Honors Calculus I and II Fall 2003 George Sparling Laboratory of Axiomatics Department of Mathematics University of Pittsburgh Pittsburgh, Pennsylvania, USA
Course Information Classes This class is Mathematics 0235 Honors B, CRN 38582, Honors Single-Variable Calculus. The classes take place in Thaw104, Mondays, Wednesdays and Fridays, 12.00-12.50pm. The first class is Monday August 25th 2003. There is no class on Labor Day, Monday September 1st, nor during the Thanksgiving Recess, Wednesday 26-30th November. The last class is Friday December 5th 2003. Recitations Each week there is a Recitation on Thursdays in BE423, CRN 38587, from 9.00-9.50am. Computer Labs Each week there is a Computer Lab in GSCC126 on Tuesdays 9-9.50am. Course Instructor: George Sparling office 609 Thackeray phone 1-412-478-1879. e-mail sparling@twistor.org. webpage http://www.math.pitt.edu/ sparling. office hours Tuesdays, Wednesdays and Thursdays, 3pm-4pm in 705 Thackeray, or by appointment. Recitation Instructor: Trisha Rossman e-mail trrst11@pitt.edu 2
Overall plan There are 42 sessions in the Fall term. We will reserve 5 sessions for 2 midterm exams and 3 reviews. So there will be 37 substantive sessions. The term is divided into three phases, each phase culminating in a review session and an examination. There will be no make-ups for the exams. Each week there will be a quiz or an exam in class and a homework assignment. All quizzes and exams are cumulative. Calendar outline Phase I Begin: Monday August 25th End: Monday September 22nd. 12 sessions. Review I, Wednesday September 24th Exam I, Friday September 26th. Phase II Begin: Monday September 29th End: Monday October 27th 13 sessions. Review II, Wednesday October 29th Exam II, Friday October 31st. Phase III Begin: Monday November 3rd End: Wednesday December 3rd 12 sessions. Review III, Friday December 5th. Final Examination, Wednesday December 10th. 3
Guiding Principles At all stages the development of your intuition will be fostered: use of pictures, relation to the real world, extrapolation from simple examples to the general case. Rigor will be maintained, but at a reasonably informal level. Numerical approximations will be discussed and used. Whenever possible, the errors in such approximations will be analyzed. Your problem solving skills will be developed. At least four kinds of technology will be available: graphing calculators, Microsoft Excel 2000, Maple, Mathematica and Matlab. You will be encouraged to be selective in your use of technology, learning to use the right tool (or no tool at all) to achieve the desired result. Every effort will be made to ensure that you are comfortable with the various calculational aids. However at the same time, we are determined to provide a solid grounding in mathematics: we will try not to confuse the tool and the theory. Throughout the term, you will be required to maintain a dossier of computer workbook files, together with written work, containing the results of projects completed in class and at home, either individually, or as part of a team. Some projects may be returned to again as more theoretical tools or more data become available for you to use. You will submit your dossier at the end of each Phase and at the end of term, for grading. The course material is available on the Web. All computer and homework assignments will be written up for the Web, so as to be available at all times. 4
Grading Each phase there will be five homeworks, four quizzes and one exam. One quiz and one homework will be dropped from each phase. Grading Scheme Each phase will be worth 400 points for a maximum possible score of 1200pts. The breakdown for each phase is as follows: Best 4 homeworks at 25 points each Computer work/project dossier at 90 points Best 3 quizzes at 30 points each One exam at 120 points 100pts 90pts 90pts 120pts Grading is curved and based on your total score only, if you pass the final. You will be provided with a cumulative grade at the end of each Phase and you will be given your position in class. If you pass the final, grading will be in the A+ to B- range, unless your other work is severely deficient. If you fail the final, grading will be in the range C+ to F. Homework Homework will be assigned each week, for collection in the recitation on the Thursday of the following week; except for the first week, when homework will be given on the first day, for collection the Thursday of the first week. Each homework will consist of from five to ten problems, with five points per problem. 5
