Stefan's First-Year Calculus Archive

Trent University
Stefan's First-Year Calculus Archive Page

This page archives various materials, including many assignments, quizzes, tests, and exams, and solutions to these, from first-year calculus courses taught by Stefan at Trent University. The main first-year calculus course at Trent used to be Mathematics 110, later renumbered as 1100Y, with a variant that had more lecture hours numbered as 1101Y. 1100Y/1101Y was eventually split up into two half-courses, Mathematics 1110H - Calculus I: Limits, Derivatives, and Integrals and Mathematics 1120H - Calculus II: Integrals and Series.

MATH 1110H is an introduction to the concepts and techniques of single-variable differential and some integral calculus, with some applications to other areas of mathematics and science.

Prerequisite: Grade 12U Advanced Functions or equivalent with at least 60%.
Strongly Recommended: Grade 12U Calculus and Vectors or equivalent.

MATH 1120H continues the introduction to the concepts and techniques of single-variable integral calculus begun in MATH 1110H, with some applications to other areas of mathematics and science, followed by an introduction to sequences, series, and power series.

Prerequisite: MATH 1110H - Calculus I: Limits, Derivatives, and Integrals

Some useful general tips for first-year mathematics students are given in the pamphlet Enjoying Math! (pdf).

Inspiration

No doubt but magic may do much in this;
For he that reads but mathematic rules
Shall find conclusions that avail to work
Wonders that pass the common sense of men.
Robert Greene (from Friar Bacon and Friar Bungay)

MATH 1120H - Calculus II: Integrals and Series, Winter 2024

Course information:
- MATH 1120H course outline (Unofficial summary of the syllabus)
- Some useful advice for surviving university math courses: Enjoying Math!
Textbook and Supplementary Materials:
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard.
  May be downloaded for free from www.whitman.edu/mathematics/multivariable/ or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Suggested Homework Exercises.
- Handouts:
- Two useful pamphlets originally published by Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
  ... and their current successor, the Math Basics series.
- SageMath resources:
  - Getting Started with sage.trentu.ca
  - Sage Quick Reference and Sage Quick Reference: Calculus,
    by William Stein, licensed under the GNU Free Documentation License.
  - Sage for Undergraduates (online version), by Gregory Bard,
    and Additional Appendices and Index.
  - Computational Mathematics with SageMath, by Paul Zimmermann et al.
    Licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.
Assignment # 1, 2, 3, 4, 5, 2e. π+e, 6, 7, 8, 9, 10, 11,
and Solutions to Assignment # 1, 2, 3, 4, 5, 6, π+e, 7, 8, 9, 10, 11.
Final Examination and Solutions to the Final Examination.

MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, Fall 2023

Course information:
- MATH 1110H course outline (Unofficial summary of the syllabus)
- Some useful advice for surviving university math courses: Enjoying Math!
Textbook and Supplementary Materials:
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard.
  May be downloaded for free from www.whitman.edu/mathematics/multivariable/ or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Suggested Homework Exercises
- Notes from the course by Erin Blaine. Thanks, Erin!
- Handouts:
- Two useful pamphlets originally published by Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
  ... and their current successor, the Math Basics series.
- SageMath resources:
  - Getting Started with sage.trentu.ca
  - Sage Quick Reference and Sage Quick Reference: Calculus,
    by William Stein, licensed under the GNU Free Documentation License.
  - Sage for Undergraduates (online version), by Gregory Bard.
  - Computational Mathematics with SageMath, by Paul Zimmermann et al.
    Licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.
  SageMath labs (not a complete set):
Assignment # 1, 2, 3, π, 4, 5, 6,
and Solutions to Assignment # 1, 2, 3, 4, 5, 6
Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
and Solutions to Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Test and Solutions to the Test
Final Examination and Solutions to the Final Examination

MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, Summer 2023

Course information:
- MATH 1110H course outline (Unofficial summary of the syllabus)
- Some useful advice for surviving university math courses: Enjoying Math!
Textbook and Supplementary Materials:
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard.
  May be downloaded for free from www.whitman.edu/mathematics/multivariable/ or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Suggested Homework Exercises
- Handouts:
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
  ... and the Math Basics video series with additional quick references, too.
- SageMath resources:
  - Getting Started with sage.trentu.ca
  - Sage Quick Reference and Sage Quick Reference: Calculus,
    by William Stein, licensed under the GNU Free Documentation License.
  - Sage for Undergraduates (online version), by Gregory Bard.
  - Computational Mathematics with SageMath, by Paul Zimmermann et al.
    Licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.
Assignment # 1, 2, 3, 4, 5, 6,
and Solutions to Assignment # 1, 2, 3, 4, 5
Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
and Solutions to Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Test and Solutions to the Test
Final Examination and Solutions to the Final Examination
Lectures
- 2023-05-03
  Part a - Organizational, mainly going over the course outline.
  Part b - Some basics, including Cartesian coordinates and trigonometric functions
  Part c - Continuity, limits, and the epsilon-delta definition thereof.
- 2023-05-08
  Part a - We practiced some epsilonics and looked at some of the different ways that limits could fail to exist.
  Part b - We considered limits as x went to infinity, the Squeeze Theorem, and certain special limits needed to compute a few particular derivatives.
  Part c - We defined derivatives in terms of limits, did a couple of examples, and gave the Power and Sum Rules for derivatives.
- 2023-05-10
  Part a - We reviewed the limit definition of the derivative, and used it to get some common derivatives.
  Part b - We looked at the Sum and Product Rules for derivatives.
  Part c - We worked out the Quotient Rule for derivatives.
- 2023-05-15
  Part a - We briefly reviewed the differentiation rules we had already done and then moved on to the Chain Rule.
  Part b - We looked at inverse functions and computing their derivatives.
  Part c - We worked out the derivatives of two more inverse functions.
- 2023-05-17<
  Part a - We practiced the Chain Rule a bit more and got started on implicit differentiation.
  Part b - We did a bit more with implicit differentiation and then moved on to l'Hopital's Rule.
  Part c - We finished off the awful example that we ended the previous lecture part on.
- 2023-05-24
  Part a - We stated Rolle's Theorem, the Mean Value Theorem, and Fermat's Theorem, and then got started on using derivatives and other tricks to find the local maxima and minima of a function.
  Part b - We worked through some examples of finding maxima and minima.
  Part c - We started on using calculus and such to do qualitative analysis of the graph of a function, i.e. "curve sketching".
- 2023-05-29
  Part a - We added curvature (i.e. intervals of concavity and inflection points) to our qualitative analysis/curve sketching checklist and worked through a longish example.
  Part b - We did a couple of related rates problems.
- 2023-05-31
  Part a - We did one more example of a related rates problem.
  Part b - We looked at defining definite integrals and computed a simple one at great length using the Right-Hand Rule.
  Part c - We looked at properties of the definite integral, stated two forms of the Fundamental Theorem of Calculus, and started on properties of indefinite integrals.
- 2023-06-05
  Part a - We did a quick recap of integration so far and then got started on the basic Substitution Rule for integration.
  Part b - We worked through a number of examples of the Substitution Rule, interrupted by losing most of the lights for a couple of minutes...
  Part c - ... and resumed the previous segment once the lights came on again.
  Part d - We started on a couple of applications of integrations, finding areas and volumes.
- 2023-06-07
  Part a - We looked at the technique of integration by parts for indefinite integrals.
  Part b - We did some more with integration by parts.
- 2023-06-12
  Part a - We looked at computing volumes of solids by integrating the areas of their cross-sections.
  Part b - We worked through some examples of the disk/washer method for computing the volumes of solids of revolution.
  Part c - We took a brief look at the method of cylindrical shells for computing the volumes of solids of revolution, followed by a brief discussion of the structure and possible content of the exam.

MATH 1120H - Calculus II: Integrals and Series, Winter 2022:

Course information:
- MATH 1120H course outline
- Some useful advice for surviving university math courses: Enjoying Math!
Textbook and Supplementary Materials:
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard.
  May be downloaded for free from communitycalculus.org or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Suggested Homework Exercises
- Handouts:
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet.
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
  