Math 1231: Single-Variable Calculus I
Section 16
Fall 2023

Contact Info
Fall 2023

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

Office Hours:

Often in office:

Course Information

Lecture:

  • MW 4:45 PM–6:00 PM
  • MPA 309

TA

TA Office Hours:

  • TR 11:00 AM – 12:00 Noon
  • 720G

Official textbook:

Recitations

Section 48:

  • F 8:00 AM–8:50 AM
  • Monroe 351

Section 49:

  • F 9:35 AM–10:25 AM
  • Monroe 351

Section 50:

  • F 11:10 AM–12 Noon
  • Monroe 351

Course Information

Lecture:

  • MW 4:45 PM–6:00 PM
  • MPA 309

TA

TA Office Hours:

  • TR 11:00 AM – 12:00 Noon
  • 720G

Official textbook:

Recitations

Section 48:

  • F 8:00 AM–8:50 AM
  • Monroe 351

Section 49:

  • F 9:35 AM–10:25 AM
  • Monroe 351

Section 50:

  • F 11:10 AM–12 Noon
  • Monroe 351

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 0: August 24 – 25
August 25: Recitation 1 on Estimation
Week 1: August 28 – September 1
August 28: Syllabus and Functions
August 30: 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.
September 1: Recitation 2 on \(\varepsilon-\delta\) proofs
Week 2: September 4 – 8
September 4: No Class for Labor Day
September 6: Continuity and Computing Limits
September 8: Recitation 3 on Computing Limits
Week 3: September 11 – 15
September 11: More on Limits
September 13: Infinite Limits
September 15: Recitation 4 on Advanced Limits
Week 4: September 18 – 22
September 18: Intro to Derivatives
September 20: Computing Derivatives
September 22: Recitation 5 on Basic Derivatives
Week 5: September 25 – 29
September 25: Advanced Derivative Rules
  • Mastery Quiz 4 due
  • 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.
September 27: Linear Approximation
September 29: Recitation 6 on Taking Derivatives
Week 6: October 2 – 6
October 2: Speed and Rates of Change
October 4: Midterm
October 6: Recitation 7 on Rates of Change
Week 7: October 9 – 11
October 9: Tangent Lines and Implicit Differentiation
October 13: No Recitation for Fall Break
Week 8: October 16 – 20
October 16: Extreme Values and Critical Points
October 18: Mean Value Theorem
  • Read Section 3.2 of the online notes
    • See also Strang and Herman, section 4.4
October 20: Recitation 8 on Absolute Extrema and the Mean Value theorem
Week 9: October 23 – 27
October 23: Classifying Extrema
October 25: Concavity and Curve Sketching
  • Read the solutions to Mastery Quiz 8
  • Read Section 3.4-5 of the online notes
    • See also Strang and Herman, section 4.5
October 27: Recitation 9
Week 10: October 30 – November 3
October 30: Physical Optimization Problems
November 1: The Area Problem
November 3: Recitation 10 on Physical Optimization
Week 11: November 6 – 10
November 6: The Definite Integral
November 8: Midterm 2
November 10: Recitation 11 on Riemann Sums
Week 12: November 13 – 17
November 13: The Fundamental Theorem of Calculus, Part 1
November 15: Computing Integrals and the FTC Part 2
November 17: Recitation 12 on integration
Thanksgiving Break: November 20-24

Get some rest!

Week 13: November 27 – December 1
November 27: Integration by Substitution
November 29: Finding Areas
December 1: Recitation 13 on substitution and area
Week 14: December 4 – 8
December 4: Physical Applications
December 6: Volumes by Slices
December 8: Recitation 14 on integral applications
Finals Week
December 11: Volumes by cylindrical shells
  • Optional Mastery Quiz 14 due Monday, December 11
    • Topics: M4, S10
    • Single Sheet
    • Answer Blanks
    • I will be posting these solutions Monday night. Consequently I will not be accepting late submissions.
  • Read Section 6.5 of the online notes
    • See also Strang and Herman, section 6.3
December 12: Office hours
  • I’ll be in my office from roughly 3 to 7 PM. We may move down the hall to a bigger room, depending on attendance and room availability.
December 13, 5:20–7:20 PM: Final Exam
  • I’ll be in my office from 2-4 PM. I will kick everyone out at 4. This is for your own good; I strongly encourage you to take at least an hour break from studying before the final starts.
  • Solutions to Mastery Quiz 14
  • Practice Final

Course notes

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.