Daily Assignments
Optional Review Stuff
One of the biggest sources of difficulty in calculus is weak or underprepared skills at algebra and trigonometry. If you want to succeed in this course, you should be comfortable with:
- Multiplying and factoring polynomials;
- Multiplying and dividing fractions and rational functions;
- Working with exponents;
- Working with trigonometric functions and the unit circle.
I don’t have any organized review materials for these topics, but if you want to brush up on them, you may want to look at:
- OpenStax College Algebra chapters 1 and 5;
- OpenStax Precalculus chapter 5.
Week 0: August 24 – 25
August 24: Syllabus and Functions
- Please read the syllabus
- Claim your account on WeBWorK through Blackboard.
- Read Professor Bonin’s advice on study skills
- Read Section 1.1 of the online notes (about a page)
- Skim Strang and Herman §1.1-3 to remind yourself of precalculus material.
- Optional/bonus: Watch Essence of Calculus, Chapter 1 by 3Blue1Brown
Week 1: August 28 – September 1
August 29: Estimation
- Read Section 1.2-3 of the online notes
- Optional: Play with this Geogebra widget for visualizing the relationships between ε and δ for different functions.
- Optional videos:
- Watch the first ten minutes of Essence of Calculus, Chapter 7
- If you haven’t seen derivatives before, don’t worry too much about when he mentions them. The key material I want starts about five minutes in.
- Khan Academy has a series of videos that might be helpful. I’m linking the second, but the third and fourth in this series are also good for understanding limit arguments better.
- Watch the first ten minutes of Essence of Calculus, Chapter 7
August 30: Recitation on Estimation
August 31: Continuity and Computing Limits
- Mastery Quiz 1 due
- Topics: S1
- Single Sheet
- Answer Blanks
- Read Section 1.4 of the online notes
- Optional Videos:
Week 2: September 4 – 8
September 5: More on Limits
- Read the solutions to mastery quiz 1
- Read Section 1.5 of the online notes
- You can also consult Strang and Herman 2.3.6
- Bonus video: Math at Andrews on the Squeeze Theorem
September 6: Recitation 2 on Computing Limits
September 7: Infinite Limits
- Mastery Quiz 1 due Thursday, September 7
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Read Section 1.6 of the online notes
- You can also consult Strang and Herman the part of section 2.2 on infinite limits and section 4.6
Week 3: September 11 – 15
September 12: Intro to Derivatives
- Read the Solutions to Mastery Quiz 2
- Read Section 2.1-2 of the online notes
- You may find the 3Blue1Brown Essence of Calculus, Chapter 2 helpful.
September 13: Recitation 3 on Advanced Limits
- Skills quiz on M1: computing limits
- Covers all our limit computation techniques, starting from August 31
- Recitation 3 Worksheet
September 14: Computing Derivatives
- Mastery Quiz 3 due
- Topics: M1, S2
- Single Sheet
- Answer Blanks
- Read Section 2.3 of the online notes
- See also Strang and Herman, section 3.3.
Week 4: September 18 – 22
September 19: Trig Derivatives and Chain Rule
- Read the solutions to mastery quiz 3
- Read Section 2.4-5 of the online notes
- It is very important to practice taking derivatives quickly and easily.
- There are a collection of practice problems at IXL.
- I have a practice worksheet of especially challenging derivatives, with solutions. Nothing anywhere near this challenging will appear on this test, but these are a good way to push yourself if you want some extra-challenging practice.
Recitation 4 on taking derivatives
September 21: Linear Approximations and Speed
- Mastery Quiz 4 due
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks
- Read the solutions to skills quiz 1
- Read Sections 2.6 and 2.7.1 of the online notes
Week 5: September 25 – 29
September 26: Rates of Change and Tangent Lines
- Read the solutions to Mastery Quiz 4
- Read Sections 2.7.2 and 2.8 of the online notes
- See also Strang and Herman, section 3.4 and also you can look back at 3.1.1-3.1.2
September 27: Recitation 5 on linear approximation
September 28: Implicit Differentiation and Tangent Lines
- Mastery Quiz 5 due
- Topics: M1, M2, S3, S4
- Single Sheet
- Answer Blanks
- Look at Practice Midterm 1
- Read Section 2.9 of the online notes
- See also Strang and Herman, section 3.8
Week 6: October 2 – 6
Week 7: October 9 – 11
Week 8: October 16 – 20
Week 9: October 23 – 27
Week 10: October 30 – November 3
Week 11: November 6 – 10
Week 12: November 13 – 17
Thanksgiving Break: November 20-24
Get some rest!
Week 13: November 27 – December 1
Week 14: December 4 – 8
Finals Week
Course notes
Mastery Quizzes
- Mastery Quiz 1 due Thursday, August 31
- Topics: S1
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 2 due Thursday, September 7
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 3 due Thursday, September 14
- Topics: M1, S2
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 4 due Thursday, September 21
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 5 due Thursday, September 28
- Topics: M1, M2, S3, S4
- Single Sheet
- Answer Blanks
- Solutions
Major Topics
- Computing Limits
- Computing Derivatives
- Extrema and Optimization
- Integration
Secondary Topics
- Estimation
- Definition of derivative
- Linear Approximation
- Rates of change and models
- Implicit Differentiation
- Related rates
- Curve sketching
- Physical Optimization Problems
- Riemann sums
- Integral Applications
Tests
- Midterm on October 3
- Topics: M1, M2, S1, S2, S3
- Practice Midterm 1
- Midterm on November 7
- Tentative topics: M3, S4, S5, S6, S7, S8
- Practice Midterm 2
- Final Exam date Tuesday, December 19 3:00–5:00 PM
- As scheduled by the registrar
- Per the syllabus, you will not be excused from the final if you schedule travel during finals week; if you must buy your plane ticket before the registrar announces final exam, please make sure it departs after December 19.
- Practice Final
Calculators will not be allowed on tests.
Textbook
The official textbook for Math 1231 is OpenStax Calculus Volume 1 by Gilbert Strang and Edwin Herman. It is available for free online here. You can also buy copies from Amazon; a paperback is a little under $30.
I will be loosely following the textbook, but will often be giving my own take or focusing on topics the textbook doesn’t emphasize. All my course notes will be posted to the course web page.
We will be using a (free!) online homework system called WeBWorK this term. You can access it by going to Blackboard, then to “Course Links”, and clicking the WeBWorK link. This will automatically create an account for you and log you in. You may continue to log in through Blackboard, or if you wish you may create a password within WeBWorK to log in directly.
Course Goals
This is the first semester of a standard year-long sequence in single-variable calculus. The main topics are limits and continuity; differentiation and integration of algebraic and trigonometric functions; and applications of these ideas. This corresponds roughly to Chapters 1–6 of Herman–Strang.
By the end of the course, students will acquire the following skills and knowledge: students will know the intuitive and formal definitions of the limit, derivative, antiderivative, and definite integral of a function. Students will be able to distinguish continuous from discontinuous functions by visual and algebraic means; to calculate derivatives of functions both by definition and using various simplification rules; to formulate and solve related rates and optimization problems; to accurately sketch graphs of functions; to calculate antiderivatives and definite integrals of a variety of functions; to compute areas of regions in the plane and volumes of solids of revolution; and to explain the significance of important theoretical results such as the Extreme Value Theorem, Mean Value Theorem, and Fundamental Theorems of Calculus.