2018-03-13
Introduction to A-Calculus (Spring 2018) by James Cook at Liberty University
source: James Cook 2018年1月23日
1 16:55 real associative algebra and representation theory, 1-23-18, part 2
2 59:51 examples of algebras, playing with isomorphism, 1-24-18, part 1
3 21:21 examples of algebras, playing with isomorphism, 1-24-18, part 2
4 59:51 basic theory of differentiation over A, A-CR equations, 1-29-18, part 1
5 26:29 basic theory of differentiation over A, A-CR equations, 1-29-18, part 2
6 59:51 working on conformal mapping idea, 1-31-18, part 1
7 8:38 working on conformal mapping idea, 1-31-18, part 2
8 59:51 fun with the wave equation, 2-5-18, part 1
9 15:54 fun with the wave equation, 2-5-18, part 2
10 59:51 math of Khang, introduction to A-integration, 2-12-18, part 1
11 24:36 math of Khang, introduction to A-integration, 2-12-18, part 2
12 59:51 playing with differential forms, 2-14-18, part 1
13 28:59 sequences, series, power series summary of results, 2-14-18, part 1
14 41:11 connection to study of vector fields, 2-19-18, part 1
15 17:37 differential equations over an algebra, 2-19-18, part 2
16 59:51 weirdness of differential equations over algebras, 2-21-18, part 1
17 13:52 weirdness of differential equations over algebras, 2-21-18, part 2
18 57:32 proof on existence and uniqueness of A-ODEs, 2-26-18, part 1
19 21:50 proof on existence and uniqueness of A-ODEs, 2-26-18, part 2
20 59:51 helping Cooper with inverse image, looking at A-ODE paper, 2-28-18, part 1
21 12:10 how to solve constant coefficient A-ODE by extension, 2-28-18, part 2
22 59:51 solving A-ODEs with the exponential on the extension, 3-5-18, part 1
23 17:26 solving A-ODEs with the exponential on the extension, 3-5-18, part 2
Advanced Calculus (Fall 2017) by James Cook at Liberty University
source: James Cook 2017年8月29日
1 59:51 Advanced Calculus: linear algebra, norms, limits: 8-28-17, part 1
2 30:08 linear algebra, norms, limits: 8-28-17, part 2
3 59:51 limits, differentiation: 9-1-17, part 1
4 30:16 limits, differentiation: 9-1-17, part 2
5 20:12 differentiation from defn: 9-4-17, part 1
6 11:55 linearity and chain rule: 9-4-17, part 2
7 9:31 partial derivatives, Jacobian matrix: 9-1-17, part 3
8 21:58 continuously diff. implies diff theorem: 9-4-17, part 4
9 14:33 product rule: 9-4-17, part 5
10 59:51 calculus on an algebra: 9-9-17, part 1
11 28:05 calculus on an algebra: 9-9-17, part 2
12 59:51 theft for NLS, inverse mapping theorem, 9-11-17
13 26:50 implicit mapping theorem not explained well, 9-11-17
14 59:51 implicit diff, manifolds, tangents, normals, 9-15-17, part 1
15 31:24 implicit diff, manifolds, tangents, normals, 9-15-17, part 2
16 11:58 orthogonal complements, 9-18-17, part 1
17 18:25 tangents to curves on manifold form vec. space, 9-18-17, part 2
18 21:59 Lagrange Multipliers, 9-18-17, part 3
19 8:28 quadratic forms, 9-18-17, part 4
20 11:47 multivariate critical pt. analysis, 9-18-17, part 5
21 59:51 variational calculus, 9-22-17, part 1
22 26:40 variational calculus, 9-22-17, part 2
23 59:51 central forces, differential geometry begins, 9-25-17, part 1
24 22:43 tangent space ideas unfinished!, 9-25-17, part 2
