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Links:
Syllabus
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Weeks 8 - 14
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Math Lab Hours
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Writing Lab
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Reading |
Exercises to be collected at the beginning of class |
Friday
8/25
Outline
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Introduction to Math 131
- Syllabus and questions
- Review of functions
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Week 1
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Monday
8/28
Outline
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Skim Chapter 1, Sections 1.1 - 1.3. This should be a review of what we covered in class on Friday.
Read carefully Chapter 2, Sections 2.1, 2.2.
2.1 The tangent and velocity problems
2.2 The limit of a function
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Homework #1
Read Math 131: Getting started.
Read instructions for turning in homework. You are responsible for following these guidelines in your homework assignments for Math 131.
1.1 11, 20, 21, 48, 53
1.2 10, 13
1.3 36, 40, 45
2.1 2
2.2 4, 7, 10, 19, 23
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Wednesday
8/30
Outline
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2.3 Calculating limits using limit laws
2.4 The precise definition of a limit, Part 1 (computer demo)
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Homework #2
1.3 48, 55, 58, 61
2.2 27, 29, 32a, 34
2.3 1, 2, 7
2.4 1, 2, 3
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Friday
9/1
Outline
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2.4 The precise definition of a limit, Part 2
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Homework #3
Read instructions for writing mathematics essays. You are responsible for following these guidelines for your essays in Math 131. Essay #1 is due Monday.
2.3 15, 20, 23, 27, 29, 30
2.4 4, 6, 7, 8, 9, 10
Graphs for 2.4, 7 - 10
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Week 2
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Monday
9/4
Outline
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3.1 Derivatives
3.2 The derivative as a function
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Homework #4
2.4 15, 16, 17, 19
3.1 1, 2, 3, 4
3.2 1, 4, 6, 7
Essay 1: Explain the epsilon-delta definition of limit.
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Wednesday
9/6
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Exam 1
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Friday
9/8
Outline
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3.3 Differentiation formulas
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Homework #5
2.4 26, 29, 30, 32
Try these! They are challenging!
3.1 6, 7, 13, 19, 20
3.2 9, 10, 25
3.3 6, 8, 9
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Week 3
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Monday
9/11
Outline
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3.4 Rates of change in science
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Homework #6
3.1 15, 18, 24, 26
3.2 35, 37
Graphs for 3.2, 37
3.3 21, 27, 29, 30, 54, 58ab
3.4 3, 4, 17, 29
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Wednesday
9/13
Outline
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3.5 Derivatives of trig functions
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Homework #7
3.3 33, 40, 41, 58cd, 59, 65, 68, 71, 75, 83
3.5 3, 5, 6
Essay 2: Prove the product rule. Your proof must include a detailed explanation. |
Friday
9/15
Outline
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3.6 The chain rule, Part 1
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Homework #8
3.4 15, 18, 26, 33, 35
3.5 10, 18, 21, 24, 29
3.6 1, 2, 3, 7, 9
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Week 4
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Monday
9/18
Outline
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3.6 The chain rule, Part 2
3.7 Implicit differentiation, Part 1
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Homework #9
3.6 8, 13, 17, 22, 25, 30, 33, 38
3.7 1, 2, 5, 7
Essay 3: Explain why the derivative of cos(x) is -sin(x). Use the methods in 3.5. Your outline from Section 3.5 may also be helpful.
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Wednesday
9/20
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Exam 2
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Friday
9/22
Outline
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3.7 Implicit differentiation, Part 2
3.8 Higher derivatives
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Homework #10
3.5 33, 35, 36, 40
3.6 41, 46, 53, 56, 61, 62
3.7 10, 11, 14, 19, 21
3.8 1, 5, 8
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Week 5
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Monday
9/25
Outline
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3.9 Related rates
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Homework #11
3.6 63, 64
3.7 25, 30, 32ab, 36, 38
3.8 2, 10, 20, 24
3.9 1, 3, 4
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Wednesday
9/27
Outline
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3.9 Related rates
3.10 Linear approximations and differentials
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Homework #12
3.7 41, 45
Graph for 3.7, 45
Resubmit 3.7 36, 38 if you did not do them completely the first time!
3.8 33, 35, 39, 40, 46
3.9 7, 8, 11, 15
Essay 4: Rewrite Essay 3, incorporating my suggestions of your original drafts. Make sure to turn in the original essay with your rewrite.
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Friday
9/29
Outline
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Homework #13
3.9 27, 28, 33, 34, 37
3.10 1, 5, 7, 11
Graph for 3.10, 11
4.1 3, 5, 31
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Week 6
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Monday
10/2
Outline
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4.1 Maximum and minimum values
4.2 The mean value theorem, Part 1
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Homework #14
3.10 19, 23, 29, 33, 39, 44
4.1 47, 52, 61
Graph for 4.1, 61
4.2 1, 5, 6, 7
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Wednesday
10/4
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Exam 3
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Friday
10/6
Outline
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4.3 How derivatives affect the shape of a graph
4.4 Limits at infinity
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Homework #15
4.2 17, 23, 30, 33
4.3 1, 11, 13
4.4 11, 12, 16
Essay 5: Explain: if f has an absolute maximum at c, where c is in the interval [a,b], then either
1) f '(c)=0, or
2) f '(c) doesn't exist, or
3) c is an endpoint.
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Week 7
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Monday
10/9
Outline
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4.5 Summary of curve sketching
4.7 Optimization problems
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Homework #16
4.3 23, 27, 29, 30, 33, 37
4.4 20, 21, 27, 61, 62, 63
Graphs for 4.4, 61 - 63
4.5 19, 26
4.7 2, 5, 6, 9
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Wednesday
10/11
Outline
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4.7 Optimization problems
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Homework #17
4.7 11, 14, 15, 20, 22, 23, 35, 36
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Friday
10/13
Outline
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4.10 Antiderivatives
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Homework #18
4.7 40, 43, 44, 46, 50, 51, 53
4.10 3, 5, 9
Essay 6: Explain horizontal asymptotes intuitively.
Also, explain the precise definition of a limit as x appoaches ±∞.
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Monday
10/16
through
Friday
10/20
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Fall Break!!!
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