigenvalues, complex eigenvalues

Play Episode Listen Later Jun 29, 2015 46:37

complex lecture eigenvalues

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 pendulum nonlinear sketching trajectories autonomous systems critical points

Lecture 30: Decoupling linear systems with constant coefficients

Play Episode Listen Later Jun 29, 2015 47:06

lecture constant linear decoupling

Lecture 29: Matrix exponentials; application to solving systems

Play Episode Listen Later Jun 29, 2015 48:53

matrix application lecture exponential

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

Play Episode Listen Later Jun 29, 2015 44:09

transform solve lecture laplace inputs

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

system solution lecture interpretation elimination first order geometric

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

Play Episode Listen Later Jun 29, 2015 44:19

proof formula transform application lecture laplace convolution

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

matrix solution lecture constant linear distinct homogeneous eigenvalues

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

Play Episode Listen Later Jun 29, 2015 51:07

transform solve lecture linear laplace formulas derivative

Lecture 19: Introduction to the Laplace transform; basic formulas

Play Episode Listen Later Jun 29, 2015 47:40

basic transform lecture laplace formulas

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

Play Episode Listen Later Jun 29, 2015 45:48

musical hearing terms lecture resonant fourier series

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

Play Episode Listen Later Jun 29, 2015 49:29

lecture extension periods functions periodic

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

Play Episode Listen Later Jun 29, 2015 49:31

period basic lecture formulas fourier series

Lecture 14: Interpretation of the exceptional case: resonance

Play Episode Listen Later Jun 29, 2015 44:26

lecture interpretation exceptional resonance

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

Play Episode Listen Later Jun 29, 2015 46:26

lecture general theory

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

Play Episode Listen Later Jun 29, 2015 47:55

solution lecture operator involving exponential formulas

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

Play Episode Listen Later Jun 29, 2015 50:32

theory lecture uniqueness linear superposition homogeneous

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

Play Episode Listen Later Jun 29, 2015 46:28

roots complex characteristics lecture oscillations

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

Play Episode Listen Later Jun 29, 2015 50:00

lecture constant linear

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

Play Episode Listen Later Jun 29, 2015 50:36

applications lecture mixing circuit temperature decay growth models

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

Play Episode Listen Later Jun 29, 2015 45:46

applications lecture autonomous first order qualitative methods

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

Play Episode Listen Later Jun 29, 2015 50:14

methods lecture substitution first order homogeneous

Lecture 06: Complex numbers and complex exponentials

Play Episode Listen Later Jun 29, 2015 45:28

lecture exponential complex numbers

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

Play Episode Listen Later Jun 29, 2015 41:10

behavior complex methods lecture constant linear first order

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

Play Episode Listen Later Jun 29, 2015 48:56

direction fields lecture integral curves

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