Jacob Bernstein


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Math 211: Honors Multivariable Calculus


Course Description

This is the honors course in multivariable calculus. Topics covered in the course will include, basic structure of euclidean space, parameterized curves and surfaces, limits in several variables, differentiability in several variables, integration in several variables, vector calculus, Green's theorem, Stokes' theorem and Gauss's theorem. There will be 11 problem sets (30%), two midterm exams (30% of best score) and one final exam (40%).

Lectures are Monday and Wednesday 1:30-2:45 on Zoom -- see blackboard for the link. Section meets Friday 1:30-2:20 on Zoom -- see blackboard for the link.

Problem sets will be due in blackboard on Fridays (see below for dates). No late homework will be accepted. The lowest grade will be dropped.

Lecturer: Jacob Bernstein. Lecturer Office hours: by appointment

TA: Elham Matinpour. TA Office hours: TBA

References

The course text is
  • S. J. Colley, "Vector calculus", 4th ed.
You may also wish to consult the following texts:
  • H.M. Scheym, "Div, Grad, Curl and all that".
  • P.C. Matthews, "Vector Calculus".

Exams

There will be three exams. Two midterms and a final. The format is to be decided.

The dates of the exames are
First Midterm: Wednesday, March 3rd.
Second Midterm: Wednesday, April 7th.
Final Exam: TBA

(Tentative) Schedule and Homework

Week 1 (1/25 & 1/27): Vector and matrix operations

Read 1.1-4 and 1.5-6
No homework due.

Week 2 (2/1 & 2/3): Other coordinate systems and derivatives

Read: 1.7 and 2.1-2.3
PS1: 1.2: 12; 1.3: 25; 1.4: 4, 17, 18; 1.5: 2, 20; 1.6: 10, 18; 1.7:24; 2.1:4, 18, 42; 2.2: 6, 18, 46; 2.3: 14, 20

Week 3 (2/8 & 2/10): Derivatives and their properties

Read: 2.3-2.6
PS2: 2.3: 32, 38, 44, 59; 2.4: 2, 22; 2.5: 2, 8, 22, 30, 32, 36

Week 4 (2/15 & 2/17): Vector valued functions

Read: 3.1-3.4
PS3: 2.6: 8, 12, 20, 26, 41; 3.1: 8; 3.2: 10, 16; 3.3: 1, 18, 20, 24, 26

Week 5 (2/22 & 2/24): Extremal problems in several variables

Read: 4.1 -4.2
PS4: 3.3: 2, 22, 28, 31; 3.4: 12, 13, 14, 15, 30, 31; 4.1: 10, 16, 36; 4.2: 2, 18, 20, 28, 36

Week 6 (3/1 & 3/3): Extremal problems (cont.); First Midterm

Read: 4.3
No homework due.
First Midterm

Week 7 (3/8 & 3/10): Multiple Integrals

Read: 5.1-5.4
PS5: 4.3: 2, 12, 26, 38; 5.1: 2, 8; 5.2: 5, 13, 12, 16; 5.3: 4, 16, 18

Week 8 (3/15 & 3/17): Multiple Integrals (cont.)

Read: 5.5 and 6.1
PS6: 5.3: 14; 5.4: 8, 12, 18; 5.5: 2, 6, 8, 16, 34, 38

Week 9 (3/24): Line Integrals

No class Monday
Read 6.2 and 6.3
PS7: 6.1: 4, 14, 34; 6.2: 10, 12, 16, 18

Week 10 (3/29 & 3/31): Surface Integrals

Read: 7.1-7.3
PS8: 6.3: 18, 34; 7.1: 2, 8, 24, 26, 28, 32; 7.2: 4, 12, 30

Week 11 (4/5 & 4/7): Surface Integrals (cont.); Second Midterm

Read: 7.3
No homework due.
Second Midterm.

Week 12 (4/12): Maxwells equation

No class Wednesday
Read 7.4
PS9: 7.1: 6, 18, 28; 7.2: 2, 16, 22; 7.3: 6, 18, 20, 27, 34

Week 13 (4/19 & 4/21): Differential Forms

Read: 8.1-8.2
PS10: 7.3: 2, 4, 10, 12, 31; 7.4: 5, 6, 11, 14, 20

Week 14: (4/26 & 4/28): Differential Forms (cont.)

Read: 8.3
PS11: 8.1: 4, 14; 8.2: 6, 10, 12; 8.3: 2, 4, 6, 8, 10

Final TBA

Students with disabilities

Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at least two weeks prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.

JHU ethics statement

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the "Statement on Ethics" at the Ethics Board website for more information.

If a student is found responsible through the Office of Student Conduct for academic dishonesty on a graded item in this course, the student will receive a score of zero for that assignment, and the final grade for the course will be further reduced by one letter grade.


Fall 2019 -- Department of Mathematics, Johns Hopkins University.