Lecture Notes

1. 24. Final exam notes, Review
   

2. 23. Newton’s Method, Antiderivatives
   

3. 22. Optimization Problems
   

4. 21. Curve Sketching cont’d
   

5. 20. Curve Sketching
   

6. 19. Rolle’s Theorem, Mean Value Theorem
   

7. 18. Extremal Values, Critical Points
   

8. 17. Taylor Polynomials cont’d, Extremal Values
   

9. 16. Taylor Polynomials cont’d, Lagrange Remainder Formula
   

10. 15. Taylor Polynomials
    

11. 14. Related rates, Linear Approximations, Course Notes on Taylor Polynomials
    

12. 13. Related Rates
    

13. 12. Newton’s Law of Cooling and Compound Interest, wine example
    

14. 11. Natural growth and decay
    

15. 10. Logarithmic differentiation, Rates of Change in the Natural and Social Sciences
    

16. 9. Inverse Functions, derivative of arctan
    

17. 8. Implicit Differentiation, derivatives of log and arcsin
    

18. 7. Chain Rule, Implicit Differentiation
    

19. 6. Derivatives - examples, relationship with continuity, differentiation rules
    

20. 5. Intermediate Value Theorem, horizontal asymptotes, introduction to the derivative
    

21. 4. Continuity
    

22. 3. Limits cont’d 
    

23. 2. Limits (most of this lecture was on the blackboard)
    

24. 1. Introduction
    

Solution Sets

Links below are no longer active.  Past students are welcome to email me for solutions.

Quizzes:

   

Problems from Quiz “n” come from Homework Week “n”.  There were no Quizzes 3 and 8 due to the two midterms.

1. ◦Quiz 9
   

2. ◦Quiz 7
   

3. ◦Quiz 6
   

4. ◦Quiz 5
   

5. ◦Quiz 4
   

6. ◦Quiz 2
   

7. ◦Quiz 1
   

8. ◦Quiz 0
   

Midterms:

1. ◦Practice Midterm 1
   

2. ◦Solutions to Practice Midterm 1
   

3. ◦Solutions to Midterm 1
   

4. ◦Practice Midterm 2
   

5. ◦Solutions to Practice Midterm 2
   

6. ◦Solutions to Midterm 2
   

7. ◦Note on Midterm 2
   

Homework:

1. ◦Week 8: Solutions to even problems in Section 2 of Taylor Course Notes.
   

2. ◦“Extra Calculator problem” (or why not to always just trust your calculator)
   

3. ◦You’re welcome to ask me about solutions to any of the other homework problems that you are unsure about.

Homework Problems

Unless explicitly stated otherwise, you do not have to hand in the homework problems listed below.  However, the weekly quiz consists of a selection of these problems, so if you can do them all, you’ll know how to do the quiz!

Note: problems which tell you to use your calculator will not be on the quiz, because you are not allowed to use a calculator on the quiz.

Week 0

1. ◦Pg. 73-75, Chapter 1 Review: Do the True-False quiz and exercises 2,5,7,8,17,19,20,22,23,24.
   

2. ◦Quiz 0 is scheduled for Tuesday, Sept. 14, and will be comprised of a selection of these problems.
   

Week 1

1. ◦§2.1: 3, 5
   

2. ◦§2.2: 7, 9, 12, 15, 19, 21, 25, 28
   

3. ◦Extra calculator problem
   

4. ◦§2.3: 1, 13, 15, 17, 23, 25, 27, 35, 37, 43, 44, 47, 48, 49, 51, 61
   

5. ◦pg. 166 True-False Quiz: 1-8,
   

6. ◦Problems Plus, Chapter 2 (pg. 170): 2, 3, 9
   

Week 2

1. ◦§2.5: 3, 5, 9, 17, 18, 35, 39, 41, 42, 45, 47, 49, 63, 65
   

2. ◦§2.6: 3, 7, 17, 19, 25, 31, 57, 58
   

3. ◦§2.7: 5, 7, 9(a) and (b), 13, 15, 17, 19, 21, 25, 29, 31, 33, 41, 49, 51
   

4. ◦Problems Plus, Chapter 2: 8
   

Week 3

1. ◦§2.8: 1, 9, 11, 15, 21, 25, 27, 35, 43, 49, 53
   

2. ◦§3.1: 9, 11, 15, 19, 20, 23, 25, 31, 35, 45, 46, 49, 51, 53, 55, 57, 59, 61, 62, 63, 67, 69, 73, 75
   

