Basic Information for MAT194F Calculus Engineering Science 2013

Transcription

1 Basic Information for MAT194F Calculus Engineering Science Your Lecturers P.C. Stangeby Institute for Aerospace Studies To arrange a meeting, please pcs@starfire.utias.utoronto.ca D. Penneys Department of Mathematics dpenneys@math.utoronto.ca 2. Lectures and Tutorials Since changes can occur, the course timetable should always be checked at: As of 25 August: MAT194H1F LEC 01 1 Mon 11:00 12:00 KP108 * Stangeby, P. MAT194H1F 2 Wed 14:00 15:00 WB116 Stangeby, P. MAT194H1F 3 Thu 13:00 14:00 SF1105 Stangeby, P. MAT194H1F LEC 02 1 Mon 13:00 14:00 WB116 Penneys, D. MAT194H1F 2 Wed 15:00 16:00 SF1105 Penneys, D. MAT194H1F 3 Thu 16:00 17:00 WB116 Penneys, D. MAT194H1F TUT 01 1 Tue 11:00 12:00 BA3012 MAT194H1F TUT 02 1 Tue 11:00 12:00 BA3116 MAT194H1F TUT 03 1 Tue 11:00 12:00 BA3008 MAT194H1F TUT 04 1 Thu 17:00 18:00 BA3116 MAT194H1F TUT 05 1 Tue 15:00 16:00 BA3008 MAT194H1F TUT 06 1 Tue 15:00 16:00 GB404 MAT194H1F TUT 07 1 Wed 9:00 MAT194H1F TUT 08 1 Wed 9:00 10:00 BA :00 BA3116 MAT194H1F TUT 09 1 Wed 10:00 11:00 BA3012 MAT194H1F TUT 10 1 Tue 14:00 15:00 BA3116 1

2 MAT194H1F TUT 11 1 Tue 14:00 15:00 BA3012 MAT194H1F TUT 12 1 Tue 14:00 15:00 BA3008 * Koffler House at 569 Spadina Ave (entrance is at the back of the building). 3. Evaluation There will be two Term Tests. The first tutorial will occur in the week starting Monday, 9 September, but there will be no Quiz that week. Each week after that, unless there is a Term Test, there will be a Quiz, see below re material to be covered. There will be 9 Quizzes in total, of which the 6 highest marks will be counted. Thus 3 Quizzes can be skipped entirely, which is to cover conflicts with religious holidays, etc. The Term Tests will be on Thursday 17 October and Thursday 14 November, from 9 am to 10:45 am, in the Examination Centre, 255 McCaul St, room EX200. On all Quizzes, Term Test and Final Exam, no calculator or electronic device of any kind is permitted. Marking scheme: Term Tests 30% Tutorial Quizzes 20% Final Examination 50% 4. Text Material (a) Textbook: James Stewart, Calculus (7 th edition) with Student Solutions manuals, isbn# (b) Supplement: E.J. Barbeau and P.C. Stangeby, Some Foundations of Analysis for Engineering Science (MAT194F). This is available on the Course website. 5. Course Website The course name is: Fall-2013-MAT194H1-F-LEC0101.LEC0102: CALCULUS 1 You should log on as soon as possible. 2

3 6. Material to Cover for Quizzes Each Quiz will consist of one or two questions taken directly from the Stewart Textbook and/or from the Supplement. These Textbook questions will, in fact, be taken from a subset of the questions at the end of each section in the Text. These subsets of questions are indicated below in the Course Outline. The specific material to be covered in each Quiz will be posted on the course website by the start of the weekend preceding the Quiz. It will be essential for you to know the basics of trigonometry for this, as well as for many of the other courses you will take. Some of you will have covered this material already in high school, but some of you will not have. In any event, this material will, for the most part, not be covered directly in this course or in your other first year courses. You are responsible yourself for making sure that you are on top of this material. You should set out to do this as early as you can ideally in the first month of the fall term since each of the first 3 Quizzes may include a trigonometry question, taken from Appendix D of the Stewart textbook. You will probably find that the material contained in Appendix D of the Stewart Text, Trigonometry, pages A24-A33, is clear enough for you and adequate preparation for the Quizzes. The 1 st Quiz may include one of the questions from Nos. 1 34, pg A32. The 2 nd Quiz may include one of the questions from Nos , pgs A32, A33. The 3 rd Quiz may include one of the questions from Nos , page A Course Outline In the following: L = lecture number T = related section of the Textbook TP =recommended problems in the Textbook S = related section of the Supplement SP = recommended problems in the Supplement. Note: The following specifies the material that will be covered in the lectures and the order of coverage. It gives, however, only a rough indication of how the material will be divided between successive lectures. It is also important for you to know that the lectures will not cover all of the material you are responsible for in this course, and that some material will be assigned for home-study. 3

