MATH 200-Section 104-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 104 when using this page. This page is still under construction, below information might be modified.
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.
· 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.
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.
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.
Quiz 4: Wednesday Nov 9 (since Fri Nov 11 is a holiday)
Quiz 5: Friday Nov 18
Quiz 6: Friday Nov 25
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.
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.
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
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