index.md 2.57 KB
 GI committed Aug 31, 2015 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 ``````## Course Description 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. ### Tentative Syllabus * 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 * **Textbook:** *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. ## Class Policies ### Lectures * If you must sleep, don't snore! * Be courteous when you use mobile devices. ### Homework * Homework must be turned in **at the beginning of class** on the due date. `````` GI committed Mar 07, 2019 36 ``````* Late homework will **NEVER** be accepted. Really! `````` GI committed Aug 31, 2015 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 ``````* 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. ### Exams * 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 [here](https://www.cmu.edu/hub/courses/exams/index.html). Be aware of their schedule before making your travel plans. ### Grading * 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.``````