4 L1 A brief introduction, including: the problem of defining the derivative in a rigorously logical way; problem with a/0, 0/0, ; basic idea of the limit; the use of, ideas; the difference between f(c) and limf (x). x c T: A preview of calculus, pages 2-8; Sec TP: page 49: 3, 5 S: Sec. 1. L2, L3, L4 The real number system, including: field and order axioms; absolute value; function; roots; intervals; increasing/decreasing; inequalities; intervals described by inequalities; inequalities involving, ; triangle inequality. A brief introduction to trigonometry. T: Secs. 1.1, 1.2, 1.3, Appendix D. TP: pages 19-23: 22, 25, 27, 28, 35, 41, 45, 50, 62, 67, 71, 76; pages 33-35: 1, 2, 3, 4, 10, 15, 20, 23; pages 42-44: 3, 6, 7, 9, 13, 23, 26, 31, 38, 43, 58; page 102: 1, 2; all questions on pages A S: Secs. 2.1 to 2.7. SP: Ex 3, Ex 5d, Ex 7a,b,c,d,e, Ex 8a,b,c Ex 9c, Ex 10a,c, Ex 11 all, Ex 12 all. L5, L6 Rigorous definition of the limit; examples using, ; right-hand/left-hand limits; vertical asymptotes; infinite limits. T: Secs. 1.5, 1.7. TP: pages 59-61: 5, 9, 13, 15,17, 21, 29, 42; pages 80-81: 3, 4, 6, 9, 13, 17, 19, 22, 34, 38, 42. S: Secs. 3.1, 3.2. SP: Ex 14, Ex 15, Ex 18, Ex 20. L7, L8 Limit theorems/laws; continuity; Intermediate Value Theorem. T: Secs. 1.6, 1.8. TP: pages 69-71: 1, 2, 5, 7, 10, 15, 26, 37, 46, 47, 50. pages 90-93: 3, 4, 9, 13, 17, 19, 22, 25, 30, 35, 39, 43, 44, 49, 51, 56, 63, 69. S: Secs. 2.8, 3.3, 3.4, 4.1. SP: Ex 22, Ex 24, Ex 25, Ex 26, Ex 27. L9, L10 Tangents, velocities, rates of change; the derivative; the derivative as a function; differentiability implies continuity; differentiation formulas; rates of change. T: Secs. 2.1, 2.2, 2.3, 2.7. TP: pages : 5, 8, 14, 15, 27, 29, 33, 38, 42, 44, 46, 47, 51, 54. pages : 1, 3, 19-29, 38, 42, 49, 54. pages : 1-22, 24, 30-40, 55, 65, 67, 81, 85, 100, 101. pages : 1, 11, 13, 18, 23, 30, 35. 4