Textbook and Syllabus Text The text for this course is: Calculus, by Elgin H. Johnston and Jerold C. Mathews Ist Edition, Addison Wesley Publishing ISBN 0-321-00682-8 6
Fall Term Calendar, version of 08/25/04 Phase I Week 1: Chapter I, Rates of Change, Limits and the Derivative M08/25 Functions and their Composition Homework 1 assigned T08/26 Lab 1 W08/27 Slope, Rates of change and Limits H08/28 Recitation 1 Homework 1 due F08/29 The derivative Quiz 1 Homework 2 assigned Week 2: Chapter 1, Rates of Change, Limits and the Derivative M09/01 Labor day: enjoy! T09/02 Lab 2 W09/03 Derivative rules H09/04 Recitation 2 Homework 2 due F09/05 Implicit differentiation Quiz 2 Homework 3 assigned 7
Week 3: Chapter 2, Finding the Derivative M09/08 Derivatives of trigonometric and exponential functions T09/09 Lab 3 W09/10 Logarithms Inverse functions H09/11 Recitation 3 Homework 3 due F09/12 Inverse Trigonometric Functions Quiz 3 Homework 4 assigned Week 4: Chapter 2, Finding the Derivative Chapter 3, Motion, Vectors and Parametric equations M09/15 Modelling with Differential Equations T09/16 Lab 4 W09/17 Vectors Motion along a line H09/18 Recitation 4 Homework 4 due F09/19 Parametric equations Tangent vectors and velocity Quiz 4 Homework 5 assigned 8
Week 5: Chapter 3, Motion, Vectors and Parametric equations M09/22 Dot products Newton s Laws T09/23 Lab 5 W09/24 Review I H09/25 Recitation 5 Homework 5 due F09/26 Exam 1 Homework 6 assigned 9
Phase II Week 6: Chapter 4, Applications of the Derivative M09/29 The linear approximation Newton s method T09/30 Lab 6 W10/01 Concavity Asymptotes H10/02 Recitation 6 Homework 6 due F10/03 Optimization Quiz 5 Homework 7 assigned Week 7: Chapter 4, Applications of the Derivative M10/06 Related rates T10/07 Lab 7 W10/08 Indeterminate Forms H10/09 Recitation 7 Homework 7 due F10/10 Euler s Method Quiz 6 Homework 8 assigned 10
Week 8: Chapter 5, The Integral M10/13 Summation Notation The Definite Integral T10/14 Lab 8 W10/15 The Fundamental Theorem of Calculus H10/16 Recitation 8 Homework 8 due F10/17 Indefinite integrals Quiz 7 Homework 9 assigned Week 9: Chapter 5 The Integral M10/20 Substitution T10/21 Lab 9 W10/22 Areas between curves Integration by Parts H10/23 Recitation 9 Homework 9 due F10/24 Partial Fractions Quiz 8 Homework 10 assigned 11
Week 10: Chapter 5, The Integral M10/27 Differential Equations Numerical Integration T10/28 Lab 10 W10/29 Review II H10/30 Recitation 10 Homework 10 due F10/31 Exam 2 Homework 11 assigned 12
Phase III Week11: Chapter 6, Applications of the Integral M11/03 Volumes T11/04 Lab 11 W11/05 Polar Co-ordinates and Arc length H11/06 Recitation 11 Homework 11 due F11/07 Polar areas Quiz 9 Homework 12 assigned Week12: Chapter 6, Applications of the Integral Chapter 7, Infinite Series, Sequences, and Approximations M11/10 Work and Center of mass T11/11 Lab 12 W11/12 Curvature Improper Integrals H11/13 Recitation 12 Homework 12 due F11/14 Taylor Polynomials and Polynomial Approximations Quiz 10 Homework 13 assigned 13
Week13: Chapter 7, Infinite Series, Sequences, and Approximations Chapter 8, Vectors and Linear Functions M11/17 Sequences Infinite Series T11/18 Lab 13 W11/19 Convergence tests Power series H11/20 Recitation 13 Homework 13 due F11/21 Working with Power Series 3-D vectors Quiz 11 Homeworks 14 and 15 assigned Week14: Chapter 8, Vectors and Linear Functions M11/24 Determinants Cross-product T11/25 Lab 14 W11/26 Thanksgiving Recess: enjoy! 14
Week15: Chapter 8, Vectors and Linear functions M12/01 Linear Functions T12/02 Lab 15 W12/03 Planes 3-D Motion H12/04 Recitation 14 Homeworks 14 and 15 due F12/05 Review III 15