Math2210 - Multivariable Calculus, Spring 2012

Instructor: Paweł Nurowski

Homework grader:Dayna Hinchcliff, email: dayna.hinchcliff@aggiemail.usu.edu

Lectures:
Section 002 Mon-Wed-Fri 10:30-11:20, ENGR203.
Section 005 Mon-Wed-Fri 12:30-1:20, AGSC302.

Office hours: Mon, Wed 2:00-3:00 p.m.

Textbook: University Calculus, by Hass, Weir and Thomas, Pearson-Addison Wesley, 2007.
We will cover the majority of material from chapters 12-14.

Homework: Homework (problem sets) are due each Wednesday in class except weeks of exams. These problem sets will be posted on this web page each Wednesday. Late homework is NOT accepted. They should be folded and stapled with your name and the class (Math 2210) written on the outside. These problem sets are essential in learning calculus. They are not a test and you are encouraged to talk to other students about difficult problems - after you have found them to be difficult. You must write out your own solutions. Be neat to get maximum credit.

Exams: There will be two one hour exams during class. See approximate schedule below for time and content. The use of calculators, notes, etc. is not permitted during exams.

Grading Policy: There will be two midterm examinations, a final comprehensive examination, and weekly problem sets given to determine your final grade. Each midterm examination will be worth 20% of your final grade; the final examination is worth 40% of your final grade, and the weekly assignments will amount to 20% of your final grade.

A Note on Incompletes: I have a very strict, personal policy on incomplete grades: I will not give an incomplete grade unless the student has been ill for a good part of the semester and can obtain a doctor's medical certificate to authenticate the illness. NO EXCEPTIONS!

Provisional Schedule:
Chapter 12: Partial derivatives
TEST # 1: Wednesday, Feb, 15th.
Chapter 13: Multiple Integrals
TEST # 2 Wedenesday, Mar, 28th.
Chapter 14: Integration in Vector Fields

FINAL EXAM:
Section 002: Wednesday, May 2, 9:30 - 11:20 am
Section 005: Wednesday, May 2, 11:30 am - 1:20 pm

Practice exam: Click here.

Answers to the practice exam: Click here.

Topics and Assignments

 

           Week                                                                  Topics                         Assignments
Jan 9-15
12.1 Functions of several variables
12.2 Limits and continuity in higher dimensions
 Exs Section 12.2: 1, 6, 9, 13, 19, 27 a,b, 35, 36, 42, 45, 47
Due Jan 23th
Jan 16-22
12.3 Partial derivatives
 Exs Section 12.3: 4, 12, 13, 24, 29, 33, 44, 49, 52
Due Jan 30th
Jan 23-29
12.4 The chain Rule
12.5 Directional derivatives and gradient vectors
 Exs Section 12.4: 5, 9, 10, 11, 25, 27, 29
Due Feb 6th
Jan 30-Feb 5
12.6 Tangent planes and differentials
12.7 Extreme values and saddle points
Exs Section 12.5: 9, 16, 18, 32; Section 12.6: 1, 2, 3, 8
Due Feb 13th
Feb 6- 12
12.9 Taylor's formula for two variables
****Review of Chapter 12
Exs Section 12.7: 1, 2, 4, 5, 13, 31, Understand 55 (not a report on this is needed!) and write down solutions to 56, 57
Exs Section 12.9: 1, 4
Due Feb 22nd
Feb 13-19
*** Test #1
13.1 Double and iterated integrals over rectangles
 
Feb 20-26
13.2 Double integrals over general regions
13.3 Area by double integration
Exs Section 13.1: 6, 8, 10, 13, 14
Exs Section 13.2: 3, 6, 10, 35, 39
Due Feb 29th
Feb 27-Mar 4
13.4 Double Integrals in Polar Form
13.5 Tripple Integrals in Rectangular Coordinates
13.6 Average values, volume, area, mass, center of mass and moments of inertia
Exs Section 13.3: 11, 13, 15
Exs Section 13.4: 12, 13, 31
Exs Section 13.5: 3, 22, 25, 32
Due: Mar 7th
Mar 5-11
13.7 Tripple Integrals in Cylindrical and Spherical Coordinates
13.8 Substitutions in Multiple Integrals
Exs Section 13.6: 1, 2, 21
Exs Section 13.7: 33, 38, 43, 44, 48
Exs Section 13.8: 6, 12
Due: Mar 21
Mar 19-25
*** Review of Chapter 13 and Examples
 
Mar 26-Apr 1
*** Test #2
14.1 Line integrals
14.2 Vector fields, work, circulation and flux
Exs Section 14.1: 10, 11, 15, 16, 18, 23, 30
Due: Apr 11th
Apr 2-8
14.3 Path Independence, Potential Functions and Conservative Fields. Finding potentials for conservative fields.
Exs Section 14.2: 7, 9, 11, 22, 23, 24, 25, 26, 27, 28, 34, 37, 38, 39, 40, 41
Due: Apr 11th
Apr 9-15
14.4 Green's theorem in the plane
14.5 Surfaces and area.
Exs Section 14.3: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Exs Section 14.4: 6, 13, 17, 18, 19, 20, 24
Due: Apr 18th
Apr 16-22
14.6 Surface integrals and flux
14.7 Stokes' Theorem
Exs Section 14.5: 4, 5, 13, 15, 17-25, 37, 41
Exs Section 14.6: 4, 7, 8, 16, 17, 18, 25, 35
Due: Apr 25th
Apr 23-27
14.8 The divergence theorem and a unified theory
*** Final review
 
Wednesday, May 2nd
 
FINAL EXAM

Note the time:
Section 002: 9:30 - 11:20 am
Section 005: 11:30 am - 1:20 pm
 
 

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Email corrections and comments to nurowski@fuw.edu.pl