22M:42
Engineering Multivariate Calculus
Section 111
Fall 2001

Contact/class information

Instructor:	Dr. David Stewart
Phone:	335-3832
Email:	dstewart@math.uiowa.edu
WWW URL:	http://www.math.uiowa.edu/~dstewart/
Office:	MLH 325B
Office hours:	TBA
Class times:	MWF 11:30am-12:30pm
Class location:	219 Jessup Hall

 

You can see me outside the office hours provided it is mutually convenient. You can use email to set up an appointment time.
 
 

Description

This course is about understanding vectors, matrices, and using multivariate calculus to understand and analyze vector-valued functions and functions of several variables; find lengths of curves, areas of surfaces, and volumes of regions; find minima and maxima; etc. We will also see how to compute limits, and find integrals of functions over areas and volumes. The last chapter we plan to study is about vector-valued functions of several variables which are vital for modeling fluid flow, elastic bodies (as in structural analysis), and electromagnetism.
 
 

Textbook

Calculus and Analytic Geometry by R. Ellis and D. Gulick, 5th edition (1994). Published by Saunders College Publishing. This course covers chapters 12-15 and some of chapter 11. This textbook is available through the University bookstore.
 
 

Syllabus

1. Chapter 11: Review of lines, planes, vectors, dot and cross products.
2. Chapter 12: Vector-valued functions of a single variables; curves: length, tangents, normals and curvature.
3. Chapter 13: Functions of several variables: partial derivatives (imagine only one variable changes); limits and continuity; chain rule; higher order partial derivatives; directional derivatives, and gradients; maxima and minima and the Lagrange multiplier rule.
4. Chapter 14: Multiple integrals: double integrals; polar co-ordinates; surface area; triple integrals; cylindrical and spherical co-ordinates; change of variables rules.
5. Chapter 15: Vector fields: line integrals; Green's theorem; surface integrals; Stoke's theorem: curl, div and all that.

Assessment

There will be weekly homework assignments, two mid-semester exams, and a final comprehensive exam. The homework will count for 30% of the final assessment, the mid-semester exams will count 20% of the final assessment each, and the final exam will count for the remaining 30% of the assessment. There will also be ungraded exercises to help you exercise your skills.

The homework is a vital part of the course. If you don't do it, you won't just miss out on 30% of the assessment, but you probably won't get the practice or learn what you need for doing the exams either.
 
 

Notes

The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes.

You should also make a habit of reviewing the class web page:

http://www.math.uiowa.edu/~dstewart/classes/22m042/

This page will have homework details and other information posted to it as the class progresses.

The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.

Please let you instructor know if you have a disability that requires special arrangements. I need to hear from anyone who has a disability which may require some modification of seating, testing or other class requirements so that appropriate arrangements can be made. Please see me after class or during my office hours.

Be sure to read the section titled Student Complaints Concerning Faculty Actions on page 23 of the Schedule of Classes (Fall 1999).