Differential Equations (MIT 2003) by Arthur Mattuck

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source: tawkaw OpenCourseWare     2015年4月22日

Lecture 01 The geometrical view of y'=fx,y direction fields, integral curves 48:56
Lecture 02 Euler's numerical method for y'=fx,y and its generalizations 50:45
Lecture 03 Solving first order linear ODE's; steady state and transient solutions 50:23
Lecture 04 First order substitution methods Bernouilli and homogeneous ODE's 50:14
Lecture 05 First order autonomous ODE's qualitative methods, applications 45:47
Lecture 06 Complex numbers and complex exponentials 45:29
Lecture 07 First order linear with constant coefficients behavior of solutions, use of complex metho 41:10
Lecture 08 Continuation; applications to temperature, mixing, RC circuit, decay, and growth models 50:36
Lecture 09 Solving second order linear ODE's with constant coefficients the three cases 50:01
Lecture 10 Continuation complex characteristic roots; undamped and damped oscillations 46:24
Lecture 11 Theory of general second order linear homogeneous ODE's superposition, uniqueness, Wronsk 50:32
Lecture 12 Continuation general theory for inhomogeneous ODE's Stability criteria for the constant 46:24
Lecture 13 Finding particular solutions to inhomogeneous ODE's operator and solution formulas involve 47:56
Lecture 14 Interpretation of the exceptional case resonance 44:26
Lecture 15 Introduction to Fourier series; basic formulas for period 2pi 49:32
Lecture 16 Continuation more general periods; even and odd functions; periodic extension 49:29
Lecture 17 Finding particular solutions via Fourier series; resonant terms;hearing musical sounds 45:47
Lecture 19 Introduction to the Laplace transform; basic formulas 47:40
Lecture 20 Derivative formulas; using the Laplace transform to solve linear ODE's 51:08
Lecture 21 Convolution formula proof, connection with Laplace transform, application to physical pro 44:20
Lecture 22 Using Laplace transform to solve ODE's with discontinuous inputs 44:08
Lecture 23 Use with impulse inputs; Dirac delta function, weight and transfer functions 44:55
Lecture 24 Introduction to first order systems of ODE's; solution by elimination, geometric interpre 47:05
Lecture 25 Homogeneous linear systems with constant coefficients solution via matrix eigenvalues rea 49:07
Lecture 26 Continuation repeated real eigenvalues, complex eigenvalues 46:38
Lecture 27 Sketching solutions of 2x2 homogeneous linear system with constant coefficients 50:27
Lecture 28 Matrix methods for inhomogeneous systems theory, fundamental matrix, variation of paramet 46:53
Lecture 29 Matrix exponentials; application to solving systems 48:54
Lecture 30 Decoupling linear systems with constant coefficients 47:07
Lecture 31 Non linear autonomous systems finding the critical points and sketching trajectories; the 47:11
Lecture 32 Limit cycles existence and non existence criteria 45:53
Lecture 33 Relation between non linear systems and first order ODE's; structural stability of a syst 50:10