MATH 230 Spring 2007

CALCULUS II (4 semester hours) Continuation of Math 229.

PREREQUISITE: MATH 229 with a grade of C or better

COURSE OBJECTIVES:

• To understand and connect concepts of the calculus with real world problems and other scientific disciplines.
• To value mathematics and develop an ability to communicate mathematics, both in writing and orally.
• To develop mathematical reasoning, and an ability to solve problems.
• To attain computational facility in integral calculus, and sequences and series.

SYLLABUS: The course will cover most of Chapters 6-9 and 12 of the text.

• Applications of the definite integral:
  Area between curves. Finding volumes by the methods of slicing and of cylindrical shells. Work. Arc length.
• Transcendental functions:
  Inverse functions. Derivatives of the inverse trigonometric functions. The natural logarithm and the exponential function. The functions a^x and log_a(x). Applications.
• L'Hopital's rule.
• Methods of integration:
  Basic formulas. Integration by parts. Integration of trigonometric expressions. Trigonometric substitutions. Partial fractions. Integrals involving quadratic expressions. Improper integrals. Using a table of integrals.
• Sequences and series:
  Sequences and series; convergence tests (comparison, integral, ratio and root tests); alternating series; power series; Taylor and MacLaurin series; and calculations with series. Taylor's formula with remainder.

WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course is Friday, March 9.

GRADING: Grades will be assigned on the basis of 600 points, as follows:

3 hour exams worth 100 points each

Quizzes and/or homework, 100 points total

Final exam, 200 points

CALCULATORS: Students are asked to have a graphing calculator with roughly the capabilities of the TI-83. You will find this useful for investigating the concepts of the class, so you can experiment with additional examples. You may also want to verify parts of your homework calculations. Please note, however, that graphing calculators will not be allowed on the final exam.

TEXT: Calculus (5th ed.) Volume II, by Stewart (publ. by Brooks-Cole)
Some additional references:
    Thomas and Finney, Calculus and Analytic Geometry.
    Edwards and Penney, Calculus and Analytic Geometry.
    Swokowski, Calculus with Analytic Geometry.
    Leithold, The Calculus with Analytic Geometry.

STUDENT HANDOUTS: Please note that any information provided by your instructor supersedes these data.

Syllabus

Homework

Student Information Sheet

SPRING BREAK: Spring Break is from 3/10 through 3/18.

FINAL EXAM: The Final Exam is scheduled for 4:00 - 5:50 p.m. Tuesday, March 8. The final exam will be a comprehensive, departmental examination. All sections of this course will take the same final exam at the same time. Please note that the exam will likely NOT be in your regular classroom. Room assignments from the university are usually made one to two weeks before the final exam week. We will post them as soon as they are available.

Previous final exams (these are pdf files again):
   Sample final, Spring 2002
   Sample final, Spring 2003
   Sample final, Spring 2004
   Sample final, Spring 2006

Note: The course changes and the exams change. Our goal is to help you learn the material in Calculus 2, not specifically to prepare you for the final exam. We may choose to assess your command of these ideas rather differently this semester, should the opportunity arise.

RESOURCES ON THE WEB:

Understanding Mathematics: a study guide, from the University of Utah

How to Ace Calculus: the Streetwise Guide, from UC Davis

COW: Calculus on the Web, from Temple University -- problems with hints and answers available on-line.

Calculus resource list from the Math Archives, from the University of Tennessee at Knoxville

Calculus resource list from the Math Forum, from Swarthmore College

"Symbolic calculators" on-line which will compute derivatives and integrals. (Here's an alternative site for integrals)

ADVICE: Perhaps the single most important factor in your success in this course is your study habits . Think of learning math as "working out" in the gym. Study at least 3 times per week; do not wait until the day before the exam. Learn mathematics like you would learn a language. Work on the concepts until they make sense. Don't just memorize facts and then forget them a few weeks later. You will need to know this stuff for Calc III and other courses. Master each homework problem - beyond just getting a correct answer. Be on the lookout for mistakes in algebra and trig. Always come to class! While you're there, listen, think, and ask questions.

Last update: January 8, 2007