Differential Equations by Ariel Cintron-Arias at ETSU

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source: East Tennessee State University      2017年10月24日
MATH 2120 - Differential Equations
ETSU Online Programs - http://www.etsu.edu/online
Dr. Ariel Cintron-Arias ETSU Online Programs - http://www.etsu.edu/online
Many of the following lectures are based on material from the open-textbook "Notes on DiffyQ's" by J. Lebl. Free copies of this book can be downloaded from http://www.jirka.org/diffyqs/

1 7:53 MATH 2120 What is an O.D.E.?
2 13:44 MATH 2120 Introduction to Diffy Qs Part 1
3 10:29 MATH 2120 Introduction to Diffy Qs Part 2
4 17:38 MATH 2120 Derivatives of Invertible Functions
5 6:58 MATH 2120 Integration by Change of Variables
6 6:23 MATH 2120 Integration by Trigonometric Substitution
7 12:38 MATH 2120 Integration by Parts
8 16:51 MATH 2120 Trigonometric Integrals
9 5:47 MATH 2120 Partial Fractions
10 12:28 MATH 2120 Integrals as Solutions Part 1
11 5:19 MATH 2120 Integrals as Solutions Part 2
12 9:32 MATH 2120 Integrals as Solutions Part 3
13 12:46 MATH 2120 Slope Fields
14 10:29 MATH 2120 Existence and Uniqueness
15 11:59 MATH 2120 Separable Equations Part 1
16 7:48 MATH 2120 Separable Equations Part 2
17 7:32 MATH 2120 Separable Equations Part 3
18 33:34 MATH 2120 Separable Equations with Partial Fractions Part 1
19 16:24 MATH 2120 Separable Equations with Partial Fractions Part 2
20 17:25 MATH 2120 Integrating Factor Part 1
21 11:16 MATH 2120 Integrating Factor Part 2
22 14:31 MATH 2120 Integrating Factor Part 3
23 7:22 MATH 2120 Integrating Factor Part 4
24 15:10 MATH 2120 Substitution Part 1
25 13:32 MATH 2120 Substitution Part 2
26 14:58 MATH 2120 Substitution Part 3
27 16:37 MATH 2120 Substitution Part 4
28 17:34 MATH 2120 Substitution Part 5
29 11:33 MATH 2120 Autonomous Equations Part 1
30 12:08 MATH 2120 Autonomous Equations Part 2
31 14:07 MATH 2120 Autonomous Equations Part 3
32 13:44 MATH 2120 Autonomous Equations Part 4
33 13:09 MATH 2120 Exponential Mathematical Models Part 1
34 10:15 MATH 2120 Exponential Mathematical Models Part 2
35 12:51 MATH 2120 Logistic Mathematical Models Part 1
36 13:32 MATH 2120 Logistic Mathematical Models Part 2
37 11:02 MATH 2120 Cooling Law Part 1
38 17:53 MATH 2120 Cooling Law Part 2
39 16:47 MATH 2120 Mixing Problems Part 1
40 18:48 MATH 2120 Mixing Problems Part 2
41 11:32 MATH 2120 Elementary Mechanics Part 1
42 19:36 MATH 2120 Elementary Mechanics Part 2
43 14:18 MATH 2120 Elementary Mechanics Part 3
44 21:05 MATH 2120 Second Order Linear ODEs
45 11:06 MATH 2120 Linear Combinations Part 1
46 11:19 MATH 2120 Linear Combinations Part 2
47 13:46 MATH 2120 Hyperbolic Functions and 2nd Order ODE
48 10:40 MATH 2120 Determinants
49 15:13 MATH 2120 Wronskian and Second Order ODEs
50 20:05 MATH 2120 Constant Coefficient Second Order Linear ODEs Part 1
51 8:38 MATH 2120 Constant Coefficient Second Order Linear ODEs Part 2
52 8:51 MATH 2120 Constant Coefficient Second Order Linear ODEs Part 3
53 6:31 MATH 2120 Constant Coefficient Second Order Linear ODEs Part 4
54 21:46 MATH 2120 Higher Order Linear ODEs Part 1
55 11:03 MATH 2120 Higher Order Linear ODEs Part 2
