Mathematics 109: Calculus and Analytic Geometry I (Spring 2006)
Lecture: Mon-Wed-Fri 1:30pm-2:35pm (Room HRN-509)
Instructor:
Allan Cruse
cruse@usfca.edu
Phone: (415) 422-6562
Office: 212 Harney Science Center
Office Hours: (see my homepage)
Course Assistant:
Naod Shifferaw
nshifferaw@usfca.edu
Synopsis:
This is the first in a three-semester course-sequence (Math 109-110-211)
covering standard topics in introductory calculus for college undergraduates.
It is assumed that each student has previously studied algebra, geometry, and
trigonometry, and has encountered examples in which mathematical principles
were used to analyze real-world situations (such as in elementary physics or
accounting). With that background, this course explores the role of continuous
processes and limits in devising basic calculation-rules for analyzing problems
which involve variables that undergo change and that may attain extreme values.
Specific topics include differentiation of algebraic, exponential, logarithmic,
trigonometric and hyperbolic functions (and their inverses); implicit differentiation;
curve-sketching; indeterminate forms; velocity and acceleration; optimization,
related rates, and other applications of derivatives; introduction to integrals
and the fundamental theorem of calculus, with application to the calculation of
areas, volumes, and averages. The course will consist of readings, lectures,
discussions, demonstrations, quizzes, and frequent homework exercise-sets.
Textbook:
Learning Outcomes:
- You will be able to compute derivatives of common mathematical functions
- You will know major techniques for sketching graphs and evaluating limits
- You will be able to determine what area lies inside a curvilinear region
- You will have acquired some experience with devising mathematical models
- 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
Course Resources
Handouts
- 0206-130-01: Course syllabus (PDF)
- Lecture on tangent-lines in Plane Geometry
(Powerpoint Slides)
- Our proof for one of the logarithmic laws
in Stewart's calculus textbook (page 68)
- On approximating Euler's number e
using ideas in Stewart's calculus (Chapter 1)
- On our in-class discussion of Exercise 23
in Section 2.3 of Stewart's Calculus
- On our in-class discussion of Exercise 36
in Section 2.4 of Stewart's Calculus
- Demo program: areademo.cpp
showing C/C++ code for a short program that illustrates area-approximation
- Program output: areademo.out
produced when the 'areademo' program was executed on a Linux system
Homework
- For Wed, 25 Jan 2006: Section 1.1: #43, 51, 52, 54, 59.
- For Fri, 27 Jan 2006: Section 1.2: #2, 4, 8(a), 11(a,c), 15(a,b).
- For Mon, 30 Jan 2006: Appendix B: #1, 7, 11, 35, 53;
and Appendix C: #1, 5, 21, 33, 35.
- For Wed, 01 Feb 2006: Appendix D: #13, 29, 52, 61, 67.
- For Fri, 03 Feb 2006: Section 1.3: #25, 43, 54, 57, 61.
- For Mon, 06 Feb 2006: Section 1.5: #7, 13, 15, 17, 19.
- For Wed, 08 Feb 2006: Section 1.6: 21, 24, 35, 41, 49, 53, 63, 65, 69, 71.
- For Fri, 10 Feb 2006: No new assignment; review for Midterm I
- For Mon, 13 Feb 2006: Section 2.1: #2, 5;
and Section 2.2: #5, 9, 10.
- For Wed, 15 Feb 2006: Section 2.3: #4, 11, 15, 19, 30, 37, 40, 45, 55, 59.
- For Fri, 17 Feb 2006: Section 2.4: #2, 3, 5, 19, 41.
- For Mon, 20 Feb 2006: University Holiday.
- For Wed, 22 Feb 2006: Section 2.5: #9, 18, 31, 32, 38, 42, 43, 45, 48, 61.
- For Fri, 24 Feb 2006: Section 2.6: #3, 4, 6, 14, 16, 26, 29, 31, 44, 53.
