COURSE OUTLINE for Mathematics 1000A, Calculus I, Fall 2002

TEXTBOOK

1. "Calculus - Concepts and Contexts", Second Edition" by James Stewart. Available at the Dal Bookstore in the SUB. Either the single variable or the full edition of this book can be used for Math 1000 and 1010. However, students intending to continue next year with the second year multivariable calculus classes Math 2001 and 20022 will save money by purchasing the full edition, which will be used for those courses as well.

2. "The Student Solution Manual" contains worked-out answers to the odd-numbered problems.

CHAPTERS

Sections 2.1 to 2.10, 3.1 to 3.7, 4.1 to 4.3, 4.5, 4.6, 4.9, and 5.1 to 5.5. These sections are not all covered in equal detail.

PRACTICE PROBLEMS

for students in all sections of Math 1000, Fall 2002:

Odd-numbered practice problems have fairly complete answers in the solutions manual, so you do not pass these in for correction. Try some of these problems, listed below, writing them up coherently, during and following the relevant week. Use the solutions manual only as a last resort! You will need to spend more than an hour or two each week (often a lot more if the material is unfamiliar), on these practice problems. A group of friends and/or the Math Learning Centre may help make the activity more enjoyable.

Chapter 1 and (later) Appendix C on trig. are calculus-free, but good background. See Section 1.1, 1.5, 1.6 as warm-up, perhaps.
Section 2.1 Tangent and velocity: #1.
Section 2.2 Limit of a function:#'s 1, 3, 5, 9, 11, 13.
Section 2.3 Calculating limits: #'s 9-19, 25, 33.
Section 2.4 Continuity: #'s 1-7, 15, 33-37.
Section 2.5 Limits involving infinity, which arise in the context of asymptotes and curve-sketching and may be postponed until section 4.3: #'s 9, 13, 15, 19, 21, 25-29, 35, 43.
Section 2.6 Tangents, velocities, other rates of change: #'s 1-9,13,15.
Section 2.7 Derivatives: #'s 1-7, 13, 27, 29.
Section 2.8 Derivative as a function: #'s 3-11, 15, 21, 25, 31, 39.
Section 2.10 f from f': #'s 1-5, 9-21.
Section 3.1 Derivatives of polynomials and exponential functions: #'s 1-21, 31-37, 43-47.
Section 3.2 Product and quotient rules: #'s 1-21, 33, 35.
Section 3.3 Rates of change in real world: #'s 1, 3, 7, 9, 29.
Section 3.4 Trig derivatives: #'s 1-19, 27.
Section 3.5 Chain Rule: #'s 1-9, 17, 21, 55, 67. Refer to Section 1.7 for parametric equations.
Section 3.6 Implicit differentiation: #'s 1-5, 9-17, 27-33, 47. Orthogonal trajectories omitted. ( Appendix C explains inverse trig. functions. Do #'s 41-45.)
Section 3.7 Derivatives of logarithmic functions: #'s 1-13, 17, 25-33. (Section 1.6 reviews the log function: Do #'s 35-41, 49-53.)
Section 3.8 Linear approximation: #'s 1-5. Read Section 2.9. This topic may be postponed until the end of term. (It is expanded in Math 1010.)
Section 4.1 Related rates: #'s 1-9, 21, 23.
Section 4.2 Maximum and minimum values: #'s 1-11, 15-27, 33-43.
Section 4.3 Shape of curves: #'s 3, 5, 7, 11, 17, 19, 25, 27, 41, 43, 49. Tables of signs are encouraged, for ease of marking, although the solutions manual does not have space to include them. When curve-sketching, consideration of domain and intercepts usually precedes differentiation.
Section 4.5 Asymptotes (more). Indeterminate forms. l'Hospital's Rule: #'s 5-25, 41, 43.
Section 4.6 Optimization: #'s 1-13, 19, 21.
Section 4.9 Antiderivatives: #'s 1-23, 27, 37, 43.
Section 5.1 (Lead-up to integration.) Areas and distances: #'s 3, 11, 15.
Section 5.2 The definite integral: #'s 1, 7, 21, 23, 31, 33.
Section 5.3 Evaluating definite integrals: #'s 1, 3, 9-33, 45, 47, 57.
Section 5.4 Fundamental Theorem of Calculus. #'s 1-7, 19, 21
Section 5.5 Integration by substitution. #'s 1-23, 35-43, 57.
Section 3.8 See entry above.

CALCULATORS

These will often be useful when you are working at home, but will not be allowed (or required) during tests or examination.

STUDENTS WITH DISABILITIES

Students with permanent or temporary disabilities who would like to discuss classroom or examination accommodation are asked to see their instructor as soon as possible. There is an office in the Student Union Building, SUB 120, offering Services to Students with Disabilities.

DIAGNOSTIC TEST

This test on the departmental web-site gives you the opportunity to identify weak topics in a non-threatening way. A mark of over 27 out of 32 on that pre-calculus test is very good, and less than 10 is cause for extreme concern. The results of this diagnostic test will not be included in the grading scheme. The test is intended to give students an idea of how well prepared they are for Math 1000, so that appropriate action can be taken. If you get a mark below 14, consider whether it would be more appropriate for you to enroll in Math 1000X/Y or a Pre-Calculus class through Henson College.

ASSIGNMENTS

Most sections of Math 1000 will pass in nine written ASSIGNMENTS as arranged in class. (Sections taught by Jason Brown and Suraj Sikka have other arrangements.) The questions are posted on the website www.mathstat.dal.ca/m1000a/home.html. Your lowest mark of these nine assignments will be dropped. With regard to consultation with other students about assigned work which is to be handed in, please read the "Intellectual Honesty" section on page 23 of the 2002/2003 Undergraduate Calendar.

2 TESTS

as arranged in class for most sections. The evening section will have one longer test.

The FINAL EXAMINATION

will be scheduled by the registrar's office. It is common to all sections of Math 1000. It will consist mostly of questions of the style and level of difficulty of the practice problems. Other questions may require short answers, for example True/False or fill-in-the-blanks type, for which the Concept Checks and True/False exercises at the end of Chapters 2-5 are helpful review. The final exam is worth 45% of the term mark.

Letter grades in the course will be determined according to the following scheme:

MATHEMATICS and STATISTICS LEARNING CENTRE

The MLC in Room 009 of the Chase Building will normally have a calculus tutor available on weekdays between 9 am and 7 pm (except 5 pm on Fridays). Pierre Stevens is the director of the Centre and also teaches Math 1000X/Y. Solutions to the assignments will be posted outside the Learning Centre.