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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