1. Introduction to Calculus

2. The Area Problem The red line is a straight line. What is the area of the shape?

3. The Area Problem The red line is a parabola. What is the area of the shape?

4. Formulas

5. Ellipse

6. Cubic

7. Root

8. The Slope Problem What is the slope of this line?

9. The Slope Problem What is the slope of this line…

10. The Slope Problem Slope doesn’t really make sense for graphs other than straight lines But we can find something similar

11. The Slope Problem This is called the tangent line It touches the curve at only one point We then determine the slope of the tangent line

12. The “divide by zero” problem

15. The Proof Problem 1+2+3 = 6 which is a multiple of 3 8+9+10 = 27 which is a multiple of 3 101+102+103 = 306 which is a multiple of 3 But is this always true?

16. The Proof Problem We want to investigate the “area”, “slope”, and “divide by zero” problems But we need to do so systematically This will require you to learn how to construct proofs A proof is a general argument for why a statement is true

17. Example

19. Proof Techniques Proofs will involve the following: ◦Technical language (definitions) ◦Algebra ◦Other results (Theorems) ◦Clever insights You should understand the proofs and commit them to memory

20. Course problem

22. Course Outline Instructor: Jehu Peters Email: jehu.peters@7oaks.orgjehu.peters@7oaks.org Required Text: James Stewart, Calculus 8 th Edition. Thomson Brooks/Cole. Grading: 60% Final Exam: Friday, June 3, 2016. Check with instructor to confirm final exam room and time. 30% Tests: Feb 26, March 24, April 28, May 27 10% Assignments

23. Course Outline Factoring polynomials, sign diagrams and inequalities, absolute value: Appendix A. Limits and Continuity: 2.2–2.6 Derivatives: 2.7, 2.8, 3.1–3.6 Applications of the derivative: 4.1–4.5, 3.8, 4.7 The Integral: 4.9, Appendix E, 5.1–5.5 Applications of the integral: 6.1, 6.2, 6.3, 6.5 The natural log, exponential functions: Appendix G Techniques of integration: 7.1–7.5 Indeterminate forms and l'Hospital's Rule: 4.4 Improper Integrals: 7.8 Arc Length: 8.1

24. Notes Calculators will not be allowed during tests or the final exam. Assignments need to be handed in on or before the due date. No late assignments will be accepted. Cell phones and other electronic devices must be turned off during tests and the final exam. If you miss a class, it is your responsibility to borrow the notes from another student. There will not be any makeup tests available in this course. If an emergency arises, documentation (e.g. doctor’s note, obituary, etc.) must be provided before your final exam may be weighted to compensate for the missed test.

25. Course Outline First class: February 8, 2016 Last class: June 30, 2016 Withdrawal Date: May 20, 2016

26. Grades Tentative Grading System: A+93 – 100 A85 – 92 A-80 – 84 B+75 – 79 B69 – 74 C+63 – 68 C55 – 62 D50 – 54 F0 – 49

27. Expectation You will be expected to: Review the day’s notes Attempt homework problems (2 hours) Complete assignments Watch supplementary videos

28. Website https://themathbehindthemagic.wordpress.com/ca lculus/https://themathbehindthemagic.wordpress.com/ca lculus/ I will post videos, notes, and handouts You are expected to check the website regularly Example: https://youtu.be/3ZhUdleD1lQhttps://youtu.be/3ZhUdleD1lQ

30. WolframAlpha.com This website will help you check your answers

31. Remind 101 To help remind you about upcoming tests, assignments, or homework practice, I will be sending out periodic text messages. Please follow these instructions to get the updates: Enter this number: (204) 808-8974 Text this message: @uwcalculus

32. Course Calendar MondayTuesdayWednesdayThursdayFriday Feb 8 – 12 Introduction / Review Introduction, course overview Algebra Review notes Hmw HANDOUT Algebra review Extra time Factoring Sign Diagram Notes HANDOUT Hmw HANDOUT Limits: Properties and Evaluate Hmw HANDOUT Limits: By Factoring Hmw HANDOUT Feb 15 – 19 Limits Louis Riel Day NO CLASSES Limits: one sided and squeeze theorem Continuity Notes HANDOUT Continuity IVT Trig Limits Identities HANDOUT Hmw HANDOUT

33. Questions?