This is a schedule for a ~15 week course covering
limits, continuity, explicit and implicit differentiation,
Newton’s method, analytic geometry, optimization,
introductory integration, and the fundamental theorem of calculus,
with a focus on the computational aspects of calculus.
Within each section there are links to
textbook chapters, recommended readings, video lectures,
Desmos demonstrations,
problem sheets, and past midterm exams.
Chapters enumerated with § refer to
Calculus 9E by Stewart .
Topics marked like
are extracurricular and won’t appear on exams.
Prerequisite Topics
Arithmetic & Algebra
Analytic Geometry
Graphing Lines by Solving for y and Plotting Points , Professor Leonard (Video)
Finding x and y Intercepts on a Graph , Professor Leonard (Video)
Graphing Lines with the Intercept Method , Professor Leonard (Video)
Horizontal and Vertical Lines , Professor Leonard (Video)
Introduction to the Slope of a Line , Professor Leonard (Video)
Discovering the Slope Formula , Professor Leonard (Video)
Finding the Slope of a Line Graphically , Professor Leonard (Video)
Using the Slope Formula Given Two Points , Professor Leonard (Video)
Graphing Lines Using a Point and the Slope , Professor Leonard (Video)
Introduction to Slope-Intercept Form , Professor Leonard (Video)
How to Use Slope-Intercept Form , Professor Leonard (Video)
Finding Equations of Parallel and Perpendicular Lines , Professor Leonard (Video)
Discovering Point-Slope Form , Professor Leonard (Video)
Using the Point-Slope Equation of a Line , Professor Leonard (Video)
Finding the Equation of a Line From Two Points , Professor Leonard (Video)
Introduction to Solving Quadratics , Professor Leonard (Video)
The Square Root Method in Solving Quadratics , Professor Leonard (Video)
Using Factoring to Solve Quadratics , Professor Leonard (Video)
Completing the Square Made Easy , Professor Leonard (Video)
Proving the Quadratic Formula , Professor Leonard (Video)
Using the Quadratic Formula , Professor Leonard (Video)
Graphing Quadratic Functions , Professor Leonard (Video)
Functions & Graphs
Introduction to Functions , Professor Leonard (Video)
How to Evaluate Functions , Professor Leonard (Video)
Finding the Domain of Functions , Professor Leonard (Video)
Operations of Functions , Professor Leonard (Video)
Using the Vertical Line Test , Professor Leonard (Video)
Features of Graphs, Domain, Range , Professor Leonard (Video)
Properties of Functions - Even vs Odd , Professor Leonard (Video)
Properties of Functions - Increasing vs Decreasing , Professor Leonard (Video)
Properties of Functions - Extrema , Professor Leonard (Video)
Average Rate of Change of a Function , Professor Leonard (Video)
How to Graph Piecewise Functions , Professor Leonard (Video)
Graphs You Must Know , Professor Leonard (Video)
Introduction to Graph Transformations , Professor Leonard (Video)
How to Graph with Transformations , Professor Leonard (Video)
Composition of Functions , Professor Leonard (Video)
One to One Functions , Professor Leonard (Video)
Finding Inverse Functions , Professor Leonard (Video)
Trigonometry
Review of Trigonometry , Professor Leonard (Video)
Introduction to Angles , Professor Leonard (Video)
Introduction to Radians , Professor Leonard (Video)
Converting Radians and Degrees , Professor Leonard (Video)
Convert From Polar Coordinates to Rectangular Coordinates , Professor Leonard (Video)
Convert From Rectangular Coordinates to Polar Coordinates , Professor Leonard (Video)
Trigonometric Functions and the Unit Circle , Professor Leonard (Video)
How to Use the Unit Circle in Trigonometry , Professor Leonard (Video)
Basic Properties of Trigonometric Functions , Professor Leonard (Video)
Reciprocal Identities in Trigonometry , Professor Leonard (Video)
Pythagorean Identities for Trigonometric Functions , Professor Leonard (Video)
Introduction to Right Triangle Trigonometry , Professor Leonard (Video)
Finding Sides and Angles with Right Triangle Trigonometry , Professor Leonard (Video)
Introduction to Inverse Trigonometric Functions , Professor Leonard (Video)
How to Use Inverse Trigonometric Functions , Professor Leonard (Video)
How to Find Inverse Trigonometric Functions , Professor Leonard (Video)
