Undergraduate Topology by James Cook at Liberty University

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source: James Cook    2016年1月21日
Undergraduate Topology: These are from a short course based on Manetti's text. We hope to cover the essential topics in point set topology.

Undergraduate Topology: Jan 20, definition of topology, examples 59:51 Here we begin a short course in Topology. We're following Marco Manetti's text with insights added from Munkres and other things sitting around my office. There are three students in this course and they are of course responsible for my mistakes and oversights.
Keep in mind, this course is aimed at these three students in particular. They have already worked with metric topology in other coursework and the big picture of topology was covered in their previous class. I also decided to cover background material as we come to it.
Jan 20, definition of topology, examples part 2 18:58
Jan 27, Zariski topoology described, continuity 59:51
Jan 27, continuity, subspace topology (part 2) 21:40
Jan 29, nbhds, boundary points, continuity at pt (part 1) 59:51
Jan 29, nbhds, boundary points, continuity at pt (part 2) 25:55
Feb 3, immersion, product, Hausdorff (part 1) 59:51
Feb 3, immersion, product, Hausdorff (part 2) 34:24
Feb 7, connectedness (part 1) 59:51
Feb 7, connectedness (part 2) 35:54
Feb 10, connected components 25:18
Feb 17, theory of compact topologies (part 1) 59:51
Feb 17, theory of compact topologies (part 2) 21:46
Feb 19, topological groups (part 1) 59:51
Feb 19, topological groups (part 2) 29:16
Feb 24, identification maps 40:53
Feb 26, quotient topology (part 1) 59:51
Feb 26, quotient topology (part 2) 25:14
March 2, quotienting by group of homeomorphisms (part 1) 59:51
March 2, quotienting by group of homeomorphisms (part 2) 37:18
March 4, projective space (part 1) 35:53
March 4, projective space (part 2) 47:13
March 9, separable, 1 and 2 countable, sequences (part 1) 59:51
March 9, separable, 1 and 2 countable, sequences (part 2) 21:15
MVI 5959 59:51
March 11, totally bounded, T1-T4, etc. 34:55
April 1, existence theorem for ODEs 59:51
April 1, existence theorem for ODEs (part 2) 35:36
April 6, basic manifold theory (part 1) 59:51
April 6, basic manifold theory (part 2) 35:35
April 8, vector bundles and a word on fiber bundles (part 1) 59:51
April 8, global triviality, Riemannian Geometry begins (part 2) 29:40
April 27, supermath: introduction to supernumbers (part 1) 59:51
April 27, supermath: introduction to supernumbers (part 2) 16:29
May 4, a few words on supermanifolds 47:14

Elementary PDEs with applications to Physics (Fall 2016) by James Cook

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source: James Cook     2016年8月24日
Elementary PDEs with applications to Physics
These are from Fall 2016 semester. This course will examine the standard introductory PDEs; the heat, wave and Laplace equations. We'll see how Fourier decompositions are used to match initial conditions. We also consider characteristics, Green's functions, Laplace and Fourier transforms. I plan to work from Logan's Third Edition of Applied Partial Differential Equations. Also, the texts of Haberman, Weinberg and Gustafson. I also used Nagle Saff and Snider to prepare the notes I sometimes reference. See http://www.supermath.info/DifferentialEqns.pdf for my elementary differential equations notes. The last chapter is on PDEs, I'll cover it in these videos. Basically, we'll be bouncing from book to book as the semester unfolds.

Intro to PDEs: standard BVP solutions, homogenous bounded case 58:40
heat equation solution technique introduced 48:45
solution to wave equation, 8-29-2016 57:52
L3, Laplace Equation on rectangle, 9-2-16, part 1 59:51
L3, Laplace Equation on rectangle, 9-2-16, part 2 12:02
L4, a word on Dirac Delta "function", 9-5-16, part 1 31:26
L4, why the delta in Dirac Delta "function", 9-5-16, part 2 2:36
L4, quantum mechanics and separation, just the basic idea, 9-5-16 30:09
L5, Fourier Series, full, sine and cosine, 9-12-16, part 1 59:51
L5, Fourier Series, full, sine and cosine, 9-12-16, part 2 15:18
PDEs and Physics, quantum mechanical this and that, 9-30-16, part 1 59:51
PDEs and Physics, quantum mechanics basics, part 2, date unsure 9:20
PDEs 9-16-16 part 1 59:51
PDEs 9-16-16 part 2 18:00
PDEs 9-26-16 part 1 59:51
PDEs 9-26-16 part 2 18:50
PDEs and Physics, whirlwind intro to complex calculus, 10-3-16, 59:51
PDEs and physics, complex madness part 2, 10-3-16 13:05
PDEs 10-10-16 part 1 59:51
PDEs 10-10-16 part 2 7:25
PDEs 10-14-16 part 1 59:51
PDEs 10-14-16 part 2 21:20
PDEs 10-17-16 part 1 59:51
PDEs 10-17-16 part 2 24:25
PDEs 10-24-16 part 1 7:15
PDEs 10-24-16 part 2 54:47
PDEs 10-28-16 part 1 59:51
PDEs 10-28-16 part 2 2:28
PDEs 11-7-16 part 1 59:51
PDEs 11-7-16 part 2 13:18
PDEs 11-11-16 part 1 59:51
PDEs 11-11-16 part 2 19:31
PDEs 11-14-16 part 1 59:51
PDEs 11-11-14 part 2 8:40

Introductory Mechanics (Spring 2016) by James Cook at Liberty University

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source: James Cook      2016年1月21日
I intend to post Lectures from Spring 2016 of Physics 231 at Liberty University.

Physics I: Jan 19, 2016, intro. vectors 59:51
Jan 19, 2016, intro. vectors (part 2) 4:29
Jan 26, 2016, calculus and vectors, one diml motion 59:51
Jan 26, 2016, calculus and vectors, one diml motion (part 2) 12:40
Jan 28, 2016, one diml motion, projectile motion 58:32
Feb 2, 2016, unsymmetric max range problem, Newt's 2nd Law 59:51
Feb 2, 2016, unsymmetric max range problem, Newt's 2nd Law (part 2) 13:03
Feb 4, 2016, use the force (part 1) 59:51
Feb 4, 2016, use the force (part 2) 14:49
Feb 9, 2016, inclined planes, pulleys, friction, circular motion (part 1) 59:51
Feb 9, 2016, inclined planes, pulleys, friction, circular motion (part 2) 15:42
Feb 11, 2016, examples on force and kinematics (part 1) 59:51
Feb 11, 2016, examples on force and kinematics (part 2) 13:01
Feb 19, 2016, calculus to derive conservation of energy (part 1) 59:51
Feb 19, 2016, calculus to derive conservation of energy (part 2) 4:50
Feb 25, 2016, on PE and KE problems (part 1) 59:51
Feb 25, 2016, on PE and KE problems (part 2) 8:36
March 1, 2016, energy analysis (part 1) 59:51
March 1, 2016, energy analysis (part 2) 14:13
March 3, 2016, momentum (part 1) 59:51
March 3, 2016, momentum (part 2) 19:34
March 8, 2016, collisions continued (part 1) 59:51
March 8, 2016, collisions continued (part 2) 8:45
March 10, 2016, homework energy and momentum madness (part 1) 59:51
March 10, 2016, homework energy and momentum madness (part 2) 7:23
March 24, 2016, rotational kinematics, moment of inertia (part 1) 59:51
March 24, 2016, rotational kinematics, moment of inertia (part 2) 11:40
March 29, 2016, angular momentum and torque (part 1) 59:51
March 29, 2016, angular momentum and torque (part 2) 14:57
April 5, 2016, rotational problems, gravity (part 1) 59:51
April 5, 2016, rotational problems, gravity (part 2) 8:10
April 7, 2016, gravity examples (part 1) 59:51
April 7, 2016, help with rotation hwk (part 2) 14:27
April 14, 2016, basic special relativity (part 1) 59:51
April 14, 2016, basic special relativity (part 2) 15:39
April 19, 2016, spacetime diagrams, 4-vector (part 1) 59:51
April 19, 2016, spacetime diagrams, 4-vector (part 2) 17:56
April 21, 2016, 4-vectors and relativity (part 1) 59:51
April 21, 2016, 4-vectors and relativty (part 2) 16:07
April 26, 2016, springs and waves, derivation of wave eqn (part 1) 59:51
April 26, 2016, springs and waves, derivation of wave eqn (part 2) 15:33
April 28, 2016, homework for Test 3 , 4-vector calculation (part 1) 59:51
April 28, 2016, homework for Test 3 , 4-vector calculation (part 2) 13:01

