Math 1231: Single-Variable Calculus I
Section 11
Spring 2024

Contact Info
Spring 2024

Office: Phillips Hall 720E
Email: jaydaigle@gwu.edu

Office Hours:

Often in office:

Course Information

Lecture:

  • TR 4:45 PM–6:00 PM
  • Phillips B156

TA

TA Office Hours:

  • TR 12:30 – 1:30
  • 720G

Official textbook:

Recitations

Section 36:

  • F 8:00 AM–8:50 AM
  • Monroe 350

Section 37:

  • F 9:35 AM–10:25 AM
  • Monroe 110

Section 38:

  • F 11:10 AM–12 Noon
  • Rome B103

Course Information

Lecture:

  • TR 4:45 PM–6:00 PM
  • Phillips B156

TA

TA Office Hours:

  • TR 12:30 – 1:30
  • 720G

Official textbook:

Recitations

Section 36:

  • F 8:00 AM–8:50 AM
  • Monroe 350

Section 37:

  • F 9:35 AM–10:25 AM
  • Monroe 110

Section 38:

  • F 11:10 AM–12 Noon
  • Rome B103

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:

Week 1: January 15 – 19
January 16: Syllabus and Functions
January 18: Estimation
  • Read Section 1.2-3 of the online notes
    • You can also consult Strang and Herman 2.2 and 2.5.
  • 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.
January 19: Recitation on Estimation
Week 2: January 22 – 26
January 23: Continuity and Computing Limits
January 25: More on Limits
January 26: Recitation 2 on Computing Limits
Week 3: January 29 – February 2
January 30: Infinite Limits
February 1: Intro to Derivatives
February 2: Recitation 3 on Advanced Limits
Week 4: February 5 – 9
February 6: Computing Derivatives
February 8: Trig Derivatives and Chain Rule
  • Read the solutions to mastery quiz 3
  • Read Section 2.4-5 of the online notes
    • See also Strang and Herman, sections 3.5 and 3.6.
  • It is very important to practice taking derivatives quickly and easily.
February 9: Recitation 4 on taking derivatives
Week 5: February 12 – 16
February 13: Linear Approximations and Speed
February 15: Rates of Change and Tangent Lines
February 16: Recitation 5 on linear approximation
Week 6: February 19 – 23
February 20: Implicit Differentiation and Tangent Lines
  • Mastery Quiz 5 due
    • Topics: M1, M2, S2, S3
    • In order to post solutions as soon as possible, I will probably not accept late submissions.
    • Single Sheet
    • Answer Blanks
  • Read Section 2.9 of the online notes
    • See also Strang and Herman, section 3.8
February 22: Midterm 1
February 23: Recitation 6 on Rates of Change
Week 7: February 26 – March 1
February 29(!): Absolute Extrema
Week 8: March 4 – 8
March 5: Mean Value Theorem
March 7: Classifying Extrema
March 8: Recitation 8 on absolute extrema and the Mean Value Theorem
Spring Break: March 11-15

No class! Go have fun!

Week 9: March 18 – 22
March 19: Concavity and Curve Sketching
March 21: Physical Optimization Problems
March 22: Recitation 9
Week 10: March 25 – March 29
March 26: The Area Problem
  • Mastery Quiz 9 due
    • Topics: M3, S7, S8
    • Like with the last midterm, I will not be accepting late submissions so I can get the solutions up quickly
    • Single Sheet
    • Answer Blanks
  • Midterm next class! Do the practice midterm!
  • Read Section 5.1 of the online notes
  • See also Strang and Herman, section 5.1
  • Watch the first 8 minutes or so of Essence of Calculus Episode 8
  • This GeoGebra widget is helpful for visualizing what’s going on.
  • You may also wish to skim Section 4 of the notes, which we won’t be covering in class.
March 28: Midterm 2
March 29: Recitation 10 on Physical Optimization
Week 11: April 1 – 5
April 2: The Definite Integral
April 4: The Fundamental Theorem of Calculus, Part 1
April 5: Recitation 11 on Riemann Sums
Week 12: April 8 – 12
April 9: Computing Integrals and the FTC Part 2
April 11: Integration by Substitution
April 12: Recitation 12 on integration
Week 13: April 15 – 19
April 16: Finding Areas
April 18: Physical and Economic Applications
April 19: Recitation 13 on substitution and area
Week 14: April 22 – 26
April 23: Volumes by Slices
April 25: Volumes by cylindrical shells
April 26: Recitation 14 on integral applications
Finals Week
April 30: Optional Mastery Quiz Due
Office Hours Schedule
  • Monday April 29: 3-5:30
  • Tuesday, April 30: 2-5
  • Wednesday, May 1: 3-5:30
  • Thursday, May 2: 2-5

  • Friday, May 3: 2-5

  • Monday, May 6: 3-7
  • Tuesday, May 7: 2:30-4
Final Exam Tuesday, May 7 5:20 &ndash 7:20 PM

Course notes

Skills Quiz Solutions

Mastery Quizzes

Major Topics

  1. Computing Limits
  2. Computing Derivatives
  3. Extrema and Optimization
  4. Integration

Secondary Topics

  1. Estimation
  2. Definition of derivative
  3. Linear Approximation
  4. Rates of change and models
  5. Implicit Differentiation
  6. Related rates
  7. Curve sketching
  8. Physical Optimization Problems
  9. Riemann sums
  10. Integral Applications

Tests

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.