Math 268: Multidimensional Calculus
MWF 9:30-10:20 in
Office Hours (instructor)
Mon 10:30--11:50, Fri 1:30--2:20
|Office Hours (TA)
Mon 3:30--4:30, Tue 11:00--12:00
||Sec A: Tu 1:30-2:20 in PH A18B, and Sec B: 3:30-4:20 in WEH 6423
||Wednesdays, at the beginning of class. Late homework will not be accepted
||Wed, Feb 14 (in class)
||Wed, Mar 28 (in class)
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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
There are plenty of references on Calculus and can be divided into isomorphism classes based on difficulty. (Translation: I’m not expanding my brief notes.)
- My brief lecture notes: for printing or for viewing online.
- Khan Academy. (Lots of examples, pictures, intuition; but not at the level of rigor that will be expected in this course.)
- Hermann, Strang Calculus Volume 3. (At a level a bit lower than this course; but available for free on OpenStax.)
- Lecture notes by Santiago Canez (also available on his website. (A bit deeper / more through than we will have time for in this course.)
- Advanced Calculus of Several Variables by C. H. Edwards, Jr (roughly chapters 2 through 5; again at a level slightly higher than we will have time for in this course.)
- Advanced Calculus (5th Edition) by Wilfred Kaplan.
(roughly chapters 2 through 5).
Note: When I initially recommended this book, it used to be a cheap paperback book.
It is not so cheap anymore, and I do not recommend buying it.
- Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Shifrin.
- The more analytically inclined can also use any of the references used for 269 any of the references used for 269
- 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 policy:
- Late homework will NOT be accepted.
In particular, homework turned in after class starts will NOT be accepted.
- To account for unusual circumstances, the bottom 20% of your homework will not count towards your grade.
- I will only consider making an exception to the above late homework policy if you have documented personal emergencies lasting at least 18 days.
- I recommend starting the homework early.
Most students will not be able to do the homework in one evening.
- I view homework more as a learning exercise as opposed to a test.
Feel free to collaborate, use books and whatever resources you can find.
I recommend trying problems independently first, and then seeking help on problems you had trouble with.
- I also strongly urge you to fully understand solutions before turning them
I will usually put a few homework problems on your exams with a devious twist.
A through understanding of the solutions (even if you didn’t come up with it yourself) will invariably help you.
But knowledge of the solution without understanding will almost never help you.
- 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.
Moreover, between 25% and 50% of your exams will consist of (possibly modified) homework questions, so I advise you to really understand the homework.
- The remainder 80% of your grade will be determined by your exams weighted as the higher of:
- 20% for each midterm, and 40% final,
- or 30% for your better midterm and 50% for the final,
- If you miss a midterm for some reason, I will not give you a makeup.
Instead, I will count your other midterm as 30% and final as 50% using the second option above.