3. ◦§3.2: 2, 3, 5, 7, 11, 12, 17, 18, 21, 25, 27, 29, 31, 33, 41, 43, 45, 49, 51, 55
   

4. ◦§3.3: 5, 9, 11, 13, 15, 19, 22, 23, 29, 33, 37, 39, 41, 45, 51
   

5. ◦Problems Plus, Chapter 2: 12
   

6. ◦Problems Plus, Chapter 3: 1, 6, 9
   

Week 4

1. ◦§3.4: 5, 11, 23, 25, 31, 37, 39, 40, 42, 49, 59, 61, 70, 71, 75, 94
   

2. ◦§1.6: 17, 23, 25, 41, 57, 59, 61, 63, 65
   

3. ◦§3.10: 2, 3, 4  (Here, “linearization” = “linear approximation” = “tangent line”)
   

4. ◦§3.5: 7, 11, 15, 17, 21, 27, 34, 35, 39, 41, 45, 47, 53, 61, 65
   

5. ◦Problems Plus, Chapter 3: 8, 11, 14
   

Week 5

1. ◦§3.6: 3, 7, 8, 11, 15, 17, 19, 26, 29, 33, 39, 40, 43, 47, 50, 53
   

2. ◦§3.7: 3, 5, 7, 9, 13, 16, 17, 20, 33
   

3. ◦Problems Plus, Chapter 3: 25
   

Week 6

1. ◦§3.8: 3, 4, 5, 7, 10, 11, 12, 13, 15, 16, 17
   

2. ◦§3.9: 5, 7, 13, 15, 18, 22, 23, 25, 27, 29, 33, 35, 38, 39, 43
   

Week 7

1. ◦§3.9: 13, 16, 20, 23, 25, 29, 31, 33, 35, 38, 39, 40, 43, 44 (Several of these are repeats from last week.)
   

2. ◦§3.10: 1, 5, 23, 27, 28, 31, 42, 43
   

3. ◦Problems Plus, Chapter 3: 30, 31
   

4. •Course Notes §1: Exercises 1, 2, 3, 4, 5  (Click odd numbered exercises for solutions.)
   

Week 8

1. •Course Notes §2: Exercises 1, 2, 3, 4 (click odd-numbered exercises for solutions)Solutions to even problems
   

2. •§4.1: 9, 11, 19, 21, 27, 33, 34, 39, 41, 52, 53, 57, 59, 61, 70, 75
   

Week 9

1. •§4.1: 9, 11, 19, 21, 27, 33, 34, 39, 41, 52, 53, 57, 59, 61, 70, 75
   

2. •Alternate solutions to 19, 21, 27 and some notes on local extrema and critical points
   

Week 10

1. •§4.2: 5, 7, 11, 14, 15, 19, 22, 23, 26, 27, 30, 31, 34, 35
   

2. •Problems Plus, Chapter 4: 2, 11
   

3. •§4.3: 5, 7, 11, 12, 13, 15, 20, 25, 27, 35, 41, 43, 50, 51, 67, 68, 81
   

Week 11

1. •§4.5: 17, 19, 23, 31, 35, 37, 48, 49, 56, 59, 65, 67, 68
   

2. •§4.7: 11, 13, 19, 24, 25, 30, 31, 37, 43, 46, 47, 49, 65, 67, 70
   

3. •§4.8: 5, 7
   

Week 12 (no quiz on problems from this week)

1. •§4.8: 11, 15, 18, 23, 24, 31, 37
   

2. •§4.9: 3, 5, 13, 19, 25, 28, 31, 37, 44, 57, 58, 61, 67, 73, 74
   

3. •Problems Plus, Chapter 4: 13
   

1. ◦Review Assignment
   

Final Exam Review Materials

1. ◦Theorem Sheet
   

2. ◦Learning objectives - a list of topics, plus practice problems for each.
   

3. ◦Information about the final exam - including exam format and a list of topics that will NOT be covered on the final exam.
   

4. ◦“Warnings” - A list of common, but serious first-year calculus errors.  (You do not need to know L’Hopital’s Rule for the final exam.)
   

5. ◦Course Outline
   

6. ◦Review Assignment and Solutions
   

Final exams from previous years:

1. ◦2009
   

2. ◦2008
   

3. ◦2007
   

4. ◦2006
   

5. ◦2005
   

Solution sets: The Math Club has printed past exam packages and they will be on sale starting next week from Monday to Friday, 11am - 3pm at the Math Club in MATX 1119. The exam packages are $5 for members and $10 for non members.  (A membership costs $2.) For more information, see their webpage, http://www.ubcmathclub.org/exams.php.