## 2017-08-30

### 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