56 6:09 MATH 2120 Higher Order Linear ODEs Part 3
57 14:38 MATH 2120 Mechanical Vibrations Part 1
58 14:24 MATH 2120 Mechanical Vibrations Part 2
59 13:47 MATH 2120 Mechanical Vibrations Part 3
60 7:05 MATH 2120 Nonhomogeneous Equations Part 1
61 9:17 MATH 2120 Nonhomogeneous Equations Part 2
62 13:46 MATH 2120 Nonhomogeneous Equations Part 3
63 16:11 MATH 2120 Nonhomogeneous Equations Part 4
64 19:25 MATH 2120 Nonhomogeneous Equations Part 5
65 5:44 MATH 2120 Nonhomogeneous Equations Part 6
66 14:17 MATH 2120 Nonhomogeneous Equations Part 7
67 13:30 MATH 2120 Variation of Parameters Part 1
68 14:23 MATH 2120 Variation of Parameters Part 2
69 13:32 MATH 2120 Example of Undetermined Coefficients Part 1
70 17:26 MATH 2120 Example of Undetermined Coefficients Part 2
71 10:56 MATH 2120 Review of Terminology for Spring-Mass System
72 15:43 MATH 2120 Free Undamped Motion Review
73 14:16 MATH 2120 Free Damped Motion Review
74 33:53 MATH 2120 Undamped Forced Motion
75 15:01 MATH 2120 Damped Forced Motion
76 4:40 MATH 2120 Forced Oscillations Exercise
77 43:54 MATH 2120 RLC Circuit Part 1
78 42:11 MATH 2120 RLC Circuit Part 2
79 8:19 MATH 2120 Laplace Transform Part 1
80 10:15 MATH 2120 Laplace Transform Part 2
81 12:26 MATH 2120 Laplace Transform Part 3
82 21:09 MATH 2120 Laplace Transform Part 4
83 7:33 MATH 2120 Laplace Transform Part 5
84 19:16 MATH 2120 Laplace Transform Part 6
85 12:20 MATH 2120 Laplace Transform Part 7
86 3:05 MATH 2120 SageMath CoCalc Sign Up
87 11:05 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 1
88 14:20 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 2
89 34:12 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 3
90 5:34 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 4
91 29:59 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 5
92 12:31 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 6
93 24:11 MATH 2120 Laplace Transforms of Derivatives and ODEs Part 7
94 7:22 MATH 2120 Matrix-Matrix Multiplication
95 12:53 MATH 2120 Example of Matrix Inverse Calculation
96 11:55 MATH 2120 Linear Independence of Column Vectors
97 5:01 MATH 2120 Example of Eigenvalue Computation
98 12:58 MATH 2120 Eigenvalues of a Triangular Matrix
99 11:01 MATH 2120 Verification of Eigenvectors and Eigenvalues Part 1
100 18:52 MATH 2120 Verification of Eigenvectors and Eigenvalues Part 2
101 12:25 MATH 2120 Linear Systems of ODEs
102 27:14 MATH 2120 Eigenvalue Method Part 1
103 24:14 MATH 2120 Eigenvalue Method Part 2
104 MATH 2120 Eigenvalue Method Part 3
105 45:17 MATH 2120 Eigenvalue Method Part 4
106 20:48 MATH 2120 Homogeneous Linear System of ODEs
107 14:48 MATH 2120 Two Dimensional Systems Part 1
108 14:26 MATH 2120 Two Dimensional Systems Part 2
109 21:42 MATH 2120 Two Dimensional Systems Part 3
110 10:28 MATH 2120 Two Dimensional Systems Part 4
111 13:32 MATH 2120 Two Dimensional Systems Part 5
112 32:03 MATH 2120 Eigenvalues and Linear Systems of ODEs
113 9:23 MATH 2120 Higher Order ODEs and First Order Systems
114 18:33 MATH 2120 Undamped Mass-Spring Systems
115 18:59 MATH 2120 Free Damped Motion & First Order Systems
116 11:40 MATH 2120 Mixing in Two Compartments Part 1
117 9:41 MATH 2120 Mixing in Two Compartments Part 2

Differential Equations (Fall 2017) by James Cook at Liberty University

source: James Cook       2017年8月29日

1 59:51 first order ODEs and select apps, 8-29-17 part 1
2 13:46 first order ODEs and select apps, 8-29-17 part 2
3 59:51 substitutions, existence, pplane: 8-31-17, part 1
4 15:15 substitutions, existence, pplane: 8-31-17, part 2
5 54:51 geometry and applications of 1st order ODEs, 9-5-17
6 59:29 applications, complex numbers and calculus, 9-7-17
7 59:51 machines to rule our lives, 9-12-17, part 1
8 15:19 machines dehumanize, 9-12-17, part 2
9 59:51 nth order solutions and Wronskian, 9-14-17, part 1
10 14:59 nth order solutions and Wronskian, 9-14-17, part 2
11 59:51 annihilator method, variation parameters, 9-21-17, part 1
12 14:44 annihilator method, variation parameters, 9-21-17, part 2
13 46:42 resonance and damping discussion, 9-26-17
14 59:51 superposition, complexification, Cauchy Euler, 9-28-17
15 59:05 end of nth order, start of systems, 10-3-17
16 59:51 systems and a bit of matrix methods, 10-12-17 part 1
17 14:26 systems and a bit of matrix methods, 10-12-17 part 2
18 59:51 eigenvector solution method, 10-17-17, part 1
19 14:25 eigenvector solution method, 10-17-17, part 2
20 59:51 complex eigenvectors, matrix exponential, 10-19-17, part 1
21 13:44 complex eigenvectors, matrix exponential, 10-19-17, part 2
22 59:51 matrix exponential solutions, nonhomog. case, 10-24-17, part 1
23 14:57 matrix exponential solutions, nonhomog. case, 10-24-17, part 2
24 59:51 nonhomog. example, energy analysis, 10-26-17 part 1
25 13:17 nonhomog. example, energy analysis, 10-26-17 part 2
26 59:51 Laplace Transformations, 10-31-17, part 1
27 10:29 Laplace Transformations, 10-31-17, part 2
28 59:51 inverse Laplace transforms, discontinuous case 11-2-17, part 1
29 10:42 inverse Laplace transforms, discontinuous case 11-2-17, part 2
30 59:51 Gamma, Dirac, Green's Function, 11-7-17, part 1
31 12:24 Gamma, Dirac, Green's Function, 11-7-17, part 2
32 59:51 series technique ordinary points, 11-9-17, part 1
33 14:49 series technique ordinary points, 11-9-17, part 2
34 59:51 singular points, Frobenius method, 11-14-17, part 1
35 14:24 singular points, Frobenius method, 11-14-17, part 2
36 56:01 homogeneous BVPs, heat equation, 11-16-17
37 59:51 wave equation for string, fixed endpoints, 11-28-17
38 59:51 wave eqn nice solution, Laplace Equation, 11-30-17, part 1
39 13:31 wave eqn nice solution, Laplace Equation, 11-30-17, part 2
40 32:30 post mortem of Test 2, comment for final exam, 12-12-17

Introduction to Differential Equations (Fall 2016) by James Cook at Liberty University

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source: James Cook      2016年8月30日

L1, terminology, first order ODEs, 8-30-2016, part 1 59:51
L1, terminology, first order ODEs, 8-30-2016, part 2 15:04
L2, substitutions and existence, 9-1-2016, part 1 59:51
L2, substitutions and existence, 9-1-2016, part 2 19:16
L3, applications of first order ODEs, orthogonal trajectories, 9-6-16, part 1 59:51
L3, applications of first order ODEs, orthogonal trajectories, 9-6-16, part 2 17:33
L4, applications, intro to complex arithmetic, 9-8-16, part 1 59:51
L4, applications, intro to complex arithmetic, 9-8-16, part 2 16:06
L5, the n-th order homogeneous problem, part 1, 9-13-16 59:51
L5, the n-th order homogeneous problem, part 2, 9-13-16 11:32
L6, linear independence and the wronskian, part 1, 9-15-16 59:51
L6, linear independence and the wronskian, part 2, 9-15-16 15:07
L7, undetermined coefficients with annihilators and naive method, part 1, 9-20-16 59:51
L7, undetermined coefficients with annihilators and naive method, part 2, 9-20-16 14:27
L8, variation of parameters, part 1, 9-22-16 59:51
L8, variation of parameters, part 2, 9-22-16 13:18
L9, Cauchy Euler, the second LI solution formula, resonance begins, 9-27-16, part 1 59:51
L9, Cauchy Euler, the second LI solution formula, resonance begins, 9-27-16, part 2 17:37
L10, resonance and applications of 2nd order, energy methods, part 1, 9-29-16 59:51
L10, resonance and applications of 2nd order, energy methods, part 2, 9-29-16 15:32
L11, solution to Test 1 of 2013 and politics, 10-4-16 34:42
L12, series techniques to solve DEqns, 10-13-16, part 1 59:51
L12, series techniques to solve DEqns, 10-13-16, part 2 17:18
L13, regular singular points, ordinary points, domain of solution, 10-18-16, part 1 59:51
L13, regular singular points, ordinary points, domain of solution, 10-18-16, part 2 9:09
L14, frobenious unfurled, 10-20-16, part 1 59:51
L14, frobenious unfurled, 10-20-16, part 2 14:36
L15, crash course in matrix algebra, intro to systems, 10-25-16, part 1 59:51
L15, crash course in matrix algebra, intro to systems, 10-25-16, part 2 16:55
L16, systems of ODEs, 10-27-16, part 1 59:51
L16, systems of ODEs, 10-27-16, part 2 16:10
L17, eigenvector solutions, 11-1-16, part 1 59:51
L17, eigenvector solutions, 11-1-16, part 2 15:53
L18, matrix exponential, 11-3-16, part 1 59:51
L18, matrix exponential, 11-3-16, part 2 15:50
L20, systems by elimination, phase plane, 11-10-16, part 1 59:51
L20, systems by elimination, phase plane, 11-10-16, part 2 8:28
L21, Laplace Transforms the basic theorems, 11-15-16, part 1 59:51
L21, Laplace Transforms the basic theorems, 11-15-16, part 2 9:35
L22, treating discontinuities with Laplace, 11-17-16, part 1 59:51
L22, treating discontinuities with Laplace, 11-17-16, part 2 11:02
L23, Dirac Delta, 11-29-16, part 1 59:51
L23, Dirac Delta, 11-29-16, part 2 10:40
L24, PDEs, heat, wave and Laplace equation an introduction, 12-1-16, part 1 59:51
L24, comments about Test 3, 12-1-16, part 2 21:00

Differential Equations (Summer 2017) by James Cook at Liberty University

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source: James Cook      2017年6月12日
This is the playlist for Math 334 of Summer 2017 at Liberty University. I'm using Nagle, Saff and Snider's "Fundamentals of Differential Equations and Boundary Value Problems" 4th edition and my notes. The course website is: http://www.supermath.info/DEqns.html where I have many resources posted. Naturally, I'll use Blackboard, wait, I should say unnaturally but out of habit to be more honest, to post the actual syllabus etc. I hope to have the Lectures posted the same day if all goes as planned.

