Math 268: Multidimensional Calculus
MWF 3:30--4:20 in
Office Hours (instructor)
Mon 11:30--12:20, Fri 10:30--11:20
|Office Hours (TA)
Tue 10:00--11:15 and 2:30--3:20
||Tu 3:30-4:20 in
||Wednesdays, at the beginning of class. Late homework will not be accepted
||Wed, Sep 30 (in class)
||Wed, Nov 4 (in class)
||Sun, Dec 20, 1:00PM-4:00PM (WEH 5415)
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This course is a serious introduction to multidimensional calculus that makes use of matrices and linear transformations.
Students will be expected to write proofs; however, some of the deeper results will be presented without proofs.
- Functions of several variables, regions and domains, limits and continuity.
- Partial derivatives, linearization, Jacobian.
- Chain rule, inverse and implicit functions and geometric applications.
- Higher derivatives, Taylor’s theorem, optimization, vector fields.
- Multiple integrals and change of variables, Leibnitz’s rule.
- Line integrals, Green’s theorem.
- Path independence and connectedness, conservative vector fields.
- Surfaces and orientability, surface integrals.
- Divergence theorem and Stokes’s theorem.
Textbook and References
Advanced Calculus (5th Edition) by Wilfred Kaplan.
(Homework problems will be assigned from this book. I will cover roughly chapters 2 through 5.)
- Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubbard.
- Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Shifrin.
- If you must sleep, don’t snore!
- Be courteous when you use mobile devices.
- Homework must be turned in at the beginning of class on the due date.
- Late homework will NEVER be accepted. Really!
- To account for unusual circumstances, the bottom 20% of your homework will not count towards your grade.
- Working in groups is encouraged, but solutions must be written up on your own.
- Nearly perfect student solutions may be scanned and hosted here, with your identifying information removed. If you don’t want any part of your solutions used, please make a note of it in the margin of your assignment.
- All exams are closed book, in class.
- No calculators, computational aids, or internet enabled devices are allowed.
- The final time will be announced by the registrar
Be aware of their schedule before making your travel plans.
- Homework will count as 20% of your grade.
- Between 25% and 50% of your exams will consist of homework questions.
- Your better midterm will count as 30% of your grade.
(Your worse midterm will not count at all.)
- Your final will count as 50% of your grade.