Mathematics 110: Calculus and Analytic Geometry II (Fall 2005)

Lecture: Mon-Wed 3:30pm-5:15pm (Room HRN-512)

Instructor: Allan Cruse
cruse@usfca.edu
Phone: (415) 422-6562
Office: 212 Harney Science Center
Office Hours: (see my homepage)

Synopsis:

This is the second in a three-semester course-sequence (Math 109-110-211) covering standard topics in introductory calculus for college undergraduates. It assumes that a student is familiar with rules for computing derivatives of algebraic, trigonometric, exponential and logarithmic functions, and has used these in solving problems involving optimization, curve-sketching, and computing rates-of-change. It also assumes that a student has been introduced to the concepts of definite integral and anti-derivative, and is aware of the so-called Fundamental Theorem of Calculus which describes the connection between derivatives and integrals. With that essential background as a starting point, this course explores applications of the integral to problems in a variety of disciplines, methods for discovering anti-derivatives, techniques for formulating and solving differential equations, usage of parametric equations and polar coordinates, and properties of infinite sequences and series. The course consists of readings, lectures, discussions, demonstrations, quizes, and homework exercise-sets.

Textbook:

Learning Outcomes:
• You will know how to compute areas and volumes for curvilinear regions
• You will be aware of common techniques for discovering anti-derivatives
• You will be able to compute the general solution to a differential equation
• You will understand how calculus is used in various scientific disciplines
• You will have a deeper appreciation for limits and for infinite processes
• You will be equipped to undertake further studies in college mathematics

Handouts

• 0206-110-01: Course syllabus (PDF)
• computer simulation: buffon.cpp illustrating the theoretical result we obtained using Integral Calculus
• demo program: simpson.cpp illustrates the use of Simpson's Rule to perform a numerical integration
• demo program: traprule.cpp illustrates use of the Trapezoid Rule to perform a numerical integration
• Powerpoint slides: Ellipse Tangents on finding the point where a given focal ray intersects an ellipse
• demo program: rootfind.cpp illustrates the Newton-Raphson Method (by calculating 12-th root of 2)
• demo program: sinedemo.cpp shows successive approximations to the sine-function by Taylor polynomials

Homework

• For Wed, 31 Aug 2005: Section 6.3: #3, 16, 17, 28, 46.
• For Wed, 07 Sep 2005: Section 6.4: #2, 7, 14, 15, 23.
• For Mon, 12 Sep 2005: Section 7.1: #3, 10, 12, 34, 52.
• For Wed, 14 Sep 2005: Section 7.2: #2, 14, 29, 30, 41.
• For Mon, 19 Sep 2005: Section 7.3: #1, 7, 9, 34; and Section 7.4: #9. 17, 21, 28, 34, 41.
• For Wed, 21 Sep 2005: Section 7.7: #17, 21, 29, 30, 42.
• For Mon, 26 Sep 2005: No new assignment. Review for Midterm Exam.
• For Wed, 28 Sep 2005: Section 7.8: #5, 7, 13, 27, 30.
• For Mon, 03 Oct 2005: pages 541-542: #1, 3, 13, 71, 75. Section 8.1: #5, 11, 13, 17, 19.
• For Wed, 05 Oct 2005: Section 8.2: #2, 4, 5, 13, 25.
• For Mon, 10 Oct 2005: Section 8.3: #1, 3, 7, 10, 12, 19, 21, 27, 29, 33.
• For Wed, 12 Oct 2005: Section 9.1: #2, 4, 9, 11, 12.
• For Mon, 17 Oct 2005: Section 9.3: #1, 2, 3, 4, 8, 9, 11, 15, 19, 20.
• For Wed, 19 Oct 2005: Section 10.1: #13, 24, 33, 40, 44(a,c).
• For Mon, 24 Oct 2005: No new assignment. Review for Midterm Exam.
• For Wed, 26 Oct 2005: Section 10.2: #1, 5, 8, 31, 65.
• For Mon, 31 Oct 2005: Section 10.3: #3, 5, 7, 12, 13, 17, 55, 57, 61, 68.
• For Wed, 02 Nov 2005: Section 10.4: #1, 6, 29, 38, 45.
• For Mon, 07 Nov 2005: Section 10.5: #2, 5, 12, 16, 24, 27. Section 10.6: #3, 4, 9, 13.
• For Wed, 09 Nov 2005: Section 11.1: #5, 13, 17, 22, 31..
• For Mon, 14 Nov 2005: Section 11.2: #9, 12, 17, 21, 23, 27, 41, 45, 49, 53.
• For Wed, 16 Nov 2005: Section 11.3: #3, 5, 12, 23, 32.
• For Mon, 21 Nov 2005: No new assignment. Review for Midterm Exam.
• For Wed, 23 Nov 2005: Section 11.4: #3, 8, 10, 25, 35.
• For Mon, 28 Nov 2005: Section 11.5: #5, 7, 15, 29, 31. Section 11.6: #3, 5, 8, 20, 27.
• For Wed, 30 Nov 2005: Section 11.7: #2, 3, 8, 18, 37.
• For Mon, 05 Dec 2005: Section 11.8: #5, 7, 17, 18, 23. Section 11.9: #3, 8, 9, 25, 32.
• For Wed, 07 Dec 2005: No new asignment. Review for Final Examination.

Announcements

• Midterm Exam 1: Monday, September 26
• Midterm Exam 2: Monday, October 24
• Midterm Exam 3: Monday, November 21
• FINAL EXAMINATION: NOON, Tuesday, December 13, 2005

Last updated on 12/04/2005