Calculus I

Section 008, UN 1101, Fall 2020

Syllabus

Welcome to Calculus I! In this course, we will study the foundations of single-variable calculus, which consists of two main components:

  • In differential calculus, we try to understand how functions change — a powerful tool for solving practical problems such as maximizing profit or minimizing costs.
  • In integral calculus, we study the accumulation of functions which allow us to compute values such as volumes and medical dosages.
These two branches of calculus are built upon the theory of limits and are closely related through the Fundamental Theorem of Calculus.

Throughout the semester, we will introduce the basics of both differential calculus and integral calculus. The aim is to gain fluency in working with infinitesimals and solving practical problems with calculus techniques. We will culminate in understanding how differential calculus and integral calculus are connected through the Fundamental Theorem of Calculus.

The only prerequisite for this class is what is called "Precalculus" in much of the United States: an understanding of polynomials, graphs, functions, conic sections, and trigonometry.

The class meets online on Zoom (see Courseworks for access) from 2:40—3:55pm (ET), Tuesdays & Thursdays.
My office hours on Zoom are: 4:00—5:00pm (ET) on Tuesdays and 2:00—3:00pm (ET) on Wednesdays.

Homework is administered through WebAssign. Exams and comprehension checks are administered through Courseworks (Canvas).
If you need further assistance with the course material, use the Virtual Help Room and Barnard Tutoring (both are available to both Columbia and Barnard students)!
To contact me, please email me directly using your Columbia UNI email.

Feel free to leave anonymous feedback!


