MATH 200-Section 103-Fall 2016
I teach 2 sections of Math 200: section 103 and section 104. The pace, quizzes, and midterms will be different, you MUST take the quizzes and midterms given to your section. Make sure YOUR SECTION IS 103 when using this page. This page is still under construction, below information might be modified.
Instructor:
Most important information: · Common page for all sections (maintained by our Instructor-in-charge Prof. Albert Chau). · Textbook: mainly use a primary textbook, and occasionally secondary textbook #1 and secondary textbook #2. These are free to download, visit the common page for more details. · Grade components: homework using WeBWorK, 6 quizzes, one midterm, and one final. Visit the common page for more details. · Only one midterm on Friday Oct 14. This midterm takes place at our normal meeting time and room. Different sections will have different midterms. At the end, the scores will be scaled to ensure fairness among all sections. · Final exam: all sections do a common final exam. The exact date will be announced later.
Some tips: · Do not hesitate to visit my office hours, other instructors’ office hours (see the common page), the Math Learning Centre,… · I follow the textbook closely. You should skim through the topics before and review the notes after each lecture, spend time on WeBWorK, and solve the suggested problems (including past exams) given in the common page. · Study with friends.
Homework: Due at 5pm on Friday. You can ask WeBWorK questions in my office hours (but NOT by emails). The first assignment is open on Friday Sep 9 and due on Friday Sep 16.
Quizzes:
Quiz 1: Friday Sep 16. Cover the lectures on Sep 7-9. Questions are very similar to examples done in the filled notes Sep07 and Sep09. Solution
Quiz 2: Friday Sep 30. Cover the notes Sep12, Sep14, Sep16, Sep19, Sep21, and the note extra-week3 (posted on Friday 9/23). Skip “torque”. For this quiz (but NOT for the midterm and final), you can skip “work”, “angle between 2 planes” and “angle between a line and a plane” (discussed in the note Sep21). I will give you the formulas for: projection of u onto v, distance from a point to a line, distance between 2 skew lines, and distance from a point to a plane. Solution
No quiz on Fri Oct 14 (midterm)
Quiz 3: Friday Oct 28. Cover Multivariable Chain Rule (including formulas for implicit differentiation), Directional Derivative and Gradient Vectors (including tangent planes of level surfaces and tangent lines of level curves using gradient vectors). These are given in the notes Oct05, Oct07, Oct12, Oct17, and Oct19. You can skip Directional Tangent Lines (first 2 pages of the note Oct19). I will give you 3 formulas: (1) formulas for implicit differentiation (when z is implicit in x and y), (2) directional derivative as dot product of gradient and the unit direction vector, and (3) tangent planes of level surfaces. Solution
Quiz 4: Wednesday Nov 9 (since Fri Nov 11 is a holiday). Cover 3 types of optimization problems given in the notes Oct21, Oct24, Oct26, Oct28, and Oct31. I will not give you any formulas (so you should know the second derivative test, identify boundaries, set up and solve the system of equations coming from the method of Lagrange multipliers on your own). Solution
Quiz 5: Friday Nov 18. Cover iterated integrals and double integrals over general domains as given in the notes Oct31, Nov02, Nov04, Nov07, and Nov09 (skip stuff involving polar coordinates in Nov09). I will not give you any formulas; you should know on your own when to move vertical (respectively horizontal) lines and do dx (respectively dy) later. Solution
Quiz 6: Friday Nov 25. Cover double integrals using polar coordinates and applications as in the notes Nov09, Nov14, Nov16, and Nov18 (skip triple integrals). I will give you the formulas for mass, moments, and center of mass. Solution
Midterms, final, and past exams: Notes and calculators are NOT allowed. Formula sheets will be provided in the midterm and final. Visit the common page for more details. Past finals: http://www.math.ubc.ca/Ugrad/pastExams/ Some past midterms: in the past, we had 2 midterms each year. So the second midterms below (held in November) contain a lot of extra materials that will not appear in our midterm. For more past midterms, visit the common page. 2014-MT1 2014-MT2 (in Fall 2014, all sections have common midterms. Each midterm is 1.5 hours long and some questions are pretty hard) 2015-104-MT1 2015-104-MT2 2015-105-MT1 2015-105-MT2 (in Fall 2015, different sections have different exam)
Important information on your midterm: MT1-Info The first page (ignore the number of questions and the scores “X” and “Y”) and the last page (formula sheet) of your midterm: MT1-First-Last Extra office hour: 2:30-3:30 on Tuesday Oct 11 at LSK300C.
Important information on your final: Final-Info
Notes: Disclaimer: these notes might contain mistakes, might not show students’ questions, any possible extra explanations, corrections, problems, and examples done in the lectures. Using these notes without going to classes might do more harm than good.
