CLASS HOURS: TR 9:30-10:45, in Gordon Palmer Room 231.

PREREQUISITES: MATH 227 and MATH 237 or MATH 257. You should be comfortable with Calculus I-III and linear algebra. It would be very helpful for you to have some experience writing proofs.

DESCRIPTION: Further study of calculus with emphasis on theory. Topics include limits and continuity of functions of several variables; partial derivatives; transformations and mappings; vector functions and fields; vector differential operators; the derivation of a function of several variables as a linear transformation; Jacobians; orthogonal curvilinear coordinates; multiple integrals; change of variables; line integrals; and Green's, Stokes', and Divergence Theorems.

GOALS:
Anyone who takes this course should in the end:
1. Become skilled in reading, writing, explaining, and hearing mathematics,
2. Understand the concepts of the limit, derivative, and integral (in all of their various incarnations), curvilinear coordinates, independence of path,
3. Understand the major definitions of the subject: limit, all of the different "derivatives" (total derivatives, partial derivatives, differentials, directional derivatives, gradient, divergence, curl), all of the different "integrals" (definite, indefinite, double, triple, multiple, line integrals, surface integrals),
4. Understand the major theorems of the subject: "the fundamental lemma", the implicit function theorem, green's theorem, the divergence theorem, stokes's theorem, Leibnitz's rule,
5. Understand the major formulas of the subject: the chain rule, change of variable formula for integrals, arc length, surface area.

REQUIRED COURSE MATERIALS:
Text: Advanced Calculus, fifth edition, by Wilfred Kaplan.

CHAPTERS COVERED:
1 Vectors and Matrices (sections 1.1-1.10, 1.14, 1.16)
2 Differential Calculus of Functions of Several Variables (sections 2.1 - 2.10, 2.12, 2.19)
3 Vector Differential Calculus (sections 3.1-3.8)
4 Integral Calculus of Functions of Several Variables (sections 4.1-4.9)
5 Vector Integral Calculus (sections 5.1 - 5.13)

READINGS:
Reading (and learning how to read) mathematics is the most important part of this course. It is important to read the text very actively: take notes, write outlines, fill in missing details, and attempt worked out examples on your own before looking at the text's approach. You are expected to read assigned sections before class and complete a few basic questions about what you read. The schedule lists the assigned readings and problems for each day. Class will be based around the fact that you are doing the reading. Each class I will end with a preview or overview of the next assigned reading, and on the next day we will go over the assigned reading problems. Then we will discuss the most important or difficult points of the assigned reading.

EXAMS: There will be three midterm exams and a final exam. Every exam will be comprehensive. The lowest midterm test score will be replaced by the final exam score if the final is higher. There will be no make-up tests: if you miss a midterm for any reason, that test will count as your lowest score and will be replaced. No student should miss two tests.

Exam	DATE
Test 1	Feb 8, 2011(Comprehensive)
Test 2	Mar 3, 2011 (Comprehensive)
Test 3	Apr 5, 2011 (Comprehensive)
FINAL EXAM	Tuesday May 3 from 8-10:30am. (Comprehensive)

Last day to drop with a grade of W: Wednesday, March 23, 2011 No withdrawals from this course can be made after this date.

HOMEWORK: Homework will be 25% of your grade. There will be two types of homework in this course.

Homework based on readings:

Weekly homework problems

SUMMARY:

Here is the grading scheme in chart form:

Assessment	Percentage towards final grade
Homework	25%
Midterm Tests	45% (15% each exam)
*Final Exam	30%

Your grade for the course will be based on the following scale:

CODE OF ACADEMIC CONDUCT STATEMENT

All acts of dishonesty in any work constitute academic misconduct. This includes, but is not limited to, cheating, plagiarism, fabrication of information, misrepresentation, and abetting any of the above. The Academic Misconduct Disciplinary Policy will be followed in the event that academic misconduct occurs. Students should refer to the Student Affairs Handbook which can be obtained from the Student Life Office in Ferguson Center. The Academic Misconduct Disciplinary Policy will be followed in the event of academic misconduct (see also Student Handbook, page 77).

DISABILITY ACCOMMODATION STATEMENT

Students with disabilities are encouraged to register with the Office of Disability Services, 348-4285 (see also Office of Disability Services). Thereafter, you are invited to schedule appointments to see me during my office hours to discuss accommodations and other special needs.