CALCULUS I
FALL 2005
SYLLABUS
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Students are required to take a pretest on these topics. The pretest is available online at PRETEST There is a website where you can find sample questions for the pretest. It will help you know what you need to review. A pretest review can be found at the site: The pretest will be available up to September 9. You must be registered in a Calculus course to take it. You are allowed 2 chances to pass. If your score is below 75% then you do not have the necessary skills to succeed in Calculus. Talk to your instructor about your options, and what you can do to better prepare yourself. The Math 112 pretest review will be held Thursday, September 1, 7-9 in Room 377 of the Clyde Building |
| SU | MN | TU | WD | TH | FR | ST | |
| September | 28 | 29 | 30 | 31 | 1 | 2 | 3 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | |
| 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
| October | 25 | 26 | 27 | 28 | 29 | 30 | 1 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
| 16 | 17 | 18 | 19 | 20 | 21 | 22 | |
| 23 | 24 | 25 | 26 | 27 | 28 | 29 | |
| November | 30 | 31 | 1 | 2 | 3 | 4 | 5 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
| 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
| 20 | 21 | 22 | 23 | H | H | 26 | |
| December | 27 | 28 | 29 | 30 | 1 | 2 | 3 |
| 4 | 5 | 6 | 7 | 8 | R | R | |
| 11 | F | F | F | F | F | 17 |
COMPUTER RESOURCES
There is also a Math Refresher Course offered by the College of Engineering&Technology
Aug 22-26 9:00-3:00 in 377 CB
Aug 31- Oct 17 MWF 4:00-4:50 in 381 CB
This non-credit course taught by Dr. Reinhard Franz is available to all interested students.
First 3 lectures will include Basic Technique of Algebra and Trigonometry
contact Dean's Office (270 CB or 422-4326) for more information
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LINKS |
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EngT295R Engineering Math Refresher Course |
OFFICE HOURS
TuTh 7-8 p.m. TMCB 136 (after class)
To be determined, Clyde Building 133
or by appointment
HOMEWORK
| hw # | date | read | homework problems |
| 1 | Aug 30 | 1.1 | read "Preface" and "To The Student": pp.iii-xiii 1.1: 1,4a(ii)ce,7bd,9,11bdf,13 |
| 2 | Sep 1 | 1.2 1.3 | 1.2: 1,2,4,6,9,10,27bd,28bd 1.3: 2bd,3bdf,4bdf,6bd,15,17 writing assigment (due Sep 8) |
| 3 | Sep 6 | 1.4 1.5 | 1.4: 2,4,6,7bd,8bcefh,9abd,11 1.5: 1bdf,2ceg,5,8begi,9bdf,13bdh,21 |
| 4 | Sep 8 | 1.6 1.7 | 1.6 1bdh,2bd,3bdf,5,8,10,12 1.7 1bdfh,2bdf,7,10 |
| 5 | Sep 13 | 1.8 1.9 | 1.8: 1bdf,3bdf,4,7,9,11,13,14b,23,29bde 1.9: 1bdfh,2,6ce,8a,9,12abc,14,17 |
| 6 | Sep 15 | 2.1 2.2 | 2.1 1bd,3,7,9,11,14 2.2 1,2,3bc,4bc,5b |
| 7 | Sep 20 | 2.2 2.3 | 2.2: 6abc,11,13a,14 2.3: 1bdfhjl,2,4 2.8: |
| 8 | Sep 22 | 2.4 | TEST #1 2.4: 1bdfhj,2bdfh,3bdf,5,7 |
| 9 | Sep 27 | 2.4 2.5 | 2.4: 10bd,11bdf 2.5: 1bdfh,5cdfh,8b,9bdf,10a,11dfh,12f,13f |
