Elementary Calculus II

Summer 2, 2002

Homework & Quizzes

Extra Credit

Either do and submit the homework problems from sections 11.8, 11.9 and 11.10, or write a computer program to do Numerical Integration.

Program

Instead of doing the problem set, you can write a computer program which performs numerical integration. Your program should have routines for calculating using the left- and right-hand sums, the midpoint sum, the trapezoid rule and Simpson's rule. This is a fairly hard assignment, so do not attempt it unless you are fairly familiar with at least one programming language.

Interface

Write your program as a library of functions. Assume that the (mathematical) function you want to integrate is a (computer) function called "f" which takes a single real number as input and outputs a single real number. Your functions should accept two real numbers and an integer (the upper and lower bounds of the interval, and the number of sub-intervals, respectively) and return a single real number (the calculated numerical integral).

Languages

I need to be able to both read and run your program. For this reason, you must write the program in one of the following languages: C, C++, Pascal, Java, Python or Perl. Please do not use any platform-specific code, as the code may be run on a machine which is different from the one you use.

Format

I need both an electronic and paper copy of your program. E-mail your code to me at cwebster@nevada.edu, preferably as an attatchment. The paper copy of the code will be due by the due date of the assignment.

Grading

The program will be graded on both correctness and style. Make sure that you include comments. It must be your own work.

Extra Credit

Any additional features you include will (if relevant) be given additional credit. Particular things which will get you a lot of extra credit are: some additional user interface (like allowing the user to type in the formula of the function at a command line rather than having to know how to program) and functions which give error estimates for each type of numerical integral (very hard, as you need to find or estimate derivatives).

Quizzes

Quiz 1: Wednesday, June 12th.: Review; Homework sections: Chapter 2, 3, 4 and 5 Reviews.
Quiz 2: Friday, June 15th.: Integration by Parts, Trigonometric Integrals; Homework sections: 7.1, 7.2 and 7.3.
Quiz 3: Tuesday, June 18th.: Partial Fractions, Integration Strategy; Homework sections: 7.4, 7.5 and 7.6.
Quiz 4: Thursday, June 20th.: Approximate Integration, Improper Integrals, Areas.; Homework sections: 7.7, 7.8, and 6.1.
Quiz 5: Tuesday, June 25th.: Volumes, Work, Averages.; Homework sections: 6.2, 6.3, 6.4 and 6.5.
Quiz 6: Thursday, June 27th.: Length, Surface Area, Physics.; Homework sections: 8.1, 8.2 and 8.3.
Quiz 7: Tuesday, July 2nd.: Parametric Equations: Tangents, Areas, Length, Surface Area.; Homework sections: 10.1, 10.2 and 10.3.
Quiz 8: Wednesday, July 3rd.: Polar Coordinates: Areas, Lengths.; Homework sections: 10.4, 10.5.
Quiz 9: Tuesday, July 9th.: Sequences, Series, Convergence Tests; Homework sections: 11.1, 11.2 and 11.3.
Quiz 10: Thursday, July 11th.: More Convergence Tests.; Homework sections: 11.4, 11.5, 11.6 and 11.7.
Extra Material: Power, Taylor and Maclaurin Series. This will not be on any quiz, will be in the final.; Sections 11.8, 11.9, 11.10.

Homework Questions

Chapter 2 Review (p175): Exercises 1, 7, 19, 31, 35, 49, 51.
Chapter 3 Review (p268): Exercises 7, 15, 31, 49, 55, 85.
Chapter 4 Review (p360): Exercises 3, 9, 17, 21, 53, 67.
Chapter 5 Review (p427): Exercises 3, 7, 13, 19, 27, 33, 59.
Section 7.1 (p474): Exercises 1, 3, 7, 15, 23, 31, 39, 57.
Section 7.2 (p482): Exercises 1, 7, 15, 23, 31, 41, 61, 63, 64, 65.
Section 7.3 (p488): Exercises 3, 7, 9, 13, 21, 25, 29, 35.
Section 7.4 (p498): Exercises 3, 5, 7, 11, 15, 23, 31, 39, 41, 47, 57, 59, 63.
Section 7.5 (p504): Exercises 7, 15, 23, 31, 39, 47, 55, 63, 71.
Section 7.6 (p509): Exercises 3, 11, 19, 27.
Section 7.7 (p520): Exercises 5, 9, 15, 21, 24, 31, 35, 42.
Section 7.8 (p531): Exercises 1, 7, 15, 23, 31, 39, 49, 59, 71.
Section 6.1 (p438): Exercises 3, 7, 15, 23.
Section 6.2 (p448): Exercises 7, 15, 23, 47, 53, 63, 69.
Section 6.3 (p454): Exercises 7, 11, 15, 23, 37, 43.
Section 6.4 (p458): Exercises 3, 7, 11, 15, 19, 23.
Section 6.5 (p462): Exercises 3, 7, 15, 19, 21.
Section 8.1 (p546): Exercises 1, 3, 7, 15, 31, 35.
Section 8.2 (p552): Exercises 3, 7, 11, 15, 21, 30, 31.
Section 8.3 (p562): Exercises 3, 7, 11, 19, 23, 29, 31.
Section 10.1: Exercises 4, 8, 12, 16, 22, 32, 38
Section 10.2: Exercises 4, 8, 16, 20, 28, 32, 36
Section 10.3: Exercises 4, 8, 14, 18, 22, 24, 30, 34
Section 10.4: Exercises 2, 4, 6, 10, 16, 20, 28, 32, 36, 40, 48, 56, 60, 64
Section 10.5: Exercises 4, 8, 12, 20, 28, 32, 40, 48.
Section 11.1: Exercises 5, 11, 15, 19, 25, 35, 47, 49, 63.
Section 11.2: Exercises 3, 5, 13, 19, 27, 33, 43, 45, 51, 65, 67.
Section 11.3: Exercises 5, 11, 15, 21, 25, 33, 38.
Section 11.4: Exercises 5, 11, 15, 21, 25, 31, 35, 37.
Section 11.5: Exercises 5, 11, 15, 19, 25, 33.
Section 11.6: Exercises 5, 11, 15, 21, 25, 31, 33.
Section 11.7: Exercises 5, 11, 15, 21, 25, 31, 35.
Section 11.8: Exercises 5, 11, 15, 21, 25, 31, 33
Section 11.9: Exercises 5, 11, 15, 21, 25, 31, 37
Section 11.10: Exercises 5, 11, 15, 21, 25, 35, 37, 43, 47, 51, 55.
Section 11.11 (if time permits): Exercises 5, 11, 15.