Date modified: Wed 2024-07-31 . 12:10 PM
Date created: Wed 2024-07-31 . 12:10 PM
# Math 7 Calculus 1 Homepage **Welcome to Math 7 Calculus 1 !** (Refresh this page often for updates.) Classes on TWR, from 12:45pm to 3:00pm at PV 175 Break time: ~1:50pm to ~2:00pm Office hours: After class each day for 30 min to an hour, we will start in PV 175 and move to Math Lab if run long. **Class held during the Fall 2023 semester, starting from week 4 to week 15.** ## ![[---images/---assets/---icons/exclaim-icon.svg]] Important Message: - We learn what we do ! - **Remember the "generation effect" -- by actively doing work, you learn and retain better !** - Buy some notebooks, or notebook paper, or have a way to keep all your notes and work (say a tablet or a folder). - You can do it ! I believe in you ! ## ![[---images/---assets/---icons/important-icon.svg]] Important links / information. - [[1 teaching/smc-fall-2023-math-7/smc-fall-2023-math-7-syllabus|Course syllabus]] - [Class Log and Assignments](#log) - [week 4](#wk4), [week 5](#wk5), [week 6](#wk6), [week 7](#wk7), [week 8](#wk8), [week 9](#wk9), [week 10](#wk10), [week 11](#wk11), [week 12](#wk12), [week 13](#wk13), [week 14](#wk14) - [Math lab tutoring](https://www.smc.edu/student-support/academic-support/tutoring-centers/math-lab/) - Textbooks (find any copy would do...) - Calculus by Thomas (12E, with Weir and Hass) - Calculus by Stewart (9E, with Clegg and Watson) ## ![[---images/---assets/---icons/pencil-icon.svg]] Assignments and reading ### Week 4. - Topics: Review of functions, algebra, geometry, trigonometry. - Suggested Reading: - Thomas: Chapters 1.1, 1.2, 1.3, 1.4 - Stewart: Chapters 1.1, 1.2, 1.3 - Homework (do them neatly, and upload them onto Canvas): - [[1 teaching/smc-fall-2023-math-7/week-4/week-4A-problems|week-4A-problems]] - [[1 teaching/smc-fall-2023-math-7/week-4/week-4B-problems|week-4B-problems]] - [[1 teaching/smc-fall-2023-math-7/week-4/week-4C-problems|week-4C-problems]] - Additional interesting things: - [Generation effect](https://en.wikipedia.org/wiki/Generation_effect) (Actively filling in the blank helps learning) - [Euler's formula](https://en.wikipedia.org/wiki/Euler%27s_formula) $e^{i\theta}=\cos\theta+i\sin\theta$ (We used it to prove the angle addition formulas) - [Prosthaphaeresis](https://en.wikipedia.org/wiki/Prosthaphaeresis) (How one used to multiply numbers with trigonometric identities) ### Week 5. - Topics: Rates of change, tangent lines, limits and continuity - Suggested Reading: - Thomas: Chapters 2.1, 2.2, 2.3, 2.4 - Stewart: Chapters 1.4, 1.5, 1.6, 1.7 - Homework (do them neatly, and upload them onto Canvas): - [[1 teaching/smc-fall-2023-math-7/week-5/week-5A-problems|week-5A-problems]] - [[1 teaching/smc-fall-2023-math-7/week-5/week-5B-problems|week-5B-problems]] - [[1 teaching/smc-fall-2023-math-7/week-5/week-5C-problems|week-5C-problems]] - [[1 teaching/smc-fall-2023-math-7/week-5/formal-definition-of-limits|Additional notes for formal definition of limits, and examples.]] ### Week 6. - Topics: Sandwich theorem, small angle approximation, one-sided limits, and continuity - Suggested Reading: - Thomas: Chapters 2.2, 2.3, 2.4, 2.5 - Stewart: Chapter 1. - Homework (do them neatly, and upload them onto Canvas): - [[1 teaching/smc-fall-2023-math-7/week-6/week-6A-problems|week-6A-problems]] - [[1 teaching/smc-fall-2023-math-7/week-6/week-6B-problems|week-6B-problems]] - **EXAM 1 INFO:** - In-class exam Thursday (10/5). You get to use the entire 2 hours and 15 minutes. - ~ 6 problems or so (some has multiple parts). - No aids: Namely, no calculators, no cheat sheets, no notes, no books, no technology. Just you. - Bring pencil / eraser or pen. - Material covered up to and including Week 6 Monday lecture and homework up to and including week 6A problems. Some topics you might want to review: - Continuity and one-sided limits - Sandwich