Introductory Mechanics (Spring 2015) by James Cook at Liberty University

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source: James Cook      2015年1月15日
These are my Lectures from the Spring 2015 offering of Physics 231 at Liberty University. This is a course in University Physics which covers the physics of motion from a calculus-based perspective. Moreover, we use vectors to communicate physical law. This course covers the topics of Kinematics, linear and rotational dynamics, linear and angular momentum, Gravity and whatever else time allows. My hand-written Lectures (not in-sync with the numbering below) are found at: http://www.supermath.info/PhysicsI.html

Introductory Mechanics: Lecture 1 part 1 33:26 We study basics of coordinates, vectors in two and three dimensions. Dot and Cross products briefly introduced at conclusion.
Lecture 1 part 2 17:36
Lecture 2 51:25
Lecture 3 51:01
Lecture 4 50:27
Lecture 5 44:49
Lecture 6 49:32
Lecture 7 47:30
Lecture 8 36:41
Lecture 9 44:10
Lecture 10 45:23
Lecture 11 51:27
Lecture 12 part 1 32:27
Lecture 12 part 2 14:18
Lecture 13 46:13
Lecture 14 49:21
Lecture 15 46:01
Lecture 16 45:01
Lecture 17 48:16
Lecture 18 48:43
Lecture 19 48:35
Lecture 20 part 1 46:35
Lecture 20 part 2 0:51
Lecture 21 46:06
Lecture 22 50:33
Lecture 23 43:59
Lecture 24 57:04
Lecture 25 42:32
Lecture 26 48:01
Lecture 28 19:12
Lecture 29 51:43

Advanced Calculus (Fall 2015) by James Cook at Liberty University

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source: James Cook      2015年8月25日
Advanced Calculus of 2015
This is the playlist for Math 332 as captured at Liberty University in Lynchburg VA during the Fall 2015 semester. This is not a real analysis course even though it is very much about analysis of real-valued functions of a real-variable. In particular, this course focuses first on the theory of differentiation for mappings on a finite-dimensional (mostly) normed linear space. We include sketches of the implicit and inverse function theorems as well as a presentation of the multivariate Talyor series and theory of optimization. Also, a brief introduction to classical variational calculus is given. Differentiating under the integral is also studied. Essentially, I try to make good on the title "advanced" calculus, I seek to present all manner of computational techniques which you probably did not see in your earlier coursework.
However, I also intend to build a bridge to higher mathematics here. I do intend to present the concept of a manifold together with some of the basic calculus of curved spaces. So, the second half of the course centers around differential forms which provide the natural calculus in higher-dimensional space. We study multilinear maps built from the tensor product, the wedge product, the exterior derivative, push-forward and pull-back and a few deeper things like the Generalize Stokes' Theorem (no proof offered here!) and the Poincare Lemma (proof given based closely on argument found in Flander's text). Also, I present a 5-dimensional electrostatics where we see how the number of ambient spatial dimensions determines the field-strength.
All of the things we study in the second half of the course have abstractions and formalizations which are deep, abstract, and beyond this course. I merely hope to get your attention and for the interested student take some of the sting out of more advanced treatments.
Finally, I have a few lectures left at the end to do something really novel. TBD by my semester and of course the interest of the students. The official text for the course is Edward's Advanced Calculus text available as a Dover. Almost everything I gloss over is treated carefully in the body of Edwards. In there you'll find a technically precise proof of the implicit and inverse mapping theorems replete with the contraction mapping technique. Also, Generalized Stokes' Theorem is established with some care.

