Math 318 Calculus of several variables

Math 318 is an advanced calculus course. Calculus will be approached from a rigorous, proof-based perspective using linear algebra implicitly.

Instructor

Tejas Kalelkar
tejas@math.wustl.edu
Room 207A Cupples I

Lectures

Monday-Wednesday-Friday 11-12 pm
Cupples 115

Office-hours

Monday-Wednesday 1:30-2:30pm
Room 207A, Cupples I

Textbook

Theodore Shifrin, "Multivariable Mathematics: Linear Algebra, multivariable calculus and manifolds", John Wiley & sons 2005.

Prerequisites

Math 233 and Math 309 or equivalent knowledge of matrix algebra and multivariable calculus.

Exams and Grading

Homework (15%)
Midterm Exam 1 on Feb 18th in regular class (25%)
Midterm Exam 2 on Mar 25th in regular class (25%)
Cumulative Final Exam on May 10, 10:30 AM - 12:30 PM (35%)

Exams will consist of a few theory questions, including definitions and proofs of selected results, and some problems involving computations and proofs. There will be no make-up exams - if you miss one midterm, the final exam counts 60%. If you take both midterms and your grade in the final is greater than your lowest midterm grade, then the grade in the midterm gets replaced by the grade in the final. For example, if midterm 1 score is 80/100, midterm 2 score is 50/100 and final score is 70/100, your score in the second midterm gets replaced by 70/100. If you choose to be graded "Pass/Fail", a "Pass" grade reqires a grade of C- or higher.

Your (final) examination room assignment will be available on the day of the exam at: www.math.wustl.edu/seatlookup/ .

Exam Absences

The exam dates have been set well in advance, and you are expected to attend them at their scheduled time. If you are away due to a university sporting event, then you may arrange for your coach to administer the exam. Excused absences may be granted in case of severe illness, bereavement or other extraordinary circumstances. Approval for absences must be obtained, preferably in advance.

Homework

Assignments can be downloaded from this website, no paper copy will be given in class. A grader will grade selected problems. No late homework is accepted and the one lowest homework grade will be dropped (which can also count for missing assignments). Homework is due at the beginning of class on the due date.

Syllabus

We shall try to cover Chapters 1-7 of the textbook. These include: "Review of Matrices. Continuity of functions of several variables. Partial derivatives, gradient. Maximum value theorem, Lagrange multipliers. Contraction mappings, inverse and implicit function theorems, integration theory." There will not be time to cover all these topics in equal detail. Shifrin's book is a source for further explanations and examples, and you are encouraged to supplement lectures by reading of the corresponding topics in the book. The following is the plan subject to changes (numbers refer to sections in Shifrin's book); this plan will be updated as the course progresses.

Day Section Homework
Jan 19 1.1 Homework 1
Jan 21 1.2
Jan 24 1.3
Jan 26 1.4
Jan 28 1.4 (cont)
Jan 31 2.1
Feb 2 2.2
Feb 4 2.2 (cont) Homework 2
Feb 7 2.2 (cont)
Feb 9 2.3
Feb 11 2.3 (cont)
Feb 14 2.3 (cont)
Feb 16 Revision Short answers
Feb 18 Midterm Exam 1 (up to Feb 14th) during class time Midterm 1
Feb 21 Correction of exam on blackboard Tutorial 1
Feb 23 Tutorials Tutorial 2
Feb 25 Tutorials
Feb 28 3.1
Mar 2 3.1 Homework 3
Mar 4 3.2
Mar 7 3.2
Mar 9 3.2
Mar 11 3.3
Mar 14 Spring break holiday
Mar 16 Spring break holiday
Mar 18 Spring break holiday
Mar 21 3.3
Mar 23 Revision Short answers
Mar 25 Mid-term exam 2 during class time Midterm 2
Mar 28 Correction of exam on blackboard
Mar 30 3.4
Apr 1 4.1 Homework 4
Apr 4 4.1
Apr 6 4.2
Apr 8 4.3
Apr 11 4.3
Apr 13 4.4
Apr 15 6.1
Apr 18 6.1, 6.2 Homework 5
Apr 20 6.2
Apr 22 6.2
Apr 25 6.2
Apr 27 Catchup Homework 5 due
Apr 29 Revision Fermat's Last Theorem documentary
May 4 Short Answers to HW4 and HW5
May 5 Tutorial 3

Grade calculations

Congratulations on a successful final exam, most of you seem to have done well. Your final grade is calculated as follows:

Let Ai be the scores of the i-th homework assignment, M1 and M2 the scores of the two midterms and F the score of the final exam.Then,

a1= A1*3.75/36
a2= A2*3.75/36
a3= A3*3.75/36
a4= A4*3.75/48
a5= A5*3.75/24
m=min(a1,a2,a3,a4,a5)
A=a1+a2+a3+a4+a5-m

F1=(M1 + M2)*50/100 + F*35/100 + A
F2=Max(M1,M2)*25/50 + F*60/100 + A
Final Score=Max(F1,F2)

Grades are assigned as follows:

A >= 90
B+ >= 84
B >= 74
C >= 60
D >= 55
F < 55

Thankyou and have an excellent break!