Differential and Integral Calculus 2 by Aviv Censor at Technion

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source: Technion     2015年12月7日
Calculus 2 - international
Course no. 104004
Technion - International school of engineering

01 - Introduction 7:04
02 - Vectors 39:15
03 - The Cartesian coordinate system 29:44
04 - The dot product 21:00
05 - The dot product - continued 16:33
06 - The cross product 37:54
07 - The triple product 22:24
08 - The equation of a plane 20:31
09 - Planes - continued 24:54
10 - The equation of a line 18:36
11 - Lines - continued 22:36
12 - Lines - continued 13:49
13 - Lines and planes 12:38
14 - Surfaces 21:13
15 - Surfaces - continued 22:41
16 - Surfaces - continued 8:46
17 - Curves 25:24
18 - Topology 55:34
19 - Sequences 19:14
20 - Functions and graphs 17:52
21 - Level curves 21:03
22 - Level surfaces 11:30
23 - Limits 26:02
24 - Properties of limits 12:05
25 - Limits along curves 20:46
26 - Limits and polar coordinates 27:40
27 - Iterated limits 12:07
28 - Continuity 11:39
29 - The intermediate value theorem 40:26
30 - Tangents to curves 37:55
31 - Partial derivatives 19:21
32 - Calculating partial derivatives 21:39
33 - The tangent plane 18:26
34 - Differentiability 30:00
35 - Differentiability - continued 26:12
36 - Differentiability, continuity and partial derivatives 34:08
37 - Directional derivatives 40:42
38 - The gradient 27:53
39 - The chain rule 28:54
40 - Higher order derivatives 23:51
41 - The Taylor polynomial 27:08
42 - The implicit function theorem 35:49
43 - The implicit function theorem - continued 37:37
44 - Proof of the implicit function theorem 21:07
45 - The gradient is perpendicular to level surfaces 30:58
46 - The implicit function theorem for systems of equations 42:11
47 - The inverse function theorem 17:01
48 - Minima and maxima 39:07
49 - Classification of critical points 56:15
50 - Exterma subject to constraints 19:53
51 - The method of Lagrange multipliers 20:26
52 - A two variable example of Lagrange multipliers 32:54
53 - A three variable example of Lagrange multipliers 16:46
54 - Proof of the Lagrange multipliers theorem 12:40
55 - Lagrange multipliers for several constraints 29:32
56 - Double integrals 40:11
57 - Properties of double integrals 30:15
58 - Iterated integrals 13:56
59 - Simple domains 9:48
60 - Double integrals on simple domains 29:31
61 - Examples of iterated integrals 32:31
62 - Changing order of integration 34:28
63 - Change of variables 21:20
64 - Examples of changing variables 25:50
65 - Examples of changing variables - continued 28:32
66 - The requirement that J is not 0 16:17
67 - The geometric meaning of J 41:31
68 - A cool example 26:00
69 - Triple integrals 28:34
70 - Triple integrals over simple domains 20:05
71 - Cylindrical coordinates 34:09
72 - Spherical coordinates 23:17
73 - One more example of changing variables 19:10
74 - The length of a curve 41:29
75 - Line integrals of scalar functions 33:57
76 - Line integrals of vector fields 33:37
77 - Green's theorem 24:37
78 - Finding area with Green's theorem 16:29
79 - Evaluating line integrals with Green's theorem 37:20
80 - Conservative fields 24:36
81 - Simply connected domains 21:27
82 - Conservative fields in simply connected domains 21:04
83 - Conservative fields in simply connected domains - examples 22:12
84 - Surfaces 36:48
85 - Area of a surface 56:56
86 - Surface integrals of scalar functions 25:00
87 - Surface integrals of vector fields 29:01
88 - Surface integrals of vector fields - example 24:25
89 - The divergence 21:49
90 - The divergence theorem (Gauss) 36:48
91 - More on the divergence 30:04
92 - The curl 19:31
93 - Stokes' theorem 27:29
94 - Using Stokes' theorem 19:15
95 - Using Stokes' theorem - continued 54:48
96 - Conservative fields in 3 dimensions 17:12
97 - An example of a conservative field 22:54
98 - More on the curl 21:34
99 - A review problem 48:23
100 - A review problem - continued 1:00:54

Algebra (2015) by Aviv Censor at Technion

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source: Technion    2015年11月23日
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International school of engineering

01 - Introduction 9:13
02 - Sets of numbers 41:58
03 - Fields 32:01
04 - More properties of fields 18:53
05 - Complex numbers 47:34
06 - The Complex conjugate, the modulus and division 51:30
07 - Polar form 27:59
08 - Multiplication, division, powers and roots 39:26
09 - Polynomials 16:40
10 - Roots of polynomials 1:06:26
11 - Matrices 35:01
12 - Operations on matrices 21:49
13 - Matrix multiplication 21:48
14 - Properties of matrix multiplication 33:42
15 - Systems of linear equations 22:20
16 - Solving systems of linear equations 17:01
17 - The method of row-reduction 1:02:06
18 - Determining the number of solutions 47:38
19 - Homogeneous vs. non homogeneous systems 45:31
20 - The space R^n 29:12
21 - Vector spaces 46:18
22 - Vector subspaces 30:24
23 - More examples of subspaces 21:23
24 - Intersections and sums of subspaces 27:05
25 - Direct sums of subspaces 29:22
26 - Linear combinations and spans 35:20
27 - Determining if v belongs to a span 18:54
28 - Linear independence 20:14
29 - Determining linear independence 59:07
30 - Theorems about linear independence 39:56
31 - More on spans and linear independence 37:26
32 - Bases of vector spaces 20:18
33 - The dimension of a vector space 21:57
34 - Properties of bases 17:44
35 - Properties of bases (continued) 1:01:48
36 - Bases and dimensions of subspaces 52:16
37 - Coordinate vectors 34:15
38 - The dimension of Row(A) and Col(A) 44:47
39 - The rank-nullity theorem 32:41
40 - Invertible matrices 20:57
41 - Determining invertibility and finding the inverse 1:01:07
42 - Determinants 34:21
43 - Properties of determinants 31:33
44 - Invertibility and the determinant 21:08
45 - The matrix adj(A) 30:43
46 - Cramer's rule 13:12
47 - Which method is better? 7:02
48 - Linear maps 37:19
49 - Ker(T) and Im(T) 34:28
50 - Some geometric examples 26:48
51 - Properties of Ker(T) and Im(T) 40:07
52 - The rank of T 25:18
53 - The rank-nullity theorem revisited 37:12
54 - Matrix representation of linear maps 42:07
55 - Matrix representation of linear maps (continued) 1:00:27
56 - Operations on linear maps 58:21
57 - Compatability with operations on matrix representations 32:28
58 - Isomorphism 41:42
59 - Hom(V,W) 44:11
60 - Similarity of matrices 1:10:35
61 - Properties of similar matrices 22:29
62 - Diagonalization 25:32
63 - Diagonalization - a simple example 47:20
64 - Finding eigenvalues and eigenvectors 1:11:38
65 - An example 34:59
66 - Multiplicities of eigenvalues 33:11
67 - More on eigenvalues 1:13:41
68 - Powers of diagonalizable matrices 10:51
69 - The Cayley-Hamilton theorem 10:35
70 - Inner product 1:05:08
71 - Norm 30:24
72 - Inner product and norm give geometry 53:46
73 - Orthogonality 57:14