Advanced Calculus: Lecture 1 part 1: normed linear spaces 59:51 Here I give a very brief overview of linear algebra, for my students, I hope the first homework helps complete the review. Then I discuss normed linear spaces, metric spaces and inner product spaces. Again, the first homework will flesh out the discussion begun here. Finally, we define open sets and limits on a NLS and explore the norm-indendence of topology in the plane.
Lecture 1 part 2: squaring the circle 13:22
Lecture 2 part 1: limit laws in normed linear spaces 59:51
Lecture 2 part 2: limit laws for normed linear spaces 17:58
Lecture 3 part 1: Frechet Derivatives 59:51
Lecture 3 part 2: Frechet Derivatives 14:40
Lecture 4 part 1: product rule to rule them all (with sound) 22:11
Lecture 4 part 2: continuous differentiability (sound added) 24:52
Lecture 4 part 3: Jacobian Matrix and Linearization Example (with sound) 5:48
Lecture 4 part 1: continuous differentiability and product rules 59:51
Lecture 4 part 2: continuous differentiability and product rules 9:59
Lecture 5 part 1: continuous differentiabilty and chain rule 59:51
Lecture 5 part 2: continuous differentiabilty and chain rule 13:42
Lecture 6 part 1: inutition on inverse and implicit function theoremstutions 9 10 59:51
Lecture 6 part 2: inutition on inverse and implicit function theorems 17:14
Lecture 7 part 1: implicit differentiation 59:51
Lecture 7 part 2: implicit differentiation 16:58
Lecture 8 part 1: tangent and normal spaces 59:51
Lecture 8 part 2: tangent and normal spaces 8:49
Lecture 9 part 1: Lagrange multipiers 59:51
Lecture 9 part 2: Lagrange multipliers 12:21
Lecture 10 part 1: 2nd derivative test and quadratic forms 59:51
Lecture 10 part 2: 2nd derivative test and quadratic forms 17:04
Lecture 11 Part 1: differentiation under integral, variational calculus 59:51
Lecture 11 Part 2: differentiation under integral, variational calculus 13:11
Lecture 12 Part 1: examples of variational calculus 59:51
Lecture 12 Part 2: examples of variational calculus 17:11
Lecture 13 Part 1: Snell's Law, method of Lagrange multipliers 59:51
Lecture 13 Part 2: Central Force Problem 15:50
Lecture 14: Part 1 : review for Test 1 59:51
Lecture 14: Part 2 : review for Test 1 16:52
Lecture 15 Part 1: tensors and coordinate change 59:51
Lecture 15 Part 2: tensors and coordinate change 15:19
Lecture 16 Part 1: duals, double duals and isomorphisms of tensor products 59:51
Lecture 16 Part 2: duals, double duals and isomorphisms of tensor products 14:54
Lecture 17 Part 1: wedge products, flux and work form, determinants 59:51
Lecture 17 Part 2: wedge products, flux and work form, determinants 16:16
Lecture 18 Part 1: more on metrics and musical morphisms 59:51
Lecture 18 Part 2: more on metrics and musical morphisms 14:00
Lecture 18 Part 3: Hodge Duality 48:58
Lecture 19: manifolds and calculus, derivations and push-forwards 59:51
Lecture 19 part 2: differentials as a dual basis to coordinate derivations 16:42
Lecture 20 Part 1: exterior derivatives and pull-backs 59:51
Lecture 20 Part 2: properties of pull-backs 18:02
Lecture 21 Part 1: pull-backs, exact and closed forms, Poincare lemma 59:51
Lecture 21 Part 2: electromagnetism in differential forms 16:22
Lecture 22 Part 1: Homotopy and De Rahm Cohomology 59:51
Lecture 22 Part 2: convex sets and the convex hull 15:39
Lecture 23 Part 1: from polytopes to k-faces, simplicial Homology 59:51
Lecture 23 Part 2: Generalized Stokes Theorem 17:52
Lecture 24 Part 1: homology of S2, proof of GST 59:51
Lecture 24 Part 2: electrostatics in 4D at end 19:05
Lecture 25 Part 1: Hodge theory, coderivative and Laplacian 59:51
Lecture 25 Part 2: on solutions to DEqns and Frobenius 13:03
Lecture 26 Part 1: Frobenius Theorem about vectors, forms and foliations 59:51
Lecture 26 Part 2: statements of the Frobenius Theorem 13:04
Lecture 27 Part 1: calculations to illustrate Frobenius Theorem 59:51
Lecture 27 Part 2: on compatibility condition for PDE example 13:48
Lecture 28 part 1: a bit on jet spaces and DEqns 21:13
Lecture 28 part 2: a bit on jet spaces and DEqns 9:57