introduction, terminology, 6-12-17, part 1 39:21
how to solve first order ODEs, 6-12-17, part 2 59:51
first order solutions and theory, 6-12-17, part 3 31:06
substitutions, reduction order, 6-13-17, part 1 47:52
applications, orthogonal trajectories, 6-13-17, part 2 59:51
vdvdx trick for constant gravity, 6-13-17, part 3 1:09
applications, 6-13-17, part 4 20:33
nth order problem, survey of theory, 6-14-17, part 1 57:17
calculus of operators, 6-14-17, part 2 57:55
nth order problem complex case, 6-14-17, part 3 20:54
undetermined coefficients, 6-15-17, part 1 55:43
annihilator method, superposition, 6-15-17, part 2 59:51
variation of parameters and such, 6-15-17, part 3 17:44
linear eqns and matrices, 6-19-17, part 1 54:13
linear eqns and matrices, 6-19-17, part 2 15:27
eigenvector solutions to systems, 6-20-17, part 1 56:50
eigenvector solutions to systems, 6-20-17, part 2 59:51
matrix exponential, 6-20-17, part 3 20:41
matrix exponential and magic formula, 6-21-17, part 1 59:13
more matrix exp, nonhomog. case, 6-21-17, part 2 59:51
stability, type of critical points intro, 6-21-17, part 3 12:15
energy analysis, 6-22-17, part 1 59:47
energy analysis, 6-22-17, part 2 22:18
Laplace Transforms, 6-22-17, part 3 50:50
inverse Laplace Transforms, 6-26-17, part 1 59:51
inverse Laplace Transforms, 6-26-17, part 2 0:23
trigonmetry, discontinuous terms, 6-26-17, part 3 59:51
trigonmetry, discontinuous terms, 6-26-17, part 4 12:07
Dirac Delta and examples, 6-27-17, part 1 59:51
Dirac Delta and examples, 6-27-17, part 2 3:02
convolution, transfer fnct, power series begins, 6-27-17, part 3 56:37
power series solutions, 6-28-17, part 1 48:43
power series solutions, 6-28-17, part 2 59:51
nearest singularity theorem, 6-28-17, part 3 3:23
Frobenius method, 6-29-17, part 2 59:51
Frobenius method, 6-29-17, part 3 15:45
review for Test 2, 7-3-17, part 1 53:54
review for Test 2, 7-3-17, part 2 5:16
Fourier Series intro, BVPs, 7-3-17, part 3 59:51
heat equation, 7-3-17, part 4 5:21
heat equation, 7-5-17, part 1 59:51
heat and wave equation, 7-5-17, part 2 5:35
wave equation, 7-6-17, part 1 41:10
Test 2 post mortem, Laplace Equation, 7-6-17, part 2 55:38

Differential Equations with Linear Algebra by James Cook

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source: James Cook      2015年5月6日
Differential Equations with Linear Algebra
This series of talks is a very fast overview of introductory differential equations as I usually teach it. The audience intended is students with some experience with linear algebra, preferably a course which discusses linear transformations as well as the complexification. If you thirst for applications, look elsewhere.

Differential Equations Condensed Part 1 1:33:42 Here I briefly given an overview of the main goals and terms of our study. Applications to physics are mentioned, but, little detail is given. The focus of these lectures will be on techniques for solution. If you desire discussion of application or careful proofs of existence you'll need to look up a different source. My intention here is to quickly outline the major techniques to solving or analyzing ODEs. In this part, we study the three major solution techniques followed by a brief mention of techniques of substitution. Please understand, these lectures are in part an invitation to study my notes and do homework. Only those activities will produce lasting understanding. Of course, you can read any text you like, but these lectures are based on my writings.
Differential Equations Condensed Part 1b 7:10
Differential Equations Condensed Part 2 1:25:27
Differential Equations Condensed: Part 3a 33:27
Differential Equations Condensed: Part 3b 2:51
Differential Equations Condensed: Part 4a 33:26
DEqnsP4b 33:26
DEqnsP4c 9:50
Differential Equations Condensed: Part 5a 33:27
Differential Equations Condensed: Part 5b 30:40
Differential Equations Condensed: Part 6a 33:26
Differential Equations Condensed: Part 6b 9:37
Differential Equations Condensed: Part 7a 59:51
Differential Equations Condensed: Part 7b 20:04
Differential Equations Condensed: Part 8 38:38
Differential Equations Condensed: Part 9a 59:51
Differential Equations Condensed: Part 9b 15:19

