Maths21a: Multivariable Calculus of the Harvard Summerschool 2007

Extends single variable calculus to higher dimensions;
Provides vocabulary for understanding fundamental
equations of nature like weather, planetary motion,
waves, heat, finance, epidemiology, or quantum mechanics.
Teaches important background needed for statistics,
computergraphics, bioinformatics, etc;
Provides tools for describing curves, surfaces, solids
and other geometrical objects in three dimensions;
Develops methods for solving optimization problems with
and without constraints;
Learn a powerful computer algebra system;
Prepares you for further study in other fields of
mathematics and its applications;
Improves thinking skills, problem solving skills,
visualization skills as well as computing skills;

Lectures:

Every Tuesday, Wednesday, and Thursday at 9:3011:00,
lectures start at 9:30 sharp.

Sections:

Thursday 89 Emerson Hall 307
and 12 PM, Emerson Hall 106. Every student choses one section.

Course assistant: Emil Pitkin (pitkin@fas.harvard.edu).

TBA

Office hours:

Oliver: Monday 15:3016:30, SC 434 and by appointment

Website

http://www.courses.fas.harvard.edu/~maths21a

Text:

Reading a textbook gives you a second opinion on the material.
A widely used textbook is
"Multivariable Calculus: Concepts and Contexts" by James Stewart.
but any multivariable text works. Homework will be distributed each
class during lecture. Homework problems are handed out in class.

Homework:

Weekly HW will be assigned in three parts,
one in each lecture. You will receive a handout for
each problem set. Problems will not be assigned
from books.

Exams:

Two midterm exams and one final exam. The midterms on July 12 and July 26
will be administered during class time in the usual lecture hall.
The final will take place during the examination period. The place and
time will be a announced.

Grades:

First and second hourly 40 % total
Homework 25 %
Project 5 %
Final 30 %
Active class participation and attendence can boost your final
grade by up to 5%.

Graduate Credit:

This course can be taken for graduate credit.
The course work is the same. To fulfill the graduate credit,
a minimal 2/3 score must be reached for the final project.

Computer project;

The use of computers and other electronic aids can not permitted
during exams. A Mathematica project will teach you the basics
of a computer algebra system.
Harvard has a site licence for Mathematica. Using
this software does not lead to any additional expenses.
The total time for doing the lab is a few hours. Instead of
the computer algebra project, a student can
work on some challenge problems or write a paper on a subject.
The project will be handed in at the start of the last lecture.

Calendar:

++ ++
Su Mo Tu We Th  Fr Sa Events WeekExamProj
++ ++
24 25 26 27 28  29 30 June  1   
1 2 3 4 5  6 7 July  2   
8 9 10 11 12  13 14 12. hourly 3  *  
15 16 17 18 19  20 21  4   
22 23 24 25 26  27 28 26. hourly 5  *  
29 30 31 1 2  3 4 August  6   
5 6 7 8 9  10 11  7   * 
12 13 14 15 16  17 18 final   *  
++ ++

Day to day syllabus:

1. Week: Geometry and Space
26. June: introduction, Eulidean space
27. June: vectors, dot product, projection
28. July: cross product, lines, planes, distances
2. Week: Functions and Surfaces
3. July: functions, graphs, quadrics
4. July: independence day, no class
5. July: implicit and parametric surfaces
3. Week: Curves and Partial Derivatives
10. July: curves, velocity, acceleration, chain rule
11. July: arclength, curvature, partial derivatives
12. July: first midterm (on week 12)
4. Week: Extrema and Lagrange Multipliers
17. July: gradient, linearization, tangents
18. July: extrema, second derivative test
19. July: extrema with constraints
5. Week: Double Integrals and Surface Integrals
24. July: double integrals, type I,II regions
25. July: polar coordinates, surface area
26. July: second midterm (on week 34)
6. Week: Triple Integrals and Line Integrals
31. July: triple integrals, cylindrical coordinates
1. August: spherical coordinates, vector fields
2. August: line integrals, fundamental thm of lineintegrals
7. Week: Exterior Derivatives and Integral Theorems
7. August: curl and Green theorem
8. August: curl and Stokes theorem
9. August: div and Gauss theorem
12 August: Final review
14 August: Final exam (on week 17)
Exam:
