Maths21a: Multivariable Calculus of the Harvard Summerschool 2009

This is a standard multivariable calculus course.
It extends single variable calculus to higher dimensions;
It provides vocabulary for understanding fundamental
equations of nature like weather, planetary motion,
waves, heat, finance, epidemiology, or quantum mechanics.
It teaches important background needed for statistics,
computergraphics, bioinformatics, etc;
It builds tools for describing curves, surfaces, solids
and other geometrical objects in three dimensions;
It develops methods for solving optimization problems with
and without constraints;
It makes you acquainted with a powerful computer algebra system.
It prepares you for further study in other fields of
mathematics and its applications;
It improves thinking skills, problem solving skills,
visualization skills as well as computing skills;

Lectures:

Every Tuesday and Thursday at 8:3011:30,

Sections:

Thursday 12.

Course assistant:

Chris Phillips

Office hours: Thursday 2 PM.

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 (current multivariable textbooks are
all very similar). We cover the material which can be found in chapters 912 of Stewart
or chapters 1014 in Varberg Purcell Rigdon or chapters 1015 in
Smith Minton. 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. Homework is due on Tuesdays except for the
last week, where the homework is due daily.

Exams:

Two midterm exams and one final exam. The midterms on July 9 and July 23
will be administered during class time in the usual lecture hall.
The final exam will take place during the examination period in the usual
lecture hall.

Grades:

First and second hourly 40 % total
Homework 25 %
Project 5 %
Final 30 %
Active class participation and attendance 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 Mathematica project.

Mathematica 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 license for Mathematica, a professional
computer algebra system. Using
this software does not lead to any additional expenses.
The total time for doing the lab is a few hours.
The project will be handed in at the beginning of the lecture
on July 30.

Calendar:

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

Day to day syllabus:

1. Week: Geometry and Space
June 23: space, vectors,
dot product, projection
June 25: cross product, lines,
planes, distances
2. Week: Surfaces and Curves
June 30: functions, graphs,
implicit and parametric surfaces
July 2: curves, velocity, acceleration,
chain rule and curvature
3. Week: Linearization and Gradient
July 7: partial derivatives,
partial differential equations, review
July 9: first midterm
gradient, linearization
tangent lines and planes
4. Week: Extrema and Lagrange Multipliers
July 14: extrema, second derivative test,
Lagrange multiplier method
July 16: double integrals, Type I and II regions
polar integration, surface area
5. Week: Double Integrals and Triple Integrals
July 21: triple integrals, cylindrical coordinates
integration in spherical coordinates
July 23: second midterm (on week 34)
vector fields and line integrals
6. Week: Vector fields and Integral Theorems
July 28: 2d curl and Greens theorem
3d curl and flux integrals
July 30: Stokes theorem
Gauss theorem.
7. Week: Final exam (Aug 6)