Differential Equations (Spring 2017) by James Cook at Liberty University

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source: James Cook     2017年1月18日
These are my Lectures from Math 334 of Spring 2017. We roughly base the course on Nagle Saff and Snider's excellent text. However, I have found various efficient paths which more or less ignore the text in certain arcs of the course, so, it's probably more honest to say I don't follow the book. Math is math, I don't disagree with the text. My emphasis just varies. Naturally, my Lecture Notes (free) are closer to what I present this semester. I recommend consulting my Lecture Notes as the primary reference, then perhaps the 4th edition of Nagle Saff and Snider is best (later editions seem to be missing important chapters).
Of course, much more about the structure of the course is found in the Course Planner which all students of this course should consult. You may find the Fall 2016 Differential Equations playlist useful. My teaching here is fairly close, but, I hope to cover a topic or two in better detail here. For example, PDEs are part of the required material this semester (as has classically been the case in Math 334 at Liberty)

introduction, first order ODEs, separable, linear, exact: 1-17-17, part 1 59:51
introduction, first order ODEs, separable, linear, exact: 1-17-17, part 2 16:23
exact condition and simply connectedness, substitutions: 1-19-17, part 1 59:51
exact condition and simply connectedness, substitutions: 1-19-17, part 2 15:32
applications to geometry, physics, etc... 1-24-17, part 1 59:51
applications to geometry, physics, etc... 1-24-17, part 2 16:22
isocline plots, primer in complex math, 1-26-17, part 1 59:51
isocline plots, primer in complex math, 1-26-17, part 2 14:57
nth order, constant coefficient, soln by operators, 1-31-17, part 1 59:51
nth order, constant coefficient, soln by operators, 1-31-17, part 2 14:56
LI and existence theorems, annihilators begin, 2-2-17, part 1 59:51
LI and existence theorems, annihilators begin, 2-2-17, part 2 14:31
annhilator guided undetermined coefficients, 2-7-17, part 1 59:51
annhilator guided undetermined coefficients, 2-7-17, part 2 13:43
applications to springs and RLC, 2-14-17, part 1 59:51
applications to springs and RLC, 2-14-17, part 2 16:54
review for Test 1, 2-16-17, part 1 59:51
review for Test 1, 2-16-17, part 2 13:30
systems of DEqns, intro to eigen-technique, 2-23-17, part 1 59:51
systems of DEqns, intro to eigen-technique, 2-23-17, part 2 12:37
some theory of e-vectors, applications, e-solutions, 2-28-17, part 1 59:51
some theory of e-vectors, applications, e-solutions, 2-28-17, part 2 16:09
e-vecs, and generalized e-vecs and matrix exponential, 3-2-17, part 1 59:51
e-vecs, and generalized e-vecs and matrix exponential, 3-2-17, part 2 15:55
Differential Equations: matrix exponential solutions, variation of parameters, 3-7-17, part 1 59:51
matrix exponential solutions, variation of parameters, 3-7-17, part 2 3:09
most amazing lecture ever, 3-21-17 14:16
convolution, transfer function, 3-23-17, part 1 59:51
convolution, transfer function, 3-23-17, part 2 8:41
laplace transform examples, 3-28-17, part 1 59:51
phase plane for autonomous ODEs, 3-28-17, part 2 15:32
qualitative analysis via phase plane, 4-6-17, part 1 59:51
qualitative analysis via phase plane, 4-6-17, part 2 16:17
series solutions, singularity domain theorem, 4-11-17 55:01
Cauchy Euler Problem, Frobenius method, 4-13-17, part 1 59:51
Cauchy Euler Problem, Frobenius method, 4-13-17, part 2 11:55
PDEs, heat equation, 4-18-17, part 1 59:51
PDEs, heat equation, 4-18-17, part 2 12:38
wave equation, 4-20-17 57:15
wave by Laplace, and Laplace Equation, 4-25-17, part 1 59:51
wave by Laplace, and Laplace Equation, 4-25-17, part 2 6:55
discussion of test 3, pizza party, 5-2-17, part 1 36:43

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

Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 at MIT

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source: MIT OpenCourseWare     2016年5月6日/上次更新：2016年5月23日
MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: http://ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang, Cleve Moler
Gilbert Strang and Cleve Moler provide an overview to their in-depth video series about differential equations and the MATLAB® ODE suite.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Introduction to Differential Equations and the MATLAB® ODE Suite 2:53
Overview of Differential Equations 14:04
The Calculus You Need 14:47
Response to Exponential Input 13:20
Response to Oscillating Input 15:55
Solution for Any Input  13:59
Step Function and Delta Function 15:41
Response to Complex Exponential 12:51
Integrating Factor for Constant Rate 13:47
Integrating Factor for a Varying Rate 11:23
The Logistic Equation 13:27
The Stability and Instability of Steady States 21:15
Separable Equations 13:07
Second Order Equations 19:20
Forced Harmonic Motion 15:32
Unforced Damped Motion 14:04
Impulse Response and Step Response 16:02
Exponential Response — Possible Resonance 12:20
Second Order Equations with Damping 13:14
Electrical Networks: Voltages and Currents 16:33
Method of Undetermined Coefficients 16:32
An Example of Undetermined Coefficients 15:49
Variation of Parameters 19:22
Laplace Transform: First Order Equation 22:38
Laplace Transform: Second Order Equation 16:31
Laplace Transforms and Convolution 10:29
Pictures of Solutions 21:01
Phase Plane Pictures: Source, Sink, Saddle 18:26
Phase Plane Pictures: Spirals and Centers 13:46
Two First Order Equations: Stability 10:32
Linearization at Critical Points 15:08
Linearization of Two Nonlinear Equations 21:41
Eigenvalues and Stability: 2 by 2 Matrix, A 19:30
The Tumbling Box in 3-D 22:54
The Column Space of a Matrix 12:44
Independence, Basis, and Dimension 13:20
The Big Picture of Linear Algebra 15:57
Graphs 15:27
Incidence Matrices of Graphs 19:51
Eigenvalues and Eigenvectors 19:01
Diagonalizing a Matrix 11:37
Powers of Matrices and Markov Matrices 17:54
Solving Linear Systems 15:48
The Matrix Exponential 15:32
Similar Matrices 14:51
Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors 15:55
Second Order Systems 16:50
Positive Definite Matrices 21:41
Singular Value Decomposition (the SVD) 14:11
Boundary Conditions Replace Initial Conditions 17:03
Laplace Equation 13:17
Fourier Series 16:36
Examples of Fourier Series 13:56
Fourier Series Solution of Laplace's Equation 14:04
Heat Equation 10:48
Wave Equation 15:14
Euler, ODE1 15:22
Midpoint Method, ODE2 6:46
Classical Runge-Kutta, ODE4 9:38
Order, Naming Conventions 5:26
Estimating Error, ODE23 10:37
ODE45 6:47
Stiffness, ODE23s, ODE15s 7:15
Systems of Equations 14:17
The MATLAB ODE Suite 5:35
Tumbling Box 9:52
Predator-Prey Equations 14:17
Lorenz Attractor and Chaos 10:25