Math 18: Intermediate Calculus

Emily Dumas

Brown University
Spring 2007

General Information

Lectures	Section 1: MWF 12:00pm - 12:50pm in BH158 Section 2: MWF 2:00pm - 2:50pm in BH158
Recitation	Section A: Tues 5:00pm - 5:50pm in BH158 Section B: Thurs 5:00pm - 5:50pm in BH158
Text	Multivariable Calculus by J. Stewart, 5th edition, chapters 13-17. (Same as Multivariable Calculus - Early Transcendentals chapters 12-16.)
Instructor	Emily Dumas () Office hours Mondays 3-4pm, Thursdays 2-3pm in Kassar 114.
Teaching Assistant	Charis Tsikkou () Office hours Wednesdays 3-5pm in Kassar 013
Homework Policies	Homework will be assigned in most lectures and collected weekly in class.
	Late homework will NOT be accepted. There are no exceptions to this policy.
	You can discuss the homework with other students, but you must write (and understand!) your own solutions.
	The homework problems depend on material from both the assigned reading and the lectures. Do not leave the problem sets or reading to the last minute!
Calculator Policy	A calculator is not required in Math 18, and calculators are not permitted at the exams.
	While you may use a calculator on the homework, do so with care, and never as a substitute for understanding.

Important Dates

There are two one-hour midterm exams and a final exam. (Note that Exam 1 was moved in the second week because of a conflict with Chem 35.)

Exam 1	Tues, Feb 27, 7-8pm	117 MacMillan
Exam 2	Wed, Apr 11, 7-8pm	117 MacMillan
Final Exam	Wed, May 16, 2-5pm	001 Salomon

Grading

Your course grade is determined on the following basis:

Homework	20%
Exam 1	25%
Exam 2	25%
Final Exam	30%

When computing your homework grade, the lowest homework score will be dropped.

Handouts

These documents are available for download in PDF format.

• Course Syllabus
• Exam 1 and solutions
• Exam 2 and solutions
• Final Exam

Homework and Reading

See the complete list of old homework and reading assignments

We covered chapters 13-17 in the textbook (Multivariable Calculus by J. Stewart, 5th edition). The midterm exams covered chapters 13-16 as follows:

• Exam 1 covered 13.1 - 15.4
• Exam 2 covered 15.5 - 16.9

Chapter 17 (vector fields) has been our focus since the second exam. The cumulative final exam covers all of the material from the course. The final homework assignment was due on the last day of lecture:

• Homework 13: Due Monday, May 7
  • Section 17.6 exercises: 31, 36
  • Section 17.7 exercises: 5, 7, 11, 19, 21, 23
  • Section 17.8 exercises: 5, 9, 18,19
  • Section 17.9 exercises: 9, 13, 20

Online Resources

Visualization tools

These online tools (java applets, etc.) for interactive visualization complement the material from the textbook and lectures.

• Cross product demonstration from the Syracuse University Department of Physics
• Interactive gallery of quadric surfaces by Jonathan Rogness of the University of Minnesota
• Parameterized space curves and derivatives (Rogness)
• Space curve applet from Daniel Kleitman at MIT
• Level curve applet, written by Thomas Banchoff with customization by Mike May of Saint Louis University.
• Geometry of partial derivatives and the tangent plane (Rogness)
• Tangent plane applet (Banchoff/May)
• Directional derivative applet, shows the relationship between the directional derivative and the gradient vector (Kleitman)
• Lagrange multipliers applet from Denis Auroux at MIT
• The intersection of two orthogonal cylinders:
  • Steinmetz Solid from MathWorld (includes interactive 3d view)
  • Cylinders applet by Paul Garrett

Miscellaneous

• Classification of quadric surfaces - describes how the ten coefficients (A...J) of a general quadric surface are related to its standard form (e.g. elliptic hyperboloid, ellipsoid, etc.).
• Discussion of the KdV equation; also see these animated solitons.

Resources

The following resources are available for help with Math 18:

• Recitation section. You should attend one of the weekly recitation sections run by the teaching assistant. The recitation is an ideal place to ask questions about the lectures and homework assignments.
• Other students. You are encouraged to talk to other Math 18 students about the lectures, reading, and homework assignments. (However, even if you discuss the homework with others, you must write the solutions yourself and they should represent your understanding of the material.)
• Office hours. Instructor and teaching assistant office hours are listed above. You can come during those times to discuss anything about the course, or make an appointment for a different time. E-mail is the best way to contact course personnel.
• Math Resource Center. The MRC offers walk-in help for calculus students in 105 Kassar, Monday through Thursday, 8-10pm. The MRC staff consists of graduate students in math and applied math, and some advanced undergraduates.

  The full schedule (including holidays, etc.) and other information can be found on the Math Resource Center Home Page.

  Additional group tutoring/help is available on Tuesdays and Thursdays, 7-9pm, in 129 Metcalf.

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