Course schedule

Date Title References Homework due
September 8 (first class) Introduction and functions [S]§1.1
[D]§1.1
[Open]§1.1-1.2		 —
September 10 Precalculus: Essential functions and transformations/combinations of functions [S]§1.2-1.3
[D]§1.1, 1.3-1.6
[Open]§1.2-1.3		 —
September 15 Precalculus: Exponential, inverse, and logarithmic functions [S]§1.4-1.5
[D]§1.2, 1.7-1.9
[Open]§1.4-1.5		 HW 0 (WebAssign, optional)
HW 1 (WebAssign)
September 17 Limits: Introduction and motivation [S]§2.1-2.2
[D]§2.1-2.3, 2.6
[Open]§2.1-2.2		 CC 1 (Courseworks)
September 22 Limits: Properties of limits [S]§2.3
[D]§2.4-2.5
[Open]§2.3		 HW 2 (WebAssign)
September 24 Limits: Continuity and horizontal asymptotes [S]§2.5-2.6
[D]§2.6-2.9
[Open]§2.4, 4.6		 CC 2 (Courseworks)
September 29 Derivatives: Rates of change [S]§2.7-2.8
[D]§2.1, 3.1-3.2, 4.1
[Open]§3.1-3.2, 3.4		 HW 3 (WebAssign)
October 1 Review [S]§1.1-1.5, 2.1-2.3, 2.5-2.8
[D]§1.1-1.9, 2.1-2.9, 3.1-3.2, 4.1
[Open]§1.1-1.5, 2.1-2.4, 3.1-3.2, 3.4		 CC 3 (Courseworks)
October 6 (Midterm I) Midterm I [S]§1.1-1.5, 2.1-2.3, 2.5-2.8
[D]§1.1-1.9, 2.1-2.9, 3.1-3.2, 4.1
[Open]§1.1-1.5, 2.1-2.4, 3.1-3.2, 3.4, 4.6		 Practice Problems I (WebAssign, optional)
Practice Midterm I
Practice Midterm I Solutions
October 8 Derivatives: Polynomials and products/quotients [S]§3.1-3.2
[D]§3.3-3.4, 3.6
[Open]§3.3, 3.9		 —
October 13 Derivatives: Trigonometric functions [S]§3.3
[D]§3.5
[Open]§3.5		 HW 4 (WebAssign)
October 15 Derivatives: The Chain Rule and implicit differentiation [S]§3.4-3.5
[D]§3.9-3.10, 3.12
[Open]§3.6, 3.8		 CC 4 (Courseworks)
October 20 Derivatives: Optimization and the Mean Value Theorem [S]§4.1-4.2, 4.7
[D]§4.2-4.4, 4.7-4.9
[Open]§4.3-4.4, 4.7		 HW 5 (WebAssign)
October 22 Derivatives: Logarithmic functions, inverse functions, and exponential growth/decay [S]§3.5-3.8
[D]§3.6-3.7, 3.13
[Open]§3.7, 3.9, 6.8		 CC 5 (Courseworks)
Extended to October 23
October 27 Derivatives: Related rates and linear approximations [S]§3.9-3.10
[D]§3.11, 4.11
[Open]§4.1-4.2		 HW 6 (WebAssign)
October 29 Limits: L'Hôpital's rule [S]§4.4
[D]§4.10
[Open]§4.8		 CC 6 (Courseworks)
November 3 (Election Day) Election Day (no class) - —
November 5 Derivatives: Derivative tests and curve sketching [S]§4.3, 4.5
[D]§4.5-4.6
[Open]§4.5		 —
November 10 Derivatives: More curve sketching [S]§4.5
[D]§4.5-4.6
[Open]§4.5		 HW 7 (WebAssign)
November 12 Review [S]§3.1-3.10, 4.1-4.5, 4.7
[D]§3.3-3.7, 3.9-3.13, 4.2-4.11
[Open]§3.3, 3.5-3.9, 4.1-4.5, 4.7-4.8, 6.8		 —
November 17 (Midterm II) Midterm II [S]§3.1-3.10, 4.1-4.5, 4.7
[D]§3.3-3.7, 3.9-3.13, 4.2-4.11
[Open]§3.3, 3.5-3.9, 4.1-4.5, 4.7-4.8, 6.8		 Practice Problems II (WebAssign, optional)
Practice Midterm II
Practice Midterm II Solutions
November 19 Derivatives: Antiderivatives [S]§4.9
[D]§5.1
[Open]§4.10		 —
November 24 Integrals: Areas and definite integrals [S]§5.1-5.2
[D]§5.5-5.6
[Open]§5.1-5.2		 CC 7 (Courseworks)
HW 8 (WebAssign)
November 26 (Thanksgiving) Thanksgiving (no class) - —
December 1 Derivatives and Integrals: Properties of definite integrals, the Fundamental Theorem of Calculus, and indefinite integrals [S]§5.2-5.4
[D]§5.1-5.2, 5.5-5.7
[Open]§5.1-5.4, 5.6-5.7		 HW 9 (WebAssign)
December 3 Integrals: Substitution [S]§3.10, 5.5
[D]§4.12, 5.3-5.4, 5.8
[Open]§4.2, 5.5		 CC 8 (Courseworks)
December 8 Integrals: Areas between curves and average values of a function [S]§6.1, 6.5
[D]§6.1-6.2
[Open]§5.2, 5.4, 6.1		 HW 10 (WebAssign)
December 10 (last class) Review [S]§3.10, 4.9, 5.1-5.5, 6.1, 6.5
[D]§4.12, 5.1-5.8, 6.1-6.2
[Open]§4.2, 5.1-5.5, 6.1		 CC 9 (Courseworks)
December 15 (optional) Extra review — —
December 17 (final exam) Final exam (1:10 — 4:00 PM) [S]§1.1-1.5, 2.1-2.8, 3.1-3.10, 4.1-4.5, 4.7, 4.9, 5.1-5.5, 6.1, 6.5
[D]§1.1-1.9, 2.1-2.9, 3.1-3.7, 3.9-3.13, 4.1-4.12, 5.1-5.8, 6.1-6.2
[Open]§1.1-1.5, 2.1-2.4, 3.1-3.9, 4.1-4.8, 5.1-5.7, 6.1, 6.8		 Practice Problems III (WebAssign, optional)
Practice Final A
Practice Final A Solutions
Practice Final B
Practice Final B Solutions

Course Textbook

Free online resources