5 L11 Trig functions; chain rule; implicit differentiation; higher derivatives; related rates. T: Secs. 2.4, 2.5, 2.6, 2.8. TP: pages : 13, 19, 24, 37, 41, 54. pages : 25, 37, 76, 83. pages : 10, 12, 14, 29, 49, 55, 57, 62. pages : 14, 24, 33, 39. L12 Applications of differentiation; Extreme Value Theorem; Fermat s Theorem; Maximum/minimum test. T: Sec TP: pages : 3, 13, 23, 29, 39, 47, 53, 56, 64, 68. S: Sec SP: Ex 31, Ex 32. L13, L14 Mean Value Theorem; differentials and differences; linear approximation; derivatives and shape of graphs; increasing/decreasing test; first derivative test; concavity; point of inflection; concavity test; second derivative test; limits at infinity; horizontal asymptotes. T: Secs. 2.9, 3.2 to 3.4. TP: pages : 15, 17, 21, 25, 33. pages : 9, 12, 21, 22, 26, 31, 33. pages : 9, 12, 17, 21, 29, 37, 62. pages : 4, 7, 13, 29, 36, 42, 45, 53, 62, 72. S: Sec SP: Ex 35, Ex 36, Ex 37. L15 Curve sketching. T: Secs. 3.5, 3.6. TP: pages : 1, 5, 9, 22, 30, 38, 40, 50, 56. L16 Optimization problems; Newton s method; anti-derivatives. T: Secs. 3.7, 3.8, 3.9. TP: pages : 3, 13, 16, 18, 24, 32, 48, 67, 71. pages : 6, 15, 27, 32. pages : 4, 7, 16, 22, 32, 35, 40, 51, 65. L17, L18 Integrals; areas; the definite integral. T: Secs. 4.1, 4.2. TP: pages : 3, 13, 20, 21, 23, 30. pages : 3, 12, 14, 15, 17-20, 23, 29, 37, 47, 49, 63, 71. L19 The Fundamental Theorem of Calculus. T: Sec TP: pages : 2, 5, 9, 13, 24, 31, 37, 42, 47, 52, 68, 69. 5

6 L20 Indefinite integrals; substitution rule. T: Secs. 4.4, 4.5 TP: pages : 4, 11, 16, 23, 37, 41, 46, 49, 53, 57. pages : 3, 5, 7-30, 57, 59. L21 Applications of integration; areas between two curves. T: Sec TP: pages : 5-28, 50, 51. L22 Volumes. T: Sec TP: pages : 1, 5, 11, 17, 33, 41, 47, 53, 63. L22, L24 Volumes by cylindrical shells; work; average value of functions. T: Secs. 5.3 to 5.5 TP: pages : 3, 7, 11, 25, 42, 46. pages : 9, 13, 19, 27, 29, 30. page : 7, 9, 13, 17, 20, 21, 22. L25 Inverse functions. T: Sec TP: pages : 3, 5, 7, 11, 16, 22, 23, 25, 39-42, 46, 50. L26 The natural log function. T: Sec. 6.2*. {Note: not Sec. 6.2.} TP: pages : 11-14, 17, 25, 33, 37, 41, 51, 63, 67, 69, 71, 77, 79, 85, 89. L27 The natural exponential function. T: Sec. 6.3* TP: pages : 2-12, 15, 19, 22, 29, 31, 33-52, 61, 81-92, 107, 109. L28 General log and exp functions. T: Sec. 6.4*. TP: pages : 3-10, 13, 23, 25-42, L29, L30 The inverse trig functions; hyperbolic trig functions; indeterminate forms and L Hospital s Rule. T: Secs. 6.6 to

7 TP: pages : 22-35, 48, 62, 69, 78. pages : 14, 17, 18, 41, 43, 51, 52. pages: : 22, 35, 39, 50, 51, 57, 58, 71, 93. L31 Differential equations; modeling with diff eqns; separable equations. T: Secs. 9.1, 9.3. TP: pages : 3, 12, 14. pages : 1-14, 43, 46, 50. L32 Exponential growth and decay. T: Sec TP: pages : 4, 8, 11, 13, 17, 19. L33 Models for population growth; linear equations. T: Secs. 9.4, 9.5. TP: pages : 3, 7, 9, 11, 19. pages : 3, 9, 12, 19, 27, 35. L34, L35 Second order linear differential eqns. T: Sec TP: page 1172: 5, 7, 11, 13, 17, 19, 21, 25, 27, 29, 32. S: Sec. 5. L36 Non-homogeneous liner diff eqns. T: Sec TP: pages : 3, 7, 9, 13, 17, 19, 21, 23, 25. L37, 38 Spare and review 7