How to Solve Basic Inverse Trigonometric Functions , Professor Leonard (Video)
An Indepth Look at Using Inverse Trig Functions , Professor Leonard (Video)
How to Use the Law of Sines , Professor Leonard (Video)
How to Use the Law of Cosines , Professor Leonard (Video)
How to Find the Area of a Triangle , Professor Leonard (Video)
The Graphs of Sine and Cosine , Professor Leonard (Video)
Graphing Transformations with Sine and Cosine , Professor Leonard (Video)
How to Graph Tangent and Cotangent , Professor Leonard (Video)
Graphing Transformations with Tangent and Cotangent , Professor Leonard (Video)
How to Graph Cosecant and Secant , Professor Leonard (Video)
How to Graph Phase Shifts of Trigonometric Functions , Professor Leonard (Video)
Introduction to Using Trigonometric Identities , Professor Leonard (Video)
How to Prove Trigonometric Identities , Professor Leonard (Video)
Introduction to Sum and Difference Formulas , Professor Leonard (Video)
Using Sum and Difference Formulas , Professor Leonard (Video)
Proving the Double and Half Angle Formulas , Professor Leonard (Video)
How to Use the Double and Half Angle Formulas , Professor Leonard (Video)
How to Use Product to Sum and Sum to Product Formulas , Professor Leonard (Video)
Week One · August 19
Monday – Differential Calculus Overview
Tuesday – Secants, Tangents, and Rates
Wednesday – Problem Solving Session
Thursday – Syllabus + Early-Term Assessment
Week Two · August 24
Monday – Introduction to Limits
Tuesday – Evaluating Limits using Limit Laws
Wednesday – Continuity & Some Theorems
Thursday – Problem Solving Session
Week Three · August 31
Monday – Calculator Tutorial
Tuesday –
Wednes/Thursday – First Midterm Exam
Past Midterm Exams
Week Four · September 7
Monday – The Derivative at a Point
Tuesday – The Derivative as a Function
Wednesday – Basic Differentiation Formulas
Thursday – Problem Solving Session
Week Five · September 14
Monday – Derivatives of Trigonometric Functions
Tuesday – The Chain Rule
Wednesday – Implicit Differentiation
Thursday – Problem Solving Session
Week Six · September 21
Monday – Implicit Differentiation
Tues/Wednesday – Related Rates of Change
Thursday – Problem Solving Session
Week Seven · September 28
Mon/Tuesday –
Wednes/Thursday – Second Midterm Exam
Past Midterm Exams
Prior to Spring 2026, the second and third midterm exams were a single exam.
Week Eight · October 5
Monday – Extrema and Inflection Points
Tuesday – Asymptotics & Some Theorems
Wednesday – Sketching the Graph of a Function
Thursday – Problem Solving Session
Week Nine · October 12
Mon/Tuesday – Optimization
Wednesday – Newton’s Method
Thursday – Problem Solving Session
Week Ten · October 19
Mon/Tuesday –
Wednes/Thursday – Third Midterm Exam
Past Midterm Exams
Prior to Spring 2026, the second and third midterm exams were a single exam.
Week Eleven · October 26
Monday – Antiderivatives
Monday – Summation Notation
Monday – Integral Calculus Overview
Monday – Definite Integrals
Thursday – Problem Solving Session
Week Twelve · November 2
Monday – The Fundamental Theorem of Calculus
Tuesday – Indefinite Integrals
Wednesday – Integration by Substitution; Change of Coordinates
Thursday – Problem Solving Session
Week Thirteen · November 9
Monday – Areas Between Curves
Tuesday – Volumes of Solids from their Cross-Sections
Wednesday – Work
Thursday – Problem Solving Session
Week Fourteen · November 16
Mon/Tuesday –
Wednes/Thursday – Fourth Midterm Exam
Past Midterm Exams
Prior to Spring 2026, this midterm was the third midterm exams.
Week Fifteen · November 23
Thanksgiving Break, No Class
Week Sixteen · November 30
Final Exam
Probably Wednesday December 9 @ 10am
References
Stewart’s Calculus 9E
James Stewart, Daniel Clegg, and Saleem Watson
© 2021, 2016 Cengage Learning Inc
www.stewartcalculus.com
Spivak’s Calculus Fourth Edition
Michael Spivak © 2008
Publish or Perish, Inc.
ISBN: 978-0-914098-91-1
Calculus: An Intuitive and Physical Approach
Morris Kline
© 1967, 1977 John Wiley & Sons Inc
Republished 1998 by Dover
Strang’s Calculus
Gilbert Strang © 1991
Published by Wellesley-Cambridge Press
ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/