Week 1: Coordinates and vectors. Sections 10.1 and 10.2 from the primary textbook (we will do “cylinders and quadric surfaces” LATER, ignore them for the moment). Raw notes: Sep07 Sep09. Filled notes: Sep07 Sep09
Week 2: Dot product, cross product, equations of lines. Sections 10.3, 10.4, and 10.5 from the primary textbook. Raw notes: Sep12 Sep14 Sep16. Filled notes: Sep12 Sep14 Sep16 These topics correspond to Sections 12.3, 12.4, and 12.5 in Stewart’s book. Highly recommended problems: any problems involving dot product, cross product, lines, and planes in past finals such as Problem 1(a)(b) in 2015-WT1, Problem 1 in 2013-WT2, Problem 1(a) in 2013-WT1 or past midterms (posted above) such as Problems 1,2,3,4 in 2014-MT1, all problems in 2015-104-MT1, and all problems 2015-105-MT1
Week 3: continue on lines, planes, then study how to sketch cylinders and quadric surfaces (skip surfaces of revolution, you can read it yourselves), an introduction to multivariable functions. Sections 10.5, 10.1, and 12.1 from the primary textbook. Raw notes: Sep19 Sep21 Sep23. Filled notes: Sep19 Sep21 extra-week3 Sep23
Week 4: continue on multivariable functions, brief discussion on limits and continuity, partial derivatives, total differentials, linear approximations, and tangent planes. Sections 12.1, 12.2, 12.3, and 12.4 from the primary textbook (and Sections 14.3 and 14.4 in Stewart’s book). Raw notes: Sep26 Sep28 Sep30. Filled notes: Sep26 Sep28 Sep30 These topics correspond to Sections 14.1, 14.2, 14.3, and 14.4 in Stewart’s book. Highly recommended problems: problems in past finals such as Problem 1(d) in 2013-WT1, Problem 2(ii) in 2015-WT1, Problem 2 in 2011-WT2, and Problem 1(b)(c) in 2011-WT1; problems in past midterms (posted above) such as Problem 6(a)(b) in 2014-MT1, Problem 1 in 2014-MT2 and Problem 1(a)(b) in 2015-104-MT2; problems from STEWART: Section 14.1: 59-64, Section 14.3: 10, 22, 50, 77, Section 14.4: 3, 5, 17, 19, 21, 28.
Week 5: continue on tangent planes, linear approximations, and differentials, multivariable chain rule (and formulas for implicit differentiation applying multivariable chain rule). Sections 12.4 and 12.5 APEX (and Sections 14.4 and 14.5 in Stewart’s book). Raw notes: Oct03 Oct05 Oct07. Filled notes: Oct03 Oct05 Oct07 These topics correspond to Sections 14.4 and 14.5 in Stewart’s book. Highly recommended problems: as in Week 6.
Week 6: finish the formulas for implicit differentiation using chain rule, start on directional derivatives. Sections 12.5 and 12.6 APEX (and Sections 14.5 and 14.6 in Stewart’s book). Raw notes: Oct12. Filled notes: Oct12 These topics correspond to Sections 14.5 and 14.6 in Stewart’s book. Highly recommended problems: problems in past finals such as Problem 2 and Problem 3 in 2012-WT1, Problem 1(c) in 2013-WT1, Problem 2(a) in 2013-WT2, Problem 2 and Problem 3 in 2014-WT1, and Problem 3 in 2015-WT1; problems in past midterms (posted above) such as Problem 2 in 2014-MT2, Problem 1(c) in 2015-104-MT2, and Problem 1(c) in 2015-105-MT2; problems in Section 14.5 STEWART: 4, 11, 22, 31, 33, 45, 48, 50, 53.
Week 7: directional derivatives, gradient vectors, directional tangent lines, tangent planes of level surfaces, normal lines, max-min. Sections 12.6, 12.7, and 12.8 APEX (and Sections 14.6 and 14.7 in Stewart’s book). Raw notes: Oct17 Oct19 Oct21. Filled notes: Oct17 Oct19 Oct21 Except for directional tangent lines, these topics correspond to Section 14.6 in Stewart’s book. Highly recommended problems: problems in past finals such as Problem 5 in 2012-WT1, Problem 1(b),(e),(f) and Problem 2 in 2013-WT1, Problem 2(b)(c) in 2013-WT2, Problem 1 and 7(a) in 2014-WT1, and Problem 1(c) and 2 in 2015-WT1; problems in past midterms (posted above) such as Problem 3 in 2014-MT2, Problem 2 and Problem 3 in 2015-104-MT2, and Problem 2 and Problem 3 in 2015-105-MT2; problem in Section 14.6 STEWART: 7, 15, 23, 25, 29, 31, 33, 34, 45, 49, 51, 54, 55, 57, and 59.
