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Calculus I

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Fall 2023

This is the non-Courseworks version of the webpage for section 10 of calculus I, as offered in Fall 2023. The syllabus can be found here. Lecture notes, homework, and other materials will be posted throughout the course.

**Instructor:** Avi Zeff

**Time/place:** Tuesday and Thursday 4:10 - 5:25 PM, in 407 Mathematics

**Office hours:** Tuesday 6-7 PM and Thursday 2-3:30 PM, in 528 Mathematics

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Lecture notes

Lecture 1: introduction and functions

Lecture 2: more functions

Lecture 3: introduction to limits

Lecture 4: limit laws and the squeeze theorem

Lecture 5: infinite limits

Lecture 6: continuity

Lecture 7: introduction to derivatives

Lecture 8: product and quotient rules

Lecture 9: chain rule

Lecture 10: differentiability

Lecture 11: exponentials and logarithms

Lecture 12: general functions and digressions

Lecture 13: first applications and related rates

Lecture 14: extrema and critical points

Lecture 15: optimization

Lecture 16: mean value theorem and L'Hopital's rule

Lecture 17: Newton's method and first integrals

Lecture 18: the fundamental theorem of calculus

Lecture 19: u-substitution

Lecture 20: applications of integrals

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Worksheets

Worksheet 1: limit laws

Worksheet 2: infinite limits

Worksheet 3: introduction to derivatives

Worksheet 4: derivatives of rational functions

Worksheet 5: product and quotient rules

Worksheet 6: differentiability

Worksheet 7: maximization

Worksheet 8: Rolle's theorem

Worksheet 9: integrals in physics

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Homework

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Homework 9

Homework 10

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Other materials

Examples of standards

Survey

Objectives 1-3 practice problems

Practice problems for the midterm

Objectives 1-10 practice problems

Practice problems for the final

Extra practice on background topics like fractions and algebra