 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
graphical objects in three dimensions;
 develops methods for solving optimization problems with and
without constraints;
 prepares you for further study both in other fields of
mathematics and its applications;
 improves thinking skills, problem solving skills,
visualization skills, and computing skills;
 Prerequisites: Math 1b or equivalent
 How to Sign Up: Input your time preferences on the web by Thursday Jan 30.
 Section Types: Regular, Physics, BioChem flavors.
 Introductory Meeting: Wednesday, Jan 29, Science Center B at 8 AM
If you missed it: here are the slides (Quicktime 10 Meg).
 Lectures Start: Feb 3 for MWF sections, Feb 4 for TTh sections
 Course Head: Oliver Knill
Science Center SC434
knill@math.harvard.edu
 Sections:
 Weekly Recitations: Arranged by Course Assistants
 Question Center: 810 pm except Fridays and Saturdays in Loker Commons
 Text: "Multivariable Calculus: Concepts and Contexts" by James Stewart.
Plus handouts and other material for special sections.
 Homework: Weekly HW assigned in small parts, one part per lecture.
No late homework is accepted. You are encouraged to
discuss solution strategies with classmates, but you
must write up answers yourself in your own words. As
with any academic work, please cite sources consulted.
 Computers: The use of computers and other electronic aids
is not be permitted during exams. Mathematica
project is an option for a project.
 Exams:
First Hourly at 7:00 p.m. on Monday, Mar 10, Sci Ctr C
Second Hourly at 7:00 p.m. on Wednesday, Apr 23. Sci Ctr D and E.
Final Examination: will be scheduled by registrar.
 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.
 Calendar: 12 weeks
Su Mo Tu We Th Fr Sa Week Special dates Month
+
26 27 28 29 30 31 1 29. Jan. Intro Meeting Jan
2 3 4 5 6 7 8 1 3. Feb. Classes start Feb
9 10 11 12 13 14 15 2
16 17 18 19 20 21 22 3 17. Feb. Presidents day
23 24 25 26 27 28 1 4
2 3 4 5 6 7 8 5 Mar
9 10 11 12 13 14 15 6 10. Mar. 1. Hourly
16 17 18 19 20 21 22 7
23 24 25 26 27 28 29 Spring break
30 31 1 2 3 4 5 8 Apr
6 7 8 9 10 11 12 9
13 14 15 16 17 18 19 10
20 21 22 23 24 25 26 11 23. Apr. 2. Hourly
27 28 29 30 1 2 3 12 May
4 5 6 7 8 9 10 Reading period > 14.
11 12 13 14 15 16 17 Exam period > 23.
18 19 20 21 22 23 24
+
 Day to Day syllabus:
Hour Topic Book section
1. Geometry of Space
1  coordinates 9.1
 distance
2  vectors 9.2
 dot product 9.3
3  cross product 9.4
2. Functions and Graphs
1  lines and planes 9.5
 distance formulas
2  functions 9.6
graphs
3  level curves
 quadrics
3. Curves
1  holiday (presidents day)
2  curves in space 10.1
 velocity
 acceleration 10.2
3  arc length 10.3
 curvature 10.4
4. Surfaces
1  cylindrical coordinates 9.7
 spherical coordinates
2  parametric surfaces 10.5
3  functions 11.1
 continuity 11.2
5. Partial Derivatives
1  partial derivatives 11.3
Solutions to PDE's I
2  linear approximation 11.4
3  review for first hourly
First Midterm (on chapters 910, 11.111.2)
6. Chain rule
1  chain rule 11.5
implicit differentiation
2  gradient
gradient and level curves
3  directional derivative 11.6
direction with steepest slope
7. Extrema
1  maxima, minima, saddle points 11.7
2  Lagrange multipliers 11.8
3  Combined problems
Spring break
8. Double Integrals
1  double integrals 12.1
 iterated integrals 12.2
2  general regions 12.3
 polar coordinates 12.4
3  surface area 12.6
9. Triple Integrals
1  triple integrals 12.7
2  cylinder spherical coordinates 12.8
3  change of variables 12.9
10. Line Integrals
1  vector fields 13.1
2  line integrals 13.2
3  fundamental thm line integrals 13.3
Second Midterm (through chapter 12, 13.1)
11. Integral Theorems I
1  some inclass review
2  Greens theorem 13.4
3  curl and divergence 13.5
12. Integral Theorems II
1  surface integrals 13.6
2  Stokes theorem 13.7
3  Gauss theorem 13.8
 Applications 13.9