25 59:51 abstract manifolds, differentiation, 9-29-17, part 1
26 28:44 abstract manifolds, differentiation, 9-29-17, part 2
27 59:51 differentiation on the manifold examples, 10-2-17, part 1
28 24:12 differentiation and push-forward examples, 10-2-17, part 2
29 59:51 vector fields and flows, 10-9-17 part 1
30 24:04 vector fields and flows, 10-9-17 part 2
31 59:51 dual space, tensors, exterior calc in R3, 10-13-17 part 1
32 27:45 dual space, tensors, exterior calc in R3, 10-13-17 part 2
33 59:51 wedges from determinants, ext derivative, 10-20-17, part 1
34 30:54 wedges from determinants, ext derivative, 10-20-17, part 2
35 59:51 fun with pull backs, substitution to Poincare Lemma, 10-23-17, part 1
36 29:31 fun with pull backs, substitution to Poincare Lemma, 10-23-17, part 2
37 59:51 form integration, start of E and M in diff forms, 10-27-17 part 1
38 28:43 form integration, start of E and M in diff forms, 10-27-17 part 2
39 59:51 potential forms, interior products 10-30-17, part 1
40 26:44 potential forms, interior products 10-30-17, part 2
41 59:51 Lie Derivatives and flow loops, 11-3-17, part 1
42 31:49 Lie Derivatives and flow loops, 11-3-17, part 2
43 59:51 gradient on Riemannian manifold, metric construction, 11-6-17, part 1
44 30:29 gradient on Riemannian manifold, metric construction, 11-6-17, part 2
45 59:51 connection coefficients, calculations, 11-10-17, part 1
46 22:47 derivative along a curve in Riemannian space, 11-10-17, part 2
47 59:51 parallel transport idea, curvature sketch, 11-13-17, part 1
48 16:04 parallel transport idea, curvature sketch, 11-13-17, part 2
49 59:51 isometries and fun, 11-17-17, part 1
50 25:53 isometries and fun, 11-17-17, part 2
51 59:51 contact forms and distributions in R3, 11-27-17, part 1
52 19:51 contact forms and distributions in R3, 11-27-17, part 2
53 59:51 review session for Test 2, 12-1-17, part 1
54 12:17 review session for Test 2, 12-1-17, part 2
55 59:51 contact geometry, Reeb field etc. 12-8-17, part 1
56 24:44 contact geometry, Reeb field etc. 12-8-17, part 2
57 18:15 on Frenet frame for curves, 12-11-17 part 1
58 33:56 overview of Gauss Bonnet Theorem, 12-11-17 part 2
Abstract Algebra (Fall 2017) by James Cook at Liberty University
source: James Cook 2017年8月29日
These Lectures are from the Fall 2017 offering of Math 421 at Liberty University in Lynchburg Virginia, USA. I intend to follow Nicholson's "Introduction to Abstract Algebra" fourth edition. Students who take this course have experience with proofs and have already studied some abstraction in linear algebra, consequently this course is a bit more aggressive than some algebra courses where abstract algebra appears as a lower-level course. In brief, we cover monoids, groups, subgroups, cyclic groups, permutations, homomorphism, cosets, normal subgroups, factor groups, direct products, isomorphisms, lattice of subgroups, Sylow theorems, group actions, orbit stabilizer theorem, rings, integral domains, fields, polynomials, ideals, prime ideals, maximal ideals, PIDs, euclidean domains, UFDs, factorization. Essentially Chapters 0,1,2,3,4,5 and 8 of Nicholoson.
