Northern Illinois University, MATH 230

Department of Mathematical Sciences,
Northern Illinois University

MATH 230, Fall 2009 (under construction)

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 of the text.

Applications of the definite integral:
Area between curves. Finding volumes by the methods of slicing and of cylindrical shells. 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, October 16.

GRADING: Grades will be assigned on the basis of 650 points, as follows:

3 hour exams worth 100 points each

Quizzes and/or homework, 150 points total*

Final exam, 200 points

* It is up to individual instructors to determine how these points will be distributed between quizzes and homework in their sections.

CALCULATORS: A graphing calculator with the capabilities of a TI-82 or TI-83 is required for this course. Most students find a calculator helpful for exploring concepts, and for checking answers. However you are expected to be able to set up and solve problems on your own. Please note that only a calculator without graphing capability, text memory, symbolic operations and communication ability will be allowed on the final exam. Your instructor may further regulate the use of calculators on hour tests and quizzes.

TEXT: Calculus , by Hass, Weir, and Thomas, Alt. Edition, Pearson/Addison-Wesley Publishing Co.
Some additional references:
    Stewart, Calculus .
    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:

Syllabus

Homework: Calc I Review Problems

Homework: Sections 6.1-7.4

Homework: Sections 7.6, 9.1, 8.1-8.2

Homework: Sections 8.3, 8.4, 8.7, 9.2-9.7

Student Information Sheet

FINAL EXAM: The departmental final exam is scheduled for Friday, December 11, 8-9:50 a.m. The final exam will be comprehensive. All sections of this course will take the same final exam at the same time. The location of the final exam will be announced in class near the end of the semester; it may not be in your regular classroom. We will post room assignments as soon as they are available.

Some of the 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 as 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 the Calc II material 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: August 21, 2009