Multivariate Calculus by James Cook at Liberty University

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source: James Cook     2015年8月24日
Multivariate Calculus
These are lectures captured from Math 231 at Liberty University in Lynchburg VA. Much more for this course can be found at the course website: http://www.supermath.info/MultivariateCalculus.html
This is the third semester in the usual calculus sequence. In a nutshell, we study of vector algebra, curves in 3D including Frenet-Serret equations, limits of several variables, partial differentiation, local extrema, Lagrange multipliers, closed set test, double and triple integrals, Jacobians, curvelinear coordinates, gradients, level curves, line and surface integrals, Green's Theorem, Stokes' Theorem and Gauss' Theorem. Some attention is paid to a few nontraditional topics: we do discuss the general derivative, cylindrical and spherical coordinate frame fields and the formulae for calculation of grad, div, curl and Laplacian in noncartesian setting. Finally, I'll probably include some discussion of differential forms if time permits. Some proofs are given in this course, but, deeper theorems are just sketched. Past this course, for the student who also has some experience with linear algebra, I recommend study of my advanced calculus course if you like my take on calculus III.

Multivariate Calculus: Lecture 1: points and vectors 26:40 here we set the terms R2 and R3 and explain the geometric meaning of xhat, yhat and zhat (other texts call these i, j and k respective due to their historic correspondence with the versors in Hamilton's quaternions). We derive the 3D-distance formula from the 2D-formula and a little picture. Next time, the dot-product ! See http://www.supermath.info/Multivariat... for more resources on multivariate calculus including my lecture notes and oodles of solutions from previous years.
Lecture 2 part 1: the dot product and vector length 59:51
Lecture 2 part 2: projections and dot products 11:03
Lecture 3: the cross product 42:12
Lecture 4 part 1: lines and planes 59:51
Lecture 4 part 2: lines and planes 14:39
Lecture 5: problem solving session 47:57
Lecture 6: curves and surfaces 50:34
Lecture 7 part 1: surfaces and coordinates 59:51
Lecture 7 part 2: surfaces and coordinates 10:35
Lecture 8: frames and calculus of curves 43:37
Lecture 9 part 1: product rules and arclength 59:51
Lecture 9 part 2: product rules and arclength 12:40
Lecture 10: Frenet Serret Frame and Equations 51:47
Lecture 11: Frenet Serret non-unit speed 50:12
Lecture 12 part 2: kinematics in 3D 9:20
Lecture 13: help with Mission 2 46:44
Lecture 14: problem solving session 56:31
Lecture 15: mission 2 solution 30:45
Lecture 16: questions for Test 1 47:39
Lecture 17: limits and concepts of topology 49:15
Lecture 18 part 1: directional derivatives 59:51
Lecture 18 part 2: directional derivatives 14:24
Lecture 19: partial derivatives 48:49
Lecture 20: sick examples and gradients and contour plots 2D 45:58
Lecture 21 part 1: gradients in 3D, deriving unit-vector fields 59:51
Lecture 21 part 2: gradients in 3D, general derivative 12:26
Lecture 22: linearization and tangent planes 47:14
Lecture 23 part 1: chain rules 59:51
Lecture 23 part 2: chain rules 17:45
Lecture 24: Mission 3 help session 48:23
Lecture 25 Part 1: Normal Vector Fields to Surfaces in R3 14:34
Lecture 25 Part 2: Normal Vector Fields to Surfaces in R3 55:27
Lecture 26: curvelinear calculus, gradient in polar coordinates 49:28
Lecture 27 Part 1: exact differential equations 59:51
Lecture 27 Part 2: exact differential equations 10:06
Lecture 28 Part 1: help with Mission 4 59:51
Lecture 28 Part 2: help with Mission 4 6:53
Lecture 29: questions before Test 2 and Mission 4 solution 44:16
Lecture 30: Lagrange Multiplier Technique 47:17
Lecture 31 Part 1: Lagrange Multiplier Examples, Multivariate Taylor 59:51
Lecture 31 Part 2: Lagrange Multiplier Examples, Multivariate Taylor 15:45
Lecture 32: Inuition and examples of the Second Derivative Test 48:32
Lecture 32: closed set test for two variables 45:11
Lecture 33 Part 1: more extreme examples, help on Mission 5 59:51
Lecture 33 Part 2: more extreme examples, help on Mission 5 8:46
Lecture 34: definition and concept of multivariate integrals 45:26
Lecture 35 Part 1: integrals over nonrectangular regions 59:51
Lecture 35 Part 2: integrals over nonrectangular regions 12:39
Lecture 36: nontrivial triple integrals 51:12
Lecture 37 Part 1 integration variable change 59:51
Lecture 37 Part 2 integration variable change 13:04
Lecture 38: volume of hypersphere, more integration examples 45:06
Lecture 39 part 1: help with mission 6 59:51
Lecture 39 part 2: help with mission 6 16:57
Lecture 40: differential forms and Jacobians, centroids 52:47
Lecture 41: Review for Test 3 43:03
Lecture 42 part 1: vector fields, curl and divergence 59:51
Lecture 42 part 2: vector fields, curl and divergence 10:11
Lecture 43: paths, curves, reparametrization, arclength 50:57
Lecture 44 part 1: line integrals 59:51
Lecture 44 part 2: line integrals 14:50
Lecture 45: conservative vector fields, path independence 51:45
Lecture 46: review for Test 3 49:03
Lecture 47 part 1: circulation, flux and Green's Theorem 59:51
Lecture 47 part 2: circulation, flux and Green's Theorem 14:20
Lecture 48: electrostatics in 2D 45:41
Lecture 49: help with homeworks 47:06
Lecture 50 part 1: surface integration 59:51
Lecture 50 part 2: surface integration 12:41
Lecture 51: surface integration examples 50:26
Lecture 52 part 1: Stokes and Gauss Theorems 59:51
Lecture 52 part 2: Stokes and Gauss Theorems 3:54
Lecture 53: deformation theorem, examples using Div. and Stokes' 52:19
Lecture 54 part 1: harmonic functions, a bit of potential theory 59:51
Lecture 54 part 2: harmonic functions, a bit of potential theory 14:40
Lecture 55: centroid of cone, homework help 48:44
Lecture 56: examples of integral vector calculus 46:21
Lecture 57: introduction to differential forms 49:45
Lecture 58: review for Test 4 42:46

