MATH 316 SYLLABUS, SPRING 2008 Professor Sachs

        COURSE OVERVIEW: The main goals of this course are: to deepen your understanding
        of calculus, including proofs of the major results, and to explore calculus applications.
        This builds on Math 315. Students are expected to master both calculations and proving
        theorems, as well as using the theorems in reasoning about calculus. Multivariable calculus
        is more challenging in certain respects so we will balance rigor with interesting applications.

TEXT: An Introduction to Analysis by Wade (Prentice-Hall).

MEETING: Monday and Wednesday 4:30pm-5:45pm, Science and Tech. I, room 242

OFFICE HOURS: 201D Science and Tech I, M, W 2:30-4:20pm or by appointment.

CONTACTS: email: rsachs@gmu.edu, phone: 993-1464

COURSE WEB PAGE: math.gmu.edu/~rsachs/m316

GRADING: Grading will be fair and impartial. It is based on a mixture of graded homework,

exams and a final exam. Points used as the basis of the grade will be:

Homework (300); Three exams (300); Final (150).

        POLICIES: The GMU Honor code is in effect at all times and students are expected to be
fully aware of its requirements. Group work may be part of the course and group members
will truthfully report on non-contributing members. Absence from exams must be for a valid
reason and requires prior notification except in extreme circumstances. DON'T
ARRANGE TO LEAVE BEFORE THE FINAL AND EXPECT TO TAKE IT EARLY.
       Calculators will typically not be permitted for quizzes. They will be allowed for exams but
        be of limited usefulness there.

GIFTS: None will be given as grades. If you need a particular grade, you are responsible
for earning it. I will work with you to achieve your goal.

       IMPORTANT DATES:   Last day to drop with no tuition liability: Feb. 5
                                                  Last day to add classes: Feb. 5
                                                  Last day to drop with no academic liability: Feb. 22
                                                  Spring break: March 10–16

        For more information, see http://registrar.gmu.edu/calendars/

EXAM DATES

Exam 1 – Tentative – Monday, Feb. 18

Exam 2 – Tentative – Wednesday, April 2
Exam 3 – Tentative – Monday, April 21

Final Exam – Wednesday, May 7 4:30pm-7:15pm

MATERIAL COVERED AND TENTATIVE SCHEDULE

We will cover most of chapters 7, 8, 10 through 14 in the text. Either Chap. 15 or
a brief introduction to the calculus of variations will finish the course. Schedule is tentative!

1/23: (Sections 7.1, 7.2) Uniform convergence.
1/28: (Sections 7.3, 7.4) Power series; analytic functions.
1/30: (Sections 7.5, supplement) Applications of power series
2/4: (Sections 8.1, 8.2 ) Linear structure of Euclidean spaces
2/11: (Sections 10.1, 10.2) Metric spaces; functions on metric spaces.
2/13: (Section 10.3) Open and closed sets; Review for exam 1
2/18: Exam 1
2/20: (Section 10.4) Compactness revisited
2/25: (Sections 10.5) Connected sets
2/27: (Section 10.6): Continuous functions: Extreme and mean value theorems generalized.
3/3: (Sections 11.1): Partial derivatives and partial integrals
3/5: (Sections 11.2, 11.3): Differentiability; Derivatives, differentials, tangent planes
3/10, 3/12 SPRING BREAK
3/17: (Sections 11,4) Chain Rule
3/19: (Section 11.5) Taylor polynomials.
3/24: (Section 11.6) Inverse Function Theorem
3/26: (Sections 11.7) Optimization
3/31: (Section 12.1) Jordan regions; review for exam 2
4/2: EXAM 2
4/7: (Section 12.2) Riemann integral
4/9: (Sections 12.3, 12.4) Iterated integrals; change of variable
4/14: (Sections 13,1, 13.2) Curves; oriented curves.
4/16: (Section 13.3, 13.4) Surfaces; oriented surfaces.
4/21: EXAM 3;
4/23: (Section 13.5) Green and Gauss's theorems.
4/28: (Sections 13.6) Stokes' theorem.
4/30: Topic to be decided: intro to manifolds; calculus of variations; Fourier series; other
5/5: Review.

OPTIONS: