Calculus I

Section 009, UN 1101, Fall 2022

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 in Room 414 in Pupin Hall from 6:10—7:25pm (ET), Mondays & Wednesdays.
My office hours are: 3:00—4:00pm (ET) on Wednesdays (Zoom link in Courseworks).
The course teaching assistant is Sara Levin (szl2107@columbia.edu).

Homework is administered through WebAssign (due 6pm on Wednesdays). Comprehension checks are administered through Courseworks (due 6pm on Mondays).
If you need further assistance with the course material, use the TA office hours in the Barnard Help Room or 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 7 (first class) Introduction and functions [S]§1.1
[D]§1.1
[Open]§1.1-1.2		 —
September 12 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 14 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 19 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 21 Limits: Properties of limits [S]§2.3
[D]§2.4-2.5
[Open]§2.3		 HW 2 (WebAssign)
September 26 Limits: Continuity and horizontal asymptotes [S]§2.5-2.6
[D]§2.6-2.9
[Open]§2.4, 4.6		 CC 2 (Courseworks)
September 28 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 3 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 5 (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 10 Derivatives: Polynomials and products/quotients [S]§3.1-3.2
[D]§3.3-3.4, 3.6
[Open]§3.3, 3.9		 —
October 12 Derivatives: Trigonometric functions [S]§3.3
[D]§3.5
[Open]§3.5		 HW 4 (WebAssign)
October 17 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 19 (Zoom) 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 24 (Zoom) 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)
October 26 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 31 Limits: L'Hôpital's rule [S]§4.4
[D]§4.10
[Open]§4.8		 CC 6 (Courseworks)
November 2 Derivatives: Derivative tests and curve sketching [S]§4.3, 4.5
[D]§4.5-4.6
[Open]§4.5		 HW 7 (WebAssign)
November 7 (Election Day) Election Day (no class) - —
November 9 Derivatives: More curve sketching [S]§4.5
[D]§4.5-4.6
[Open]§4.5		 HW 8 (WebAssign)
November 14 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		 CC 7 (Courseworks)
November 16 (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 21 Derivatives: Antiderivatives [S]§4.9
[D]§5.1
[Open]§4.10		 —
November 23 (Thanksgiving) Thanksgiving (no class) - —
November 28 Integrals: Areas and definite integrals [S]§5.1-5.2
[D]§5.5-5.6
[Open]§5.1-5.2		 CC 8 (Courseworks)
November 30 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 5 Integrals: Substitution [S]§3.10, 5.5
[D]§4.12, 5.3-5.4, 5.8
[Open]§4.2, 5.5		 CC 9 (Courseworks)
December 7 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 12 (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 10 (Courseworks)
December 15 (optional) Extra review (3pm—5pm in MATH 407) — —
December 19 (final exam) Final exam (7:10 — 10:00 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