Math 1231: Single-Variable Calculus I
Section 13
Fall 2023

Contact Info
Fall 2023

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

Office Hours:

Often in office:

Course Information

Lecture:

  • TR 3:45 PM–5:00 PM
  • MPA 310

TA

TA Office Hours:

  • W 12:15 PM – 2:15 PM
  • Phillips 720G

Official textbook:

Recitations

Section 39:

  • W 8:00 AM–8:50 AM
  • Monroe 351

Section 40:

  • W 9:35 AM–10:25 AM
  • Duques 361

Section 41:

  • W 11:10 AM–12 Noon
  • Tompkins 205

Course Information

Lecture:

  • TR 3:45 PM–5:00 PM
  • MPA 310

TA

TA Office Hours:

  • W 12:15 PM – 2:15 PM
  • Phillips 720G

Official textbook:

Recitations

Section 39:

  • W 8:00 AM–8:50 AM
  • Monroe 351

Section 40:

  • W 9:35 AM–10:25 AM
  • Duques 361

Section 41:

  • W 11:10 AM–12 Noon
  • Tompkins 205

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 24: Syllabus and Functions
Week 1: August 28 – September 1
August 29: 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.
August 30: Recitation on Estimation
August 31: Continuity and Computing Limits
Week 2: September 4 – 8
September 5: More on Limits
September 6: Recitation 2 on Computing Limits
September 7: Infinite Limits
Week 3: September 11 – 15
September 12: Intro to Derivatives
September 13: Recitation 3 on Advanced Limits
September 14: Computing Derivatives
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
    • See also Strang and Herman, sections 3.5 and 3.6.
  • It is very important to practice taking derivatives quickly and easily.
Recitation 4 on taking derivatives
September 21: Linear Approximations and Speed
Week 5: September 25 – 29
September 26: Rates of Change and Tangent Lines
September 27: Recitation 5 on linear approximation
September 28: Implicit Differentiation and Tangent Lines
Week 6: October 2 – 6
October 3: Midterm 1
October 4: Recitation 6 on Rates of Change
  • Read Section 2.10 of the online notes
    • See also Strang and Herman, section 4.1
Week 7: October 9 – 11
October 10: Absolute Extrema

October 12: No Class for Fall Break

Week 8: October 16 – 20
October 17: Mean Value Theorem
October 18: Recitation 8 on absolute extrema and the Mean Value Theorem
October 19: Classifying Extrema
Week 9: October 23 – 27
October 24: Concavity and Curve Sketching
October 25: Recitation 9
October 26: Physical Optimization Problems
Week 10: October 30 – November 3
October 31: The Area Problem
November 1: Recitation 10 on Physical Optimization
November 2: The Definite Integral
  • Mastery Quiz 9 due Thursday, November 2
  • Midterm next week! Do the practice midterm!
  • Read Section 5.2 of the online notes
  • See also Strang and Herman, section 5.2
Week 11: November 6 – 10
November 7: Midterm 2
November 8: Recitation 11 on Riemann Sums
November 9: The Fundamental Theorem of Calculus, Part 1
Week 12: November 13 – 17
November 14: Computing Integrals and the FTC Part 2
November 15: Recitation 12 on integration
November 16: Integration by Substitution
Thanksgiving Break: November 20-24

Get some rest!

Week 13: November 27 – December 1
November 28: Finding Areas
November 29: Recitation 13 on substitution and area
November 30: Physical Applications
Week 14: December 4 – 8
December 5: Volumes by Slices
December 6: Recitation 14 on integral applications
December 7: Volumes by cylindrical shells
Finals Week
December 19, 3:00–5:00 PM: Final Exam
  • Solutions to Mastery Quiz 13
  • Practice Final
  • Office hours:
    • Thursday December 14: 12:30 to 3:30 or so.
    • Friday December 15: 2-5 PM
    • Monday, December 18: 3-7 PM
    • Tuesday, December 19: roughly 12:30 - 2.

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.