theorem and the small angle approximation $\lim_{x\to 0} \frac{\sin(x)}{x} = 1$. - Proving limit statements using the formal $\epsilon$-$\delta$ definition of limits. - Computing / determining limits using algebra or graphs. - Average rate of change vs instantaneous rate of change. - Finding Secant line equation and tangent line equations using limits. - Review material from your past life: Geometry / trigonometry / algebra / functions. ### Week 7. - Topics: Tangents and derivative at a point; derivative rules. - Suggested Reading: - Thomas: Chapters 3.1, 3.2, 3.3, 3.4, 3.5 - Stewart: Chapters 2.1, 2.2, 2.3, .2.4 - Homework - [[1 teaching/smc-fall-2023-math-7/week-7/exam-1-corrections-instruction|exam-1-corrections-instruction]] - [[1 teaching/smc-fall-2023-math-7/week-7/week-7a-problems|week-7a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-7/week-7b-problems|week-7b-problems]] - [[1 teaching/smc-fall-2023-math-7/week-7/week-7c-problems|week-7c-problems]] ### Week 8. - Topics: Chain rule, implicit differentiation, related rates, linearization. - Suggested Reading: - Thomas: Chapters 3.6, 3.7, 3.8, 3.9 - Stewart: Chapters 2.5, 2.6, 2.7, 2.8, 2.9 - Homework - [[1 teaching/smc-fall-2023-math-7/week-8/week-8a-problems|week-8a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-8/week-8b-problems|week-8b-problems]] - [[1 teaching/smc-fall-2023-math-7/week-8/week-8c-problems|week-8c-problems]] ### Week 9. - Topic: Extreme values of a function, Fermat's theorem of stationary points, critical points, finding absolute extrema on a closed interval. L'Hospital rule. - Suggested Reading: - Thomas: Chapters 4.1, 4.2 - Stewart: Chapters 3.1, 3.2 - Homework - [[1 teaching/smc-fall-2023-math-7/week-9/week-9a-problems|week-9a-problems]] - **EXAM 2 INFO:** - In-class exam Thursday (10/26). You get to use the entire 2 hours and 15 minutes. - ~ 6 problems or so, plus a multiple choice section. - No aids: Namely, no calculators, no cheat sheets, no notes, no books, no technology. Just you. - Bring pencil / eraser or pen. - Material covered up to and including Week 9 Monday lecture and homework up to and including week 9A problems. Some topics you might want to review: - Intermediate value theorem. - Limit definition of the derivative. - Meaning and interpretation of the derivative. - Computation using derivative rules. - Proofs of the derivative rules (constant multiple rule, power rule, sum rule, product rule, quotient rule) - Applications of chain rule and implicit differentiation. - Finding slopes of an implicitly defined curve. - Related rates problem (review lecture notes and exercises!) - Linearization and linear approximation. - Finding absolute maximum / minimum value of a differentiable function over a closed interval (to be covered Week 9 Tuesday.) ### Week 10. - Topic: Rolle's theorem, Mean value theorem, antiderivatives, first derivative test, concavity and curve sketching - Suggested reading: Thomas Chapters 4.2, 4.3, 4.4, 4.7 - Homework. - [[1 teaching/smc-fall-2023-math-7/week-10/week-10a-problems|week-10a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-10/week-10b-problems|week-10b-problems]] ### Week 11. - Topic: Curve sketching, optimization, and Newton's method. - Suggested reading: Thomas Chapters 4.4, 4.5, 4.6, 4.7 - **Note. On this upcoming exam I will let you use a non-graphing scientific calculator. Please try to find one by next week** - Homework. - [[1 teaching/smc-fall-2023-math-7/week-11/week-11a-problems|week-11a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-11/week-11b-problems|week-11b-problems]] - [[1 teaching/smc-fall-2023-math-7/week-11/week-11c-problems|week-11c-problems]] ### Week 12. - Topic: Sigma notation (summation notation), Area estimation, Riemann sum, and the definite integral. - Suggested reading: Thomas Chapter 5. Start with 5.1, 5.2, 5.3. - Homework. - [[1 teaching/smc-fall-2023-math-7/week-12/week-12a-problems|week-12a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-12/week-12b-problems|week-12b-problems]] - **IMPORTANT NOTE.