1 42:40 course intro, sets, maps, equivalence relations: 8-28-17
2 56:36 extra help with sets, maps and equivalence: 8-29-17
3 53:17 Integers and modular arithmetic: 8-30-17 (race day)
4 59:51 extra help with maps and modular arithmetic: 8-30-17
5 53:45 modular arithmetic, permutations, 9-1-17
6 55:43 monoids, associativity and inverse properties, 9-4-17 (party day)
7 54:59 extra help with permutations and map problem, 9-5-17
8 54:35 extra help with cayley tables, permutations: 9-7-17
9 51:29 groups, generators and relations, direct product, 9-8-17
10 53:46 subgroups, lattice diagrams, cyclic part 1, 9-11-17
11 58:44 couple subgroup examples, help with cyclics : 9-12-17
12 52:06 cyclic groups, 9-13-17
13 48:12 proofs about cyclic groups, hwk comments, 9-14-17
14 47:09 cyclic group end, isomorphism begin : 9-15-17
15 51:49 isomorphism theorems, automorphisms 9-20-17
16 56:10 help session, illustrating Cayley, forgot proofs, 9-21-17
17 50:48 preparing for Test 1, 9-2-17
18 50:39 cosets and Lagrange's Theorem, 9-27-17
19 42:48 post-mortem for Test 1, 9-28-17
20 50:06 applications of Lagrange's Theorem, 9-29-17
21 51:04 normal subgroups, 10-2-17
22 52:17 normal subgroup proofs, normal subgroups Dn, 10-3-27
23 51:22 the factor group construction (aka quotient group), 10-4-17
24 51:37 1st Isomorphism Theorem, 10-9-17
25 51:49 help session on order of elements in factor groups 10-10-17
26 52:01 isomorphism theorems, product theorems, 10-11-17
27 37:13 help session, silent movie time oh noes, 10-12-17
28 51:14 Cauchy's Theorem and Class Equation, 10-13-17
29 50:32 group actions part 1, 10-16-17
30 50:55 symmetry vs. motion, problem on normalizers, 10-17-17
31 49:48 Sylow Theorems, 10-18-17
32 46:34 help session, isomorphism, comment on core, 10-19-17
33 49:20 groups of units and RSA badly explained, 10-20-17
34 51:14 rings defined and basic examples, properties, 10-23-17
35 51:06 help session, fixer and Sylow examples, 10-24-17
36 49:57 subrings and algebra isomorphisms, 10-25-17
37 52:42 help session, solution to Missions discuss, 10-26-17
38 52:01 ring theorems, field of quotients, 10-27-17
39 35:41 review for Test 2, 10-30-17
40 39:45 help session, 10-31-17
41 43:11 help session, group mystery project, ring endomorphisms 11-2-17
42 50:50 factor rings, 11-3-17
43 53:16 prime and maximal ideals, simple rings, 11-6-17
44 50:14 ideal of matrix ring, 11-8-17
45 48:03 almost helpful session, 11-9-17
46 52:26 ring homomorphisms, 11-10-17
47 50:47 decomposing rings, polynomial foundations, 11-13-17
48 54:17 help session, post mortem of Test 2, 11-14-17
49 18:51 comments on Nicholson 4.1 (polynomials) , 11-15-17
50 51:46 irreducibility up to Eisenstein, 11-15-17
51 52:06 help session, polynomials and irreducibility, 11-16-17
52 52:53 associates, irreducibles, primes 11-17-17
53 52:14 irreducible polynomial generates maximal ideal, 11-27-17
54 35:48 help session rings, factor rings, select hwks, 11-28-17
55 51:13 ED implies PID implies UFD, some number theory, 11-29-17
56 53:27 help session, rings, big classification picture, 11-30-17
57 50:29 quaternions and 4 square identity, Kronecker Thm, 12-1-17
58 47:33 review for Test 3, 12-4-17
59 59:51 questions for Test 3, 12-5-17, part 1
60 2:31 questions for Test 3, 12-5-17, part 2
61 48:03 representations of groups, quarks, Test 3 p.m. 12-11-17
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
Calculus II (Fall 2017) by James Cook at Liberty University
source: James Cook 2017年8月30日
I intend to post my Calculus II lectures for the Fall 2017 Semester at Liberty University. I'll follow "Calculus Early Transcendental Functions", 6th edition by Larson and Edwards, but, if they miss something or say something I don't care for I'll probably go to my notes etc. This course covers integration techniques, sequences, series, power series, first order ODEs, polar coordinates and parametric curves in the plane. Past this we study multivariable calculus starting with vectors... before this we study differentiation and integration up to u-substitution. We also cover hyperbolic functions which are unfortunately missing from some calculus curriculum.
