Outline of MA 242 Lectures on DVD, Recorded Fall, 2004

Dr. Larry K. Norris

 Lecture # Topic 1 Overview of the course. Begin Section 9.1: Cartesian Coordinates in space 2 Begin Section 9.2: Vectors 3 Review of discussion on Vectors, with a number of worked example problems. Begin Section 9.3: The Dot Product 4 Continue discussion of the Dot Product, with examples 5 Brief review of the Dot Product. Begin discussion of Section 9.4: The Cross Product 6 Brief review of the Cross Product. Begin Section 9.5: Equations of Lines and Planes 7 Continue with discussion of equations of lines and planes, with worked examples 8 Finish working examples on lines and planes. Begin Section 10.1: Vector Functions and Space Curves 9 Finish space curves. Begin Section 10.2: Derivatives and Integrals of Vector Functions 10 Finish discussion of section 10.2. Begin Section 10.3: Arc Length and Curvature 11 Finish 10.3 Begin Section 10.4: Motion in Space 12 Covers Section 9.6: Functions and surfaces, and Section 11.1: Functions of several variables 13 Covers Section 11.1: level curves of f(x,y)and level surfaces of f(x,y,z) 14 Review day for Test #1 Test #1 covers lectures 1 - 11, with lecture 14 the “review day” for test #1. On this test I am not testing section 9.6 or 11.1 which are covered in lectures 12 and 13. 15 Covers Section 11.2: Limits and continuity of f(x,y) and f(x,y,z) 16 Covers Section 11.3: partial derivatives 17 Begin Section 11.4: differentiability of f(x,y) and f(x,y,z) 18 Finishes up Section 11.4 19 Covers Section 11.5: The Chain Rule - Mentions a pdf for distance ed students that is on Norris’ web page - problem 9, page 788 (third edition). Begin 11.6: Directional derivatives and the gradient vector. 20 Continues discussion of section 11.6 on Directional derivatives 21 Finishes discussion of 11.6 Begins 11.7: optimization 22 Finishes Section 11.7 on optimization 23 Mentions test 2 will be on 11.1 - 11.7, although additional material will be covered before the test. Covers absolute max and absolute min. Last 7 minutes begins Section 12.1: Double Integrals over Rectangles 24 Finish 12.1 Begin 12.2: Iterated integrals 25 Finish discussion of 12.2 26 Review day for test #2 Test #2 will cover the material in sections 9.6, and 11.1 - 11.7. That material is covered in lectures 12, 13, 15-23, and Lecture #26 = ”Review day for test #2”. 27 Begin Section 12.3: Double Integrals over general regions 28 Continue with 12.3 29 Finish Section 12.3. Begin Section 12.4: Double integrals in polar coordinates 30 Continue with double integrals in polar coordinates. 31 Finish 12.4. Discuss 12.5 : Applications of double integrals 32 Begin Section 12.7: Triple integrals in Cartesian coordinates 33 Continue with 12.7 34 Finish examples from Section 12.7. Begin Section 9.7: Cylindrical coordinates and Section 12.8: Triple integrals in cylindrical coordinates 35 Finish examples in cyclindrical coordinates. Continue with Section 9.7: Spherical coordinates and Continue with Section 12.8: Triple integrals in spherical coordinates 36 Finish up discussion of triple integrals in spherical coordinates: do three example problems. Begin (briefly) Section 13.1: Vector Fields 37 Finish 13.1 on vector fields and conservative vector fields. Begin 13.2: Line integrals. 38 Continue with 13.2: Line integrals of functions along parameterized curves. 39 Finish 13.2: Line integrals of vector fields along parameterized curves; The defintion of the work done by a force. 40 Review day for Test #3:   Test #3 will cover the material in all sections of chapter 12 except section 12.6 (which will be covered later). This material is covered in DVD Lectures #24 - #36. Lecture #40 is the Review day for Test #3. 41 Begin Section 13.3: The fundamental theorem for Line Integrals 42 Continue with section 13.3 - includes a number of worked example problems 43 Finish Section 13.3. Show how Newton’s second law combined with conservative forces leads to the law of conservation of total energy. Begin 13.4: Green’s Theorem 44 Finish Section 13.4 - Green’s Theorem. Begin section 13.5: Divergence and Curl 45 Finish Section 13.5 on Divergence and Curl. Begin Section 10.5: Parametric Surfaces - BEGIN MAPLE ASSIGNMENT #4 46 Finish discussion of Section 10.5 on parametric surfaces. Begin study of “tangent planes to parametrized surfaces” (Pg 787-788). 47 Review discussion of “tangent planes to parametrized surfaces” (Pg 787-788) Begin Section 12.6: Surface area of Parameterized Surfaces 48 Finish discussion of surface area (Section 12.6). Begin several day study of Section 13.6: Surface Integrals 49 Continue with Section 13.6. Finish “surface integral of a function” Begin “surface integral of a vector field”. NOTE: A slide with the title “Line integral of Vector Fields” in this lecture. The title of that slide should be “Surface Integral of Vector fields”. 50 Review day for Test #4. Contains a number of worked examples. Test #4 will cover the material in all sections of chapter 13 except sections 13.7 and 13.8 (which will be covered later). Morever, the test includes the materials in section 10.5 (Parameterized surfaces), pg. 787-788 (tangent planes to parameterized surfaces) and secton 12.6 (surface area of paramterized surfaces). This material is covered in DVD Lectures #37 - #49 (exclude #40). Lecture #50 is the Review day for Test #4. 51 Begin Section 13.7: Stoke’s Theorem 52 Finish discussion of Section 13.7 - Stokes' Theorem. Begin discussion of Section 13.8: The Divergence Theorem 53 Finish Section 13.8 - The Divergence Theorem of Guass. 54 Semester Review Day: Questions and answers with worked example problems 55 Semester Review Day: Questions and answers with worked example problems