Math 200                 Section 106    Fall 2018

Multivariable Calculus

Section Specific Information

Time/Place:  MWF  15:00-16:00,  LSK 200
Instructor:  K. Behrend

Office hours during final exam period:
Wed, Dec 5, 10:00-12:00
Fri, Dec 7, 10:00-12:00
Math Annex 1213.

TA:  N. Lawrence
contact info
No office hours during final exam period.

Math Learning Centre:
Open during exam period on Dec 3, 4, 10, 11.
LSK 301 and 302

Central Course Page  contains the syllabus, policies,
practice problems, textbook information, webwork link, etc.
Tests:  There will be four in-class tests, each approximately
20 minutes in duration.

The following applies to all tests in Math 220:
No aids of any kind: no calculators, no notes, no books.
No cell phones, no ipods, no electronic devices of any kind.

If you miss one of the tests for medical reasons, you need to
promptly inform the instructor, and provide a physician's note
specifically stating that you were medically unfit to write the missed
exam on that day. No make-up exams will be given. Your grade
will be based on the other course components.
Test 1  Friday, Sep. 21:  3-D geometry

Material: All Material covered in class up to and inluding Friday, September 14. In the textbook CLP3 this corresponds to sections 1.1, 1.2 (skip the optional ones), 1.7, 1.8, 1.9. In particular, know the distance formula between two points, understand the technique of sketching a surface by identifying its 'traces' with constant coordinate planes. Know the basics of vector arithmetic. Know the dot product, the angle formula, and projections. Know the cross product, its geometric meaning and the corresponding formulas for the area of parallelograms and volume of parallelepipeds.

Review in-class examples, webwork problems from the first two assignments, as well as suggested problems listed on the central course page.

Note. You must at least know how to sketch the following in the xy-plane: parabolas, ellipses, hyperbolas, and graphs of sine, cosine, exponential and logarithm. Do not memorize names of various 'quadtric surfaces' or other families of surfaces in 3D.

Solutions. Problem 1   Problem 2   Problem 3   Problem 4   The class average was 12/16=75%.
Test 2  Friday, Oct. 12:  Differentiation I

Material: All Materical covered in class up to and including Friday, October 5. In CLP3, this corresponds to Sections 2.1, 2.2, 2.3, 2.4 (skip 2.4.3 and 2.4.4), 2.5, 2.6 (skip 2.6.1 and 2.6.2). In particular, be able to compute limits, or show that they don't exist, compute partial derivatives, and know Clairaut's theorem. Know that continuity of partial derivatives implies differentiability, that differentiability means that the graph looks more and more like its tangent plane if you zoom in, an also that the error in f relative to the errors in x and y goes to zero as the errors in x and y go to zero, justifying the linear approximation procedure for differentiable functions. Be able to compute equations for tangent planes, and parametric equations for normal lines. Be able to linearly approximate values of several variable functions, and estimate the error terms. Read off simple properties of partial derivatives from contour plots. Apply the chain rule in several variables.

Practice Problems: The following problems from previous final exams are especially relevant:
2016WT1 #3 a
2015WT1 #2 ii
2011WT2 #2 a
2011WT2 #2 b
2011WT1 #1 b, c
2013WT2 #2 a
2013WT1 #1 c
2013WT1 #1 d

Solutions. Problem 1  Problem 2  Problem 3  Problem 3(c)  The class average was 10.4/16=65%.
Test 3  Friday, Oct. 26:  Differentiation II

Material: All Material covered in class up to and including Friday, October 19. In CLP3, this corresponds to 2.7, 2.9. In particular, know the gradient vector of a function of 2 or 3 variables and its geometric interpretation, its use in computing tangent lines/planes and normal lines, the directional derivative and how to compute it, the definitions of local maxima/minima and the fact that they only occur at critical points (in class we used the term critical point for both stationary points and singular points), or on the boundary of the domain, Second Derivative Test for functions of 2 variables.

Practice Problems: The following problems from previous final exams are especially relevant:
2016WT1 #2
2016WT1 #3
2015WT1 #1 c
2015WT1 #2
2015WT1 #4
2014WT1 #1
2014WT1 #4
2014WT1 #5
2013WT2 #2 b
2013WT2 #3 b

Solutions. Problem 1  Problem 2  Problem 3  Problem 4  The class average was 12/18=67%.
Test 4  Friday, Nov. 16:  Integration

Material: All Material about multiple integrals and iterated integrals covered in class up to and including Friday, November 9. In CLP3, this corresponds to 3.1 (including the optional section 3.1.5), 3.2 (excluding the optional section 3.2.4), and 3.3 (skip moment of inertia). In particular, know the definition of multiple integrals in terms of Riemann sums, and how to use Riemann sums to approximate the integral. Be familiar with Fubini's theorem, which says that we can evaluate multiple integrals by doing iterated integrals (and that we can choose in which order to perfrom the iterated integrals). Be able to evaluate multiple integrals and iterated integrals, with particular care to finding correct boundaries for the integrals. Be able to use multiple integrals to find volumes, areas, averages, total mass, centre of mass (this includes memorizing the necessary formulas).

Practice Problems: The following problems from previous final exams are especially relevant:
2015WT1 #6 c
2014WT1 #6
2013WT2 #5
2013WT2 #6 a
2013WT1 #5
2013WT1 #6
2012WT1 #7
2012WT1 #8

Solutions. Problem 1  Problem 2  Problem 3  The class average was 12/15=80%.
Final Exam  Wednesday, Dec. 12, 8:30-11:00.

See the common course page for important information about seating arrangements at the final exam.

Material: The final exam will cover all material treated this semester. In addition to the subjects listed above, this includes Lagrange multipliers (Section 2.10, without the optional 2.10.1, in CLP3) and triple integrals (Sections 3.5, 3.6, 3.7 in CLP3).

No electronic devices of any kind are allowed at the final exam. No books or notes are allowed. One formula sheet will be provided. This is the same formula sheet which was provided in previous years, see 2016WT1 here.

You are expected to be familiar with basic integration techniques: simple substitutions, integration by parts, antiderivatives of standard functions (polynomials, sin, cos, exp, ln, etc).

The UBC Math Club may be selling exam packages. Check them out.

Another resource for solutions to past exams is here.