- For Mon, 27 Feb 2006: Section 2.7: #2, 5, 9, 11, 27;
and Section 2.8: #4, 17, 20, 23, 26.
- For Wed, 01 Mar 2006: Section 2.9: #4, 27, 29, 38, 45;
and TRUE-FALSE (p.176): #2, 8, 9, 12, 16.
- For Fri, 03 Mar 2006: Section 3.1: #23, 45, 50,54, 63;
and Section 3.2: #11, 25, 32, 38, 42.
- For Mon, 06 Mar 2006: Section 3.4: #2, 9, 13, 15, 22, 30, 33, 36, 42, 47.
- For Wed, 08 Mar 2006: Section 3.5: #7, 16, 19, 29, 32, 46, 52, 55, 64, 65.
- For Fri, 10 Mar 2006: No new assignment; review for Midterm II
--- Spring Vacation: March 13-17 ---
- For Mon, 20 Mar 2006: Section 3.6: #7, 14, 21, 23, 27, 43, 55, 65, 68, 69.
- For Wed, 22 Mar 2006: Section 3.7: #3, 7, 10, 23, 31, 35, 40, 44, 45, 53.
- For Fri, 24 Mar 2006: Section 3.8: #3, 8, 30, 35, 44;
and Section 3.9: #3a, 7, 16, 21, 49.
- For Mon, 27 Mar 2006: Section 3.10: #1, 2, 3, 5, 7, 21, 31, 32, 35, 36.
- For Wed, 29 Mar 2006: Section 4.1: #6, 9, 33, 36, 43, 45, 48, 53, 57, 60.
- For Fri, 31 Mar 2006: Section 4.2: #2, 6, 11, 14, 15, 17, 23, 30, 33, 36.
- For Mon, 03 Apr 2006: Section 4.3: #5, 9, 11, 12, 13, 16, 17, 22, 45, 69.
- For Wed, 05 Apr 2006: Section 4.4: #6, 7, 9, 15, 21, 24, 27, 29, 53, 74.
- For Fri, 07 Apr 2006: Section 4.5: #1, 5, 8, 9, 19, 22, 33, 44, 55, 60.
- For Mon, 10 Apr 2006: Section 4.7: #2, 9, 15, 19, 25, 28, 46, 47, 56, 58.
- For Wed, 12 Apr 2006: No new assignment; review for Midterm III.
--- Good Friday: April 14 ---
- For Mon, 17 Apr 2006: Section 4.10: #2, 5, 9, 12, 13, 16, 21, 30, 43, 76.
- For Wed, 19 Apr 2006: Section 5.1: #2a, 2b, 2c, 5a, 5b, 5c, 11, 15, 22a, 22b.
- For Fri, 21 Apr 2006: Section 5.2: #17, 21, 27, 33, 36, 41, 42, 53, 47, 50.
- For Mon, 24 Apr 2006: Section 5.3: #7, 10, 13, 19, 22, 25, 28, 41, 54, 55.
- For Wed, 26 Apr 2006: Section 5.4: #1, 2, 9, 12, 32, 33, 37, 39, 43, 48.
- For Fri, 28 Apr 2006: Section 5.5: #2, 7, 12, 23, 28, 31, 41, 52, 73, 80.
- For Mon, 01 May 2006: Section 6.1: #1, 3, 7, 11, 15, 24, 27, 29, 44, 45.
--- Monday's assignment is rescheduled for Wednesday ---
- For Fri, 05 May 2006: Section 6.2: #4, 5, 20, 21, 22, 31, 49, 51, 61a, 61b.
- For Mon, 08 May 2006: Section 6.3: #3, 4, 5, 11, 16, 17, 22, 28, 41, 46.
- For Wed, 10 May 2006: No new assignment; review for Final Examination.
Announcements
- Midterm Exam 1: Friday, February 10
- Midterm Exam 2: Friday, March 10
- Midterm Exam 3: Wednesday, April 12
- FINAL EXAMINATION: Thursday, May 18, 8am
Last updated on 05/03/2006