** As announced in class on Tuesday, Exam 3 will be a **take home** exam. More details on that later (it will be assigned Thursday, and to be turned in Sunday midnight on canvas). But yes, there is still regular class on Thursday. Just to give you a bit of break but also gives us a bit more time to focus on this new section on integrals. - **EXAM 3 INFO:** - As mentioned in class on Tuesday, this upcoming exam 3 will be TAKE HOME. **You MUST come to class on Thursday 11/16 to pick up a copy**, **no digital copies will be provided**. The exam will be due on Canvas by Sunday 11/19/2023 11:59:59 PM. - If you do not pick up a copy, then you are considered absent for this exam, **no exceptions**. - There will be regular class lecture on Thursday. - You are allowed to use your notes and textbook, or work with other people or tutor if you wish. However the work you submit must be entirely your own. And you will need to write down all the resources used and your collaborators. Do not, however, use homework websites like Chegg. I really want you to learn the material covered on the exam. - The topics on the exam will include: - Extreme values of a function. - Rolle's theorem and the Mean Value theorem, their corollaries and applications (such as determining the number of roots of a function). - Concavity, asymptotes, and curve sketching. - Optimization problems. - Newton's method. - Antiderivatives. ### Week 13. - Topic: Mean value theorem for integrals, the area function, the fundamental theorem of calculus (FTC I and FTC II), indefinite integrals - Suggested reading: Thomas Chapter 5.4, 5.5, 5.6 - **No class Thursday: Happy Thanksgiving!** - Homework - [[1 teaching/smc-fall-2023-math-7/week-13/week-13a-problems|week-13a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-13/week-13b-problems|week-13b-problems]] ### Week 14. (we are almost there!) - Topic: Applications of integration: Areas, volumes, parallel plane cross-sections, solids of revolutions, disk method, shell method, arclength, differential equations, and inverses. - Turn in everything by next Wednesday! - Suggested reading: Thomas Chapter 5.6, 6.1, 6.2, 6.3 - Homework - [[1 teaching/smc-fall-2023-math-7/week-14/week-14a-problems|week-14a-problems]] - [[1 teaching/smc-fall-2023-math-7/week-14/week-14b-problems|week-14b-problems]] ### Week 15. (Last week, final exam!) - Final exam **THURSDAY IN CLASS** - Turn in everything by Wednesday midnight. - You may bring one page (both sides) 8.5 in x 11 in cheat sheet for the final exam. ## ![[---images/---assets/---icons/dates-icon.svg]] Important Dates - First day: 9/19 (Week 4 Tuesday) - Exam 1: 10/5 (Week 6 Thursday) - Exam 2: 10/26 (Week 9 Thursday) - Exam 3: 11/16 (Week 12 Thursday) - No class on 11/23 Holiday - Last day / Final exam: 12/7 (Week 15 Thursday) ## ![[---images/---assets/---icons/question-icon.svg]] Tentative Schedule Week 4: Review - Thomas Chapter 1 - Stewart Chapter 1 Week 5: Limits and continuity. - Thomas Chapter 2 - Stewart Chapter 1 Week 6: Limits and continuity. Exam 1 - Thomas Chapter 2 - Stewart Chapter 1 Week 7: Differentiation. - Thomas Chapter 3 - Stewart Chapter 2 Week 8: Differentiation. - Thomas Chapter 3 - Stewart Chapter 2 Week 9: Applications of differentiation. Exam 2 - Thomas Chapter 4 - Stewart Chapter 3 Week 10: Applications of differentiation. - Thomas Chapter 4 - Stewart Chapter 3 Week 11: Riemann sum and integrals. - Thomas Chapter 5 - Stewart Chapter 4 Week 12: Riemann sum and integrals. Exam 3 - Thomas Chapter 5 - Stewart Chapter 4 Week 13: Applications of integration. - Thomas Chapter 6 - Stewart Chapter 5 Week 14: Applications of integration. - Thomas Chapter 6 - Stewart Chapter 5 Week 15: Catch up / Review / Final exam.