| 10 | Sep 29 | 2.6 2.7 | 2.6: 1bd,2bd,3bd,4ef,5bdf,11 2.7: 1bdfh,2,3b,5,6b,7bd,11,13,17b,18 |
| 11 | Oct 4 | 3.1 3.2 | 3.1: 4,5bd,7bd,8,9bd,10,13,15ac 3.2: 1,2,4,5ad,6,8bc,17,18,19,25 |
| 12 | Oct 6 | 3.3 3.4 | 3.3: 3bdfhjl,4bdfhjl,5bdf,6,13bf,15bd 3.4: 3bdfhjl,4bdfhjl,5bdf,7,9,11,13b,18 2.8: 3.6: |
| 13 | Oct 11 | 3.5 | TEST #2 3.5: 1bdfhjl,2bdf,3bdfhjlnp,4bdhj,5bd,6,8,10bd |
| 14 | Oct 13 | 4.1 4.2 | 4.1: 2,4,6,8,10bdfhln,11bdfh 4.2: 1bdfhjlnp,3,4b,6,7bd,8bd,10 |
| 15 | Oct 18 | 4.3 4.4 | 4.3: 1bd,3b,5bfjnr,6b,7,8,17bfj,19 4.4: 1bdfhjl,2bdfhjl,6,8 |
| 16 | Oct 20 | 4.5 4.6 | 4.5: 2,4,5,6,10,12,14,17,18,20,24,26,28,30,31,32,34,35 4.6: 2,4,6,8,10,11,15b,17 |
| 17 | Oct 25 | 4.7 4.8 | 4.7: 2,6,8,11,12,18 4.8: 2,4,6,9,12,16,19,22 |
| 18 | Oct 27 | 4.9 4.10 | 4.9: 1bdfhjl,2bdfhjl,3bd,4b,6 4.10: 1,2bd,3b,4bdh,5bfjl 4.11: |
| 19 | Nov 1 | 5.1 | TEST #3 5.1: 1,2,3,4bd |
| 20 | Nov 3 | 5.1 5.2 | 5.1: 4egh,5bf,6,7,8b,9b,10,14,18,20 5.2 2bdfh,3b,5,6,10 |
| 21 | Nov 8 | 5.2 5.3 | 5.2: 2aceg,4,8,12,14,16 5.3: 1,2,3,6,8,10 |
| 22 | Nov 10 | 5.3 | 5.3: 13,16,18,19 5.4 (p.345): 1,3bcdef,4b,8,10abdf,14 |
| 23 | Nov 15 | 6.1 6.2 | 6.1: 1,3,4b,6,8bd 6.2: 2,3,5,9,10bd,11bd,13 |
| 24 | Nov 17 | 6.3 6.4 | 6.3: 1bd,2bdf,3bd,4,6,9bd 6.4: 1bdf,2,3,4,5bdfh,6,8,14bd,15,18c |
| 25 | Nov 29 | 6.5 6.6 | 6.5 1bdfhjl,2bdfhjl,3bdfh,4b,5bdf,8 6.6: 1bdfh,2bdfh,3bdfh,4b,6d,9,10b,12,13,16 |
| 26 | Dec 1 | 6.7 | 6.7: 1bdfhj,2bdfhj,3bdfghjlo,4abdf,5ab,6ab,7bdf,13 6.8: |
| 27 | Dec 6 | TEST #4 | |
| 28 | Dec 8 | Review | |
| Dec 9 | Review | STUDY! STUDY! STUDY! | |
| Dec 10 | Review | 12:00-2:00 p.m. optional review session | |
| Dec | Review | mathlab review session | |
| Dec 13 11-2 room 446 MARB |
| no books, no notes, no calculators The final exam will be given on Tuesday, December 13 from 11:00 a.m. to 2:00 p.m. (An alternate time will be provided for those students with a conflicting final exam.) PREVIOUS FINALS REVIEW PROBLEMS |
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SOLUTIONS |
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Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 |
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Summary Tables |
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Functions Limits Differentiation Integration Table of Integrals Grading |
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LINKS |
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EngT502/503 Engineering Math for Graduate Students EqWorld The World of Mathematical Equation The MacTutor History of Mathematics archive Math Aware Month Mathematics and Art |
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Origin of the Name "Mathematics" |
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Why is mathematics so named? |
TEXTBOOK ERRATA
If you find an error that the author has not discovered,
you will win a candy bar for bringing it to his attention!