Multivariate Calculus (Spring 2017) by James Cook

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source: James Cook       2017年1月16日
These are the Lectures from my section of Math 231 from the Spring 2017 Semester. While my notes are based on several calculus texts (Stewart, Thomas, Salas and Hille and Etgen etc.) these Lectures follow my notes primarily. I am doing my best to make the notes self-contained so there is no need to purchase additional materials. That said, it's probably wise to get an old edition of Salas and Hille or something for the sake of having many additional homework examples to ponder.
My understanding of multivariate calculus stems in part from my background in physics. I have much higher expectations for what multivariate calculus should encompass. On the other hand, I may spend a bit less time on certain issues of analysis than other math professors. I take up those issues in greater generality in the advanced calculus class (audience permitting).
Topics: vectors, calculus and geometry of paths, Frenet frames, limits of functions of several variables, partial derivatives, chain rules, integration over areas or volumes, optimization, Lagrange multipliers, line integrals, surface integrals, theorems of vector calculus including Green, Stokes and Divergence. Time permitting, the theory of scalar and vector potentials. We also hope to see how to present various constructions in noncartesian coordinate frames.

Multivariate Calculus: vectors, components, distance: 1-16-17 51:43
dot-product, 1-17-17, part 1 59:51
dot-product, 1-17-17, part 2 20:05
end of dot-product, start of cross-product, 1-18-17 47:50
cross product identities, planes, 1-19-17, part 1 59:51
cross product identities, planes, 1-19-17, part 2 8:51
curves and surfaces big picture, 1-20-17 51:37
graphing surfaces and parametrizations, 1-23-17 50:53
graphing surfaces and curvelinear coordinates, 1-24-17, part 1 59:51
graphing surfaces and curvelinear coordinates, 1-24-17, part 2 16:36
distance to pts, lines and planes, calculus of paths intro, 1-25-17 51:57
the way of calculus, or calculus of paths, 1-26-17,part 1 59:51
the way of calculus, or calculus of paths, 1-26-17,part 2 16:06
Isaac's Dizzy Dance 0:08
tangent lines, arclength, TNB intro, 1-27-17 51:17
Frenet Serret Equations, curvature, torsion, 1-30-17 50:49
motion, Kepler's Laws in brief, int. w.r.t. arclength, 1-31-17, part 1 59:51
motion, Kepler's Laws in brief, int. w.r.t. arclength, 1-31-17, part 2 12:57
find center of mass of variable mass helix, 2-1-17 35:17
review for Test 1, 2-6-17 45:03
directional derivative via the gradient, 2-13-17 46:52
gradient and contour plots, 2-14-17, part 1 59:51
gradient and contour plots, 2-14-17, part 2 13:50
discussion of Test 1, general concept of differentiation, 2-15-17 48:43
continuous diff dangers, chain rule, 2-16-17, part 1 59:51
more chain rules and discussion of tangent plane, 2-17-17 50:36
tangent planes from many viewpoints, 2-20-17 45:27
constrained partial differentiation, 2-21-17, part 1 59:51
constrained partial differentiation, 2-21-17, part 2 9:55
gradient in polar or spherical coordinates, 2-22-17 50:32
optimization, Lagrange Multipliers, 2-23-17, part 1 59:51
optimization, Lagrange Multipliers, 2-23-17, part 2 14:45
the quadratic form uber-example, power series, 2-24-17 49:45
second derivative test for several variables, 2-27-17 44:47
absolute extrema, 2-28-17, part 1 59:51
absolute extrema, 2-28-17, part 2 14:09
review for Test 2 on differentiation, 3-6-17 43:45
double integrals, 3-7-17, part 1 59:51
double integrals, 3-7-17, part 2 14:28
triple integrals in xyz, 3-8-17 50:42
integration in polars, 3-20-17 38:44
change of variables theorem, 3-21-17, part 1 59:51
change of variables theorem, 3-21-17, part 2 20:32
spherical volume element via wedges, integration, 3-22-17 48:15
integration, moment of intertia for solid sphere, 3-23-17, part 1 59:51
integration, moment of intertia for solid sphere, 3-23-17, part 2 12:25
integration examples, 3-24-17 49:10
integration advice, 3-27-17 45:37
the three derivatives of vector calculus, 3-28-17, part 1 59:51
the three derivatives of vector calculus, 3-28-17, part 2 12:26
review for Test 3, 4-3-17 30:42
definition of line integral, 4-5-17 47:05
line integral calculation and notation, 4-6-17, part 1 59:51
line integral calculation and notation, 4-6-17, part 2 13:52
conservative vector field theorems, 4-7-17 46:10
Green's Theorem introduction, 4-10-17 46:56
more on Green's Theorem and locally conservative, 4-11-17, part 1 59:51
more on Green's Theorem and locally conservative, 4-11-17, part 2 14:11
surface integrals over sphere, 4-12-17 43:21
surface integrals on cylinders, cones, planes, graphs, 4-13-17, part 1 59:51
surface integrals on cylinders, cones, planes, graphs, 4-13-17, part 2 13:50
Stokes Theorem polyhedral argument, two examples, 4-14-17 49:13
proof of Stokes' for graph, intuitive div. thm. , 4-18-17 42:30
Stokes and Divergence with holes, deformation thms, 4-19-17 49:25
examples of vector calculus, 4-20-17, part 1 59:51
examples of vector calculus, 4-20-17, part 2 11:24
Theory of Harmonic Functions part I, 4-21-17 46:54
Green's Third Identity and Physics, 4-24-17 48:45
differential forms and generalized Stokes' Thm, 4-25-17, part 1 59:51
differential forms and generalized Stokes' Thm, 4-25-17, part 2 7:11
comments for Test 4, 5-1-17 39:21