MATH 116 SYLLABUS, SPRING 2011 Professor Sachs

        COURSE OVERVIEW: The main goals of this course are: to extend the basic ideas of
        calculus and to develop the main results in the subject so students can use their calculus
knowledge in related courses including Math 213 and in their later studies.   Particular topics
        include: applications of integration; improper integrals; techniques of integration; sequences;
        series; power series; Euler's formula and polar coordinates. The expectation is that we will go
        faster and deeper than the non-honors version.

TEXT: Calculus Early Transcendentals (First Edition) by Briggs and Cochran (Addison-Wesley).

MEETING: Monday and Wednesday 3:55pm-5:45pm, Science and Tech. I, room 242

OFFICE HOURS: 201D Science and Tech I, W 11-11:45am, M,W 3:00-3:45pm or by appointment.

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

COURSE WEB PAGE: math.gmu.edu/~rsachs/m116

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

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

Homework (200); Quiz (100); Computer Labs (100); Three exams (300); Final (200).

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. 8
                                                  Last day to add classes: Feb. 8
                                                  Last day to drop with no academic liability: Feb. 25
                                                  Spring break: March 14- 20
                                                 Selective Withdrawal: Feb. 28 - Apr. 1

For more information, see http://registrar.gmu.edu/calendars/2011 Spring.html

EXAM DATES

Exam 1 – Tentative – Wednesday, Feb. 16

Exam 2 – Tentative – Wednesday, March 23
Exam 3 – Tentative – Wednesday, April 20

Final Exam – Wednesday, May 11 4:30pm-7:15pm

MATERIAL COVERED AND TENTATIVE SCHEDULE

We will cover most of chapters 6 through 11 in the text. Schedule is tentative!

1/24: (Sections 5.5, 6.7) Brief Calculus 1 Review; log and exponentials.

1/26: (Sections 6.8, 6.1, 6.2) Exponential models; velocity; Areas

1/31: (Sections 6.3, 6.4) Volumes by slicing; volumes of rotation

2/2: (Sections 6.5, 6.6) Length of curve; physical applications

2/7: (Section 7.1) Basic integration techniques; Integration by parts

2/9: (Section 9.1, 4.2, 4.6) Taylor polynomials; Reprise of second derivative test

2/14: (Sections 7.2, 7.3) Trig Integrals; trig substitution
2/16: Exam 1;

2/21: (extra material, Section 7.4) Partial Fractions; alternate methods

2/23: (Sections 7.5, 7.6) Using tables; Numerical integration. computer session

2/28: (Section 7.7): Improper integrals.

3/2: (Sections 7.8) Introduction to differential equations

3/7: (Sections 8.1, 8.2, additional materials) Sequences; iteration and difference equations.

3/9 (additional materials) Newton's method

3/14-3/16: SPRING BREAK

3/21: (additional material) Iterated maps and chaos; Exam 2 Review.

3/23: (Section 8.3) EXAM 2; series

3/28: (Section 8.4) Integral test; divergence test

3/30: (Section 8.5) Ratio and root tests; comparison

4/4: (Section 8.6, extra material) Alternating series; General discussion on convergence testing

4/6: (Section 9.2) Power series

4/11: (Section 9.3) Taylor and Maclaurin series

4/13: (Section 9.4) Convergence of Taylor series.

4/18: (additional material) Applications of power series; Review for EXAM 3.

4/20: (additional material): EXAM 3; Two gems from the masters.

4/25: (additional material) Fourier series.

4/27: (Sections 10.2, 10.3) Polar coordinates; calculus in polar coordinates

5/2: (Sections 10.3, 10.4, additional material) Area and arclength in polar; Kepler problem.
5/4: Review

GETTING HELP: You can get help from Professor Sachs during office hours.
As well, the math department offers FREE drop-in tutoring in JC 311C. Hours are
generally plentiful. See the web page for the tutoring center for more information. As well,
there are many publications and web pages for help with calculus.

SUGGESTED PROBLEM LIST: A list of suggested problems from the text that you should be
able to do will be distributed and posted on the web site shortly.

SOME TIPS FOR SUCCESS: Mathematics is challenging, but fun. It should always make sense to you,
but not always right away, so take time to think and to question. Think about special cases and also about counterexamples. Draw pictures. Learn from your mistakes. Write clearly. Ask good questions.