(click on the errata link)
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Common final: 11am-2pm Tuesday, December 13, 2005 Alternate schedule: 11am-2pm Monday, December 12 in 3714 HBLL Monday, December 12 from 2:30-5:30pm in 116 TMCB. 1. The first problem is a matching question (6pts) 2. Problem 2 consists of 7 T/F questions (7 pts). 3. There will be 7 multiple choice questions worth 3 points each. The answers to the multiple choice questions must be entered in a chart, otherwise they will not be graded. 4. There are 12 essay questions worth ranging from 3 to 9 points, depending on how many parts there are. 5. The total is 100 points. 6. The instructions for the 12 problems requiring hand written solutions will say something similar to "give the best answer and {\em justify} it with suitable reasons and/or relevant work." This is something students should have been doing all semester, but here are some examples you can tell your students to clarify this. a. Answers like tan (pi/4), ln 1, e0 would not be considered the best answer. b. On the other hand, because students may not use calculators on the final, on problems such as exponential growth and decay in chapter 5, students will have to leave answers in terms of logs since they cannot reasonably change such answers to a decimal. c. In solving a max-min problem, students should also justify that a critical point is a maximum or minimum by the first derivative test, the second derivative test, or by evaluating the function at all critical points and endpoints. d. If they are doing a problem by L'Hospital's rule, they should first note that the problem is an indeterminate form, e.g., 0/0, and then state they are using L'Hospital's rule. e. For rules in constant use, such as the differentiation formulas, the fundamental theorem of calculus, etc., there is no need to specifically cite the rule they are using. f. When applying the (epsilon-delta) definition for limits or other theorems, the student must not merely employ computational rules such as direct substitution but they should write down in words and symbols explaining the appropriate choice of delta for given epsilon. 7. Previous finals may be found under Exams at http://www.math.byu.edu/Courses/ Please encourage your students to work over or have a look at them. The students should be aware that the problems in the final this semester are going to be more similar to their assignments, i.e., less problems requiring special tricks or insights. 8. You may want to know about formulas students should know for the test. They should know all basic differentiation and integration formulas, power rule, product rule, quotient rule, chain rule, basic antiderivatives at the beginning of chapter 6, all key theorems (extreme value, intermediate value, Rolle's, mean value theorem, fundamental theorem of calculus, etc.), the formula for Newton's method, and the rules for numerical integration. We only thought of a few exceptions: We do not expect them to memorize Cauchy's mean value theorem, the formula for the logistic curve, or Simpson's rule as they are a little harder to remember; however, they should be able to do such a problem given the formula. We prefer not to write a comprehensive list because we might forget something they should know, but will be glad to answer specific questions. 8. Please emphasize that they remember to use the chain rule when finding derivatives, to add a constant when finding indefinite integrals, and *most importantly* that they make sure they do not integrate when they are supposed to differentiate and that they do not differentiate when they are supposed to integrate. 9. Students will receive credit for any correct method for doing a problem. For example, in the early sections of chapter 6, definite integrals are calculated several different ways ( for example, by interpreting the integral as an area) before the section on the fundamental theorem of calculus. There are several integration problems that can be done in more than one way. |
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1. There will be 7 muliple choice questions worth 4 points each. There are 11 written questions worth 6 or 8 points. (The 8 point questions have 3 parts). The total is 100 points. The answers to the multiple choice questions must be entered in a bubble grid as in winter's exam. 2. The instructions for the 11 problems requiring hand written solutions will say something similar to "give the best answer and justify it with suitable reasons and/or relevant work." This is something students should have been doing all semester, but here are some examples you can tell your students to clarify this. a. Answers like tan (pi/4), ln 1, e0 would not be considered the best answer. b. On the other hand, because students may not use calculators on the final, on problems such as exponential growth and decay in chapter 5, students will have to leave answers in terms of logs since they cannot reasonably change such answers to a decimal. c. In solving a max-min problem, students should also justify that a critical point is a maximum or minimum by the first derivative test, the second derivative test, or by evaluating the function at all critical points and endpoints. d. If they are doing a problem by L'Hospital's rule, they should first note that the problem is an indeterminate form, e.g., 0/0, and then state they are using L'Hospital's rule. e. For rules in constant use, such as the differentiation formulas, the fundamental theorem of calculus, etc., there is no need to specifically cite the rule they are using. Students may check the solutions to last semester's final on the web to see a few examples of what would be sufficient justification and work. 3. Previous finals may be found under Exams at _http://www.math.byu.edu/Courses/_ We aren't going to say any more about content than this except students should expect some problems using the definition of limit and theorems about limits. 4. You may want to know about formulas students should know for the test. They should know all basic differentiation and integration formulas, power rule, product rule, quotient rule, chain rule, basic antiderivatives at the beginning of chapter 6, all key theorems (extreme value, intermediate value, Rolle's, mean value theorem, fundamental theorem of calculus, etc.), the formula for Newton's method, and the rules for numerical integration. We only thought of a few exceptions: We do not expect them to memorize Cauchy's mean value theorem, the formula for the logistic curve, or Simpson's rule as they are a little harder to remember; however, they should be able to do such a problem given the formula. We prefer not to write a comprehensive list because we might forget something they should know, but will be glad to answer specific questions. 5. Please emphasize that they remember to use the chain rule when finding derivatives, to add a constant when finding indefinite integrals, and *most importantly* that they make sure they do not integrate when they are supposed to differentiate and that they do not differentiate when they are supposed to integrate. 6. Students will receive credit for any correct method for doing a problem. For example, in the early sections of chapter 6, definite integrals are calculated several different ways ( for example, by interpreting the integral as an area) before the section on the fundamental theorem of calculus. There are several integration problems that can be done in more than one way. |