Instructor: Ed BuelerChapman 301C (office hours online) 474-7693 elbueler@alaska.edu www.dms.uaf.edu/~bueler |
Time & Place:MWF 9:15am-10:15am GRUE 202 T 9:45am--10:45am CHAPMAN 106 Texts:Schey, Div, Grad, Curl and All That, 4th ed., 2005 Farlow, Partial Differential Equations, 1993 |

First we do a short course in vector calculus, completing multivariable calculus. That is the subject which you started in Calculus III (Math 202). This part of Math 421 gives you the tools to do classical electricity and magnetism, but just as directly helps with fluids and elastic deformation and any other "field theory" that uses vector fields. The remaining two thirds of the course is an introduction to partial differential equations (PDEs) and their solution by separation of variables. We cover the heat, wave, and potential equations (PDEs). There will be boundary value problems and initial-and-boundary value problems for PDEs on nice domains. We will develop the elementary theory of Fourier series and orthogonal functions, as this is the substance of the separation of variables technique.

Lectures and homework together form the core of the class. There is a lot of homework, both calculations and arguments. Formal proofs will not be expected. Computer experimentation is encouraged but is not a part of the course. You are expected to ask questions in class about recent lectures or homework assignments.

20 % 10 % 30 % 40 % |
Vector calculus Exam Midterm Exam (on PDEs) Final Exam (on PDEs) Homework |
Monday, Oct. 17 (one
hour
in
class;
REVISED DATE) Friday, Nov. 11 (one hour in class) Wednesday, Dec. 14 (take home; due 5pm this day) |

The final grade will be
determined by the total of your scores using the schedule at right. This is a guarantee; I reserve the right to raise grades by a small amount based on evidence of performance improvement over time. |
Percent93 - 100 % 90 - 92 % 87 - 89 % 82 - 86 % 77 - 81 % 74 - 76 % 69 - 73 % 66 - 68 % 63 - 65 % 56 - 62 % 53 - 55 % 0 - 52 % |
GradeA A- B+ B B- C+ C C- D+ D D- F |

Goals and related courses:

Why do vector calculus? It is the mathematical core of electricity & magnetism (e.g. PHYS 331/332 and EE 311). It is the mathematical core of the study of fluids of all types (e.g. air, water, ice, plasma, earth's mantle; see ME 451, MSL 629, PHYS 614, PHYS 629, ...) and the deformation of materials.

PDEs, and the Fourier series which arise in their solutions, applies in many places. They occur in all of the contexts in which vector calculus is useful, but also in quantum mechanics and vibrations and other applications with a less explicit "vector" feel. Our coverage of Fourier series is also useful in understanding signals; compare EE 451. In the development of mathematics, understanding Fourier series was central to developing real analysis as the theory of calculus, as it is taught in Math 401 for example.

There is a caviat about the PDEs part of the course, namely, that the methods we use only work (directly) for