 MathS21a: Multivariable Calculus
 Instructor: Oliver Knill, SC434, knill@math
 Course assistant Brad Burns, bpburns@fas
 Lectures: Every Tuesday, Wednesday, and Thursday at 9:3011:00,
lectures start 9:30 sharp
 Place: Lecture Hall Emerson 101
 Sections: Thursday 89 and 12 PM, Lecture Hall Emerson 104
 Office hours: Oliver: Wednesday 14:0015:30, SC434
Monday 10:0011:00, SC 434 and by appointment
Brad: Mondays 16:0017:00 Math common room.
 Website: http://www.courses.fas.harvard.edu/~maths21a/
 Text:
Handouts, other material and homework will be distributed in each class.
This allows to follow the course without book. We recommend to read besides
in a book like "Multivariable Calculus: Concepts and Contexts" by James
Stewart in addition to following the lectures.
 About this course:
 extends single variable calculus to higher dimensions;
 provides vocabulary for understanding the fundamental
equations of nature (e.g. weather, heat, planetary motion,
waves, finance, epidemiology, quantum mechanics,
bioinformatics, etc.);
 provides tools for describing curves, surfaces, and other
geometrical objects in three dimensions;
 develops methods for solving optimization problems with and
without constraints;
 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;
 Homework: Weekly HW will be assigned in three parts,
one in each lecture. Homework is collected weekly
in class on Tuesdays at the beginning of the lecture.
 Computers: The use of computers and other
electronic aids is not permitted during exams.
A Mathematica project is optional and will teach you
the basics of a computer algebra system.
 Exams:
Two midterm exams and one final exam.
 Grades:
First and second hourly 40 %
Homework 25 %
Project 5 %
Final 30 %
The higherscoring midterm will be worth 25%, the other midterm
will be worth 15%. If the grade on the final exam is higher than
the grade from the composite score, then the final grade for the
course will be equal to the grade on the final exam.
Active class participation and attendence can boost your grade by
up to 5%.
 Calendar: (21 sessions: 19 lectures plus 2 midterms in 7 weeks)
++
Su Mo Tu We Th  Fr Sa
 
22 23 24 25 26  27 28 June 1
29 30 1 2 3  4 5 July 2
6 7 8 9 10  11 12 3
13 14 15 16 17  18 19 4
20 21 22 23 24  25 26 5
27 28 29 30 31  1 2 August 6
3 4 5 6 7  8 9 7
10 11 12 13 14  15 16 [13'th 09:00 AM, Final]
++
 Day to day syllabus:
1. Week: Geometry and Space
24. June: introduction, space, coordinates, distance
25. June: vectors, dot product, projections
26. June: cross product, lines
2. Week: Functions and Graphs
1. July: planes, distance formulas
2. July: functions, graphs, quadrics
3. July: parametric surfaces
3. Week: Curves and Surfaces
8. July: curves, velocity, acceleration
9. July: arclength, curvature
10. July: first midterm (week 12)
4. Week: Extrema and Lagrange Multipliers
15. July: pde's, gradient, chain rule, tangents
16. July: extrema, second derivative test
17. July: extrema with constraints
5. Week: Double Integrals and Surface Area
22. July: double integrals, type I,II regions
23. July: general regions, polar coordinates
24. July: surface area
6. Week: Triple Integrals and line integrals
29. July: triple integrals, other coordinates
30. July: line integrals, fundamental thm of lineintegrals
31. July: second midterm (week 35)
7. Week: Vector Fields and Integral Theorems
5. August: curl and Greens theorem
6. August: curl and Stokes theorem
7. August: div and divergence theorem
13. August: Final exam (week 17)