1 59:51 trig identities, intro to hyperbolic functions, 8-29-17, part 1
2 14:46 trig identities, intro to hyperbolic functions, 8-29-17, part 2
3 38:18 hyperbolic function fun, 8-30-17
4 59:51 hyperbolics end, IBP begins, 8-31-17, part 1
5 14:03 hyperbolics end, IBP begins, 8-31-17, part 2
6 52:41 IBP, integrals of trig functions, 9-1-17
7 59:51 random problems, trig and hyperbolic subst. 9-5-17, part 1
8 15:05 random problems, trig and hyperbolic subst. 9-5-17, part 2
9 59:51 homework help, partial fractions, 9-7-17 part 1
10 17:57 homework help, partial fractions, 9-7-17 part 2
11 48:10 partial fractions with Isaac, 9-8-17
12 48:44 partial fractions again, 9-11-17
13 59:51 integration examples, 9-12-17, part 1
14 12:27 integration examples, 9-12-17, part 2
15 51:10 integration examples, 9-13-17
16 48:58 review for Test 1, 9-20-17
17 50:01 L'Hop Rule, 9-22-17
18 47:03 L'Hop, improper integrals with infinite bounds, 9-25-17
19 59:51 improper integrals, sequences, 9-26-17 part 1
20 14:53 improper integrals, sequences, 9-26-17 part 2
21 49:20 sequence theorems, series defined, 9-27-17
22 15:41 Differential Equations: p-series, comparison, integral, nth-term test, 9-28-17, part 2
23 59:51 p-series, comparison, integral, nth-term test, 9-28-17, part 1
24 45:47 estimation with integral test, geom. series examples, 9-29-17
25 46:21 Limit Comparison Test, Alternating Series Intro, 10-2-17
26 59:51 absolute convergence, root and ratio test, some proofs, 10-3-17, part 1
27 11:09 absolute convergence, root and ratio test, some proofs, 10-3-17, part 2
28 52:28 convergent implies bounded, examples, 10-9-17
29 59:51 analyzing geometric series, convergence etc. 10-10-17 part 1
30 15:32 analyzing geometric series, convergence etc. 10-10-17 part 2
31 50:23 converge or diverge that is the question, 10-11-17
32 47:02 review for Test 2, 10-16-17
33 45:47 power series and the IOC and ROC basic terms, 10-18-17
34 59:51 deriving Taylor series directly and indirectly, 10-19-17, part 1
35 11:19 deriving Taylor series directly and indirectly, 10-19-17, part 2
36 50:01 more fun with power series, 10-20-17
37 47:20 discussion of Taylor's Theorem remainder, multiplying series, 10-23-17
38 59:51 binomial series, application to limits, 10-24-17, part 1
39 10:56 binomial series, application to limits, 10-24-17, part 2
40 46:37 power series calculations, 10-25-17
41 58:07 help with power series homeworks and examples, 10-26-17, part 1
42 15:54 power series calculation, 10-26-17, part 2
43 34:01 examples of power series, 10-27-17
44 49:11 power series geometric and otherwise, 10-30-17
45 59:51 power series calculation, 10-31-17, part 1
46 16:03 power series calculation, 10-31-17, part 2
47 47:23 power series help, 11-1-17
48 49:29 review for Test 3, 11-8-17
49 48:18 conic sections and select parametrizations, 11-10-17
50 52:28 parametric curve aka path plotting ideas, 11-13-17
51 59:51 paths and calculus, tangent lines, 11-14-17, part 1
52 12:42 paths and calculus, tangent lines, 11-14-17, part 2
53 46:53 parametric calculus, arclength and fun stuff, 11-15-17
54 59:51 polar coordinates and graphing, 11-16-17, part 1
55 12:44 polar coordinates and graphing, 11-16-17, part 2
56 48:12 area in polar coordinates, 11-17-17
57 42:14 parametrics and polar problems, 11-27-17
58 59:51 higher derivative parametric calculus, polar area, 11-28-17 part 1
59 6:39 higher derivative parametric calculus, polar area, 11-28-17 part 2
60 50:46 polar coordinate graphing, areas, curves, hwk help, 11-29-17
61 32:47 discussion of Quiz 4, preparing for Test 4, 12-4-17
62 20:07 differential equations begins, 12-6-17
63 59:51 DEqns, separation and integrating factor technique, 12-7-17, part 1
64 18:00 DEqns, separation and integrating factor technique, 12-7-17, part 2
65 47:18 differential equations and geometry, orthogonal trajectories, 12-8-17
66 59:51 solved problems in DEqns, 12-11-17
67 59:51 review for final exam, 12-12-17, part 1
68 13:12 review for final exam, 12-12-17, part 2
Subscribe to:
Posts (Atom)