- 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, quanta, 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;
- taught by trained faculty and teaching fellows in small
coordinated sections rather than in one big lecture.
- Prerequisites: Math 1b or equivalent
- How to Sign Up: Input your time preferences on the web by Sept 19
by noon Sept 19. See mainpage.
- Section Types: Regular, Physics, BioChemistry, Computer Science
Flavors are helpful and interesting, but not critical.
- Introductory Meeting: Wednesday, Sept 18, Science Center C at 8 AM
- Lectures Start: Sept 23 for MWF sections, Sept 24 for TTh sections
- Course Head: Prof. Daniel Goroff
Science Center SC-427
Office Hours Tues and Weds 11:30-1:00 and by
appointment.
- Sections:
No Times
I M W F at 9 (with sufficient enrollment)
II M W F at 10
III M W F at 11
IV M W F at 12
V Tu Th 10-11:30
VI Tu Th 11:30-1
- Weekly Recitations: Arranged by Course Assistants
- Question Center: 8-10 pm except Fridays and Saturdays in Loker Commons
"How to Succeed with Calculus" session at 8pm on Sept 25.
- 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
projects as option in section project.
- Exams: First Hourly at 7:30 p.m. on Wednesday, Oct 16, Sci Ctr D
Second Hourly at 7:30 p.m. on Thursday, Nov 21. Jefferson 250
Final Examination: Monday, Jan 13, or as revised by registrar.
- Reading Period: Optional class wide reviews based on practice examinations.
Complete either a short project or an hour long section test.
- Grades: There is a total target of T=2000 points for this course.
Roughly, we expect people who end up with over 1800 points to
receive some kind of A, people who have 1600-1890 points to
receive some kind of B, etc. A maximum of 1620 points can be
obtained during the term:
12 Homeworks, each 60 points 720 points
2 Hour Exams, each 350 points 700 points
1 Project or Section Test, 200 points 200 points
Total 1620
If you earn N points during the term, your final exam will be worth
a possible T-N points. For example,
1) If you enter the final with all 1620 points and get
50% correct on the final, your course total will be:
1620 + (2000-1620) * 50/100 = 1810 (probably a low A or high B).
2) If you enter the final with 860 points and get
70% correct on the final, your course total will be:
860 + (2000-860) * 70/100 = 1588 (probably a low B).
Notice this means you can earn back on the final any point you
miss during the term, so you always have an incentive to keep
working. This grading system is very kind to anyone who
eventually masters the material by the day of the final, but very
risky for anyone who tries to wait until then. Please keep up,
work lots of problems, go over everything you did not get right
the first time, ask lots of questions, and you will do fine.
- Calendar: 12 weeks
Su Mo Tu We Th Fr Sa Week Special dates Month
-----------------------------------------------------------------+
1 2 3 4 5 6 7 SEP |
8 9 10 11 12 13 14 16.-19. Advise, 16-19. Section |
15 16 17 18 19 20 21 18th All 21a Meeting , 8am, SC-C |
22 23 24 25 26 27 28 1 23rd Calculus Lectures start |
29 30 1 2 3 4 5 2 OCT |
6 7 8 9 10 11 12 3 |
13 14 15 16 17 18 19 4 14th Columbus day holiday |
20 21 22 23 24 25 26 5 |
27 28 29 30 31 1 2 6 NOV |
3 4 5 6 7 8 9 7 |
10 11 12 13 14 15 16 8 11th Veterans Day Holiday |
17 18 19 20 21 22 23 9 |
24 25 26 27 28 29 30 10 28-30th Thanksgiving Holiday |
1 2 3 4 5 6 7 11 DEC |
8 9 10 11 12 13 14 12 |
15 16 17 18 19 20 21 13 19-1st Winter Break |
22 23 24 25 26 27 28 |
29 30 31 1 2 3 4 2-11 Reading period JAN |
5 6 7 8 9 10 11 |
12 13 14 15 16 17 18 13th Epected Final Exam Date |
19 20 21 22 23 24 25 |
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- Day to Day syllabus:
Hour Topic Book section
Geometry of Space
1 - coordinates 9.1
- distance
2 - vectors 9.2
- dot product 9.3
3 - cross product 9.4
- lines and planes 9.5
Functions and Graphs
1 - functions 9.6
graphs
2 - level curves
quadrics
3 - cylindrical coordinates 9.7
- spherical coordinates
Curves and Surfaces
1 - curves in space 10.1
examples
2 - velocity
- acceleration 10.2
3 - arc length 10.3
- curves as solutions of ODE's
Surfaces
1 - holiday
2 - parametric surfaces 10.5
3 - review for first hourly
First Midterm (on chapters 9-10)
Partial Derivatives
1 - functions 11.1
- continuity 11.2
2 - partial derivatives 11.3
3 - linear approximation 11.4
Chain rule
1 - chain rule 11.5
2 - gradient
3 - directional derivative 11.6
- Solutions to PDE's
Extrema
1 - maxima, minima, saddle points 11.7
2 - Lagrange multipliers 11.8
3 - Combined
Double Integrals
1 - Veterans day
2 - double integrals 12.1
- iterated integrals 12.2
- general regions 12.3
3 - polar coordinates 12.4
- surface area 12.6
Triple Integrals
1 - triple integrals 12.7
2 - cylinder spherical coordinates 12.8
- change of variables 12.9
3 - review for second hourly
Second Midterm (through chapter 12)
Line Integrals
1 - vector fields 13.1
- gradient fields
2 - line integrals 13.2
3 - Thanksgiving
Integral Theorems I
1 - fundamental thm line integrals 13.3
2 - Greens theorem 13.4
3 - curl and divergence 13.5
Integral Theorems II
1 - surface integrals 13.6
2 - Stokes theorem 13.7
3 - Gauss theorem 13.8
- Applications 13.9
Note: Special sections may diverge from this syllabus after Thanksgiving.
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