Week 8: continue on 3 types of max-min problems: (1) find and classify critical points, (2) global max-min on a closed and bounded domain, (3) Lagrange multipliers. Sections 12.7 of APEX only treats the first 2 types, for the method of Lagrange multipliers we need to use ``Secondary textbook #1” (or you can use Sections 14.7 and 14.8 in Stewart’s book which treat all 3 types of problems). Raw notes: Oct24 Oct26 Oct28. Filled notes: Oct24 Oct26 Oct28 These topics correspond to Sections 14.7 and 14.8 in Stewart’s book. Highly recommended problems: problems in past finals such as Problem 4 and 6 in 2012-WT1, Problem 3 and 4 in 2013-WT1, Problem 3 and 4 in 2013-WT2, Problem 5 in 2014-WT1, and Problem 4 and 5 in 2015-WT1; problems in past midterms (posted above) such as Problem 4 and 5 in 2014-MT2, Problem 4 and 5 in 2015-104-MT2, and Problem 3 and 4 in 2015-105-MT2. Section 14.7 STEWART: 12, 29, 34, 41, 47. Section 14.8 STEWART: 5, 9, 19, and 43 (two constraints).
Week 9: finish the method of Lagrange multipliers, double integrals using volume and Riemann sums, iterated integrals, and express a double integral as an iterated integral. We (should) use Chapter 13 of APEX and since it does not treat cylindrical and spherical coordinates, we (should) use Chapter 14 of secondary textbook #2 for those topics. Alternatively, we can use Chapter 15 of Stewart. Raw notes: Oct31 Nov02 Nov04. Filled notes: Oct31 Nov02 Nov04 An extra note on some integration techniques. I posted this for my sections last year (so you should ignore the words “written assignment” at the end of the first page) extra-week9 These topics correspond to Sections 14.8, 15.1, 15.2, and 15.3 in Stewart’s book. Highly recommended problems: as in Week 10.
Week 10: finish changing from double integrals to iterated integrals, then start on polar coordinates. Sections 13.1, 13.2, and 13.3 of APEX. Alternatively, we can use Sections 15.3 and 15.4 of Stewart. Raw notes: Nov07 Nov09. Filled notes: Nov07 Nov09 These topics correspond to Sections 15.3 and 15.4 in Stewart’s book. Highly recommended problems: problems in past finals such as Problem 7 in 2012-WT1, Problem 5(a) and Problem 6 in 2013-WT1, Problem 6(a) in 2013-WT2, and Problem 6 in 2015-WT1; as many problems as you can from Section 15.3 of Stewart: 3, 5, 7, 9, 13, 15, 16, 17, 19, 20, 23, 25, 29, 31, 32, 43-56, 60, 63-67.
Week 11: finish double integrals using polar coordinates, applications of double integrals (only: mass, moments, and center of mass), then start on triple integrals. Sections 13.3, 13.4, and 13.6 of APEX. Alternatively, we can use Sections 15.4, 15.5 (only Mass, Moments, and Center of Mass), and 15.7 of Stewart. Raw notes: Nov14 Nov16 Nov18. Filled notes: Nov14 Nov16 Nov18 These topics correspond to Sections 15.4, 15.5, and 15.7 of Stewart’s book. Highly recommended problems: problems in past finals such as Problem 8 in 2012-WT1, Problem 5(b) in 2013-WT1, Problem 5 in 2013-WT2, Problem 6 in 2014-WT1; as many problems as you can from Section 15.4 Stewart: Problems 1-14, 19-27, 29-32 and Section 15.5 Stewart: Problems 1-16.
Week 12: triple integrals in Cartesian (rectangular) coordinates x,y,z, then triple integrals using cylindrical coordinates. Use APEX then Secondary Textbook #2 for cylindrical coordinates (since APEX does not treat cylindrical coordinates). Alternatively, we can use Sections 15.7 and 15.8 of Stewart. Raw notes: Nov21 Nov23 Nov25. Filled notes: Nov21 Nov23 Nov25 These topics correspond to Sections 15.7 and 15.8 of Stewart’s book. Highly recommended problems: posted below together with recommended problems for Week 13. Based on previous final exams, topics in Week 12 and Week 13 (triple integrals in Cartesian coordinates, cylindrical coordinates and spherical coordinates) constitute around 25% of the final.
Week 13: triple integrals in spherical coordinates, then review for the final depending on how much time we have. Use Secondary Textbook #2 (since APEX does not treat spherical coordinates). Alternatively, we can use Section 15.9 of Stewart. Raw notes: Nov28 Nov30 Dec02. Filled notes: Nov28 Nov30
Extra notes with solutions of problems suggested previously: An extra note on differential calculus: extra-differential. Warning: most of these problems are hard and not very common. Don’t spend too much time on them before you have learned the basics. An extra note on integral calculus: extra-integral. Unlike problems in the note extra-differential above, these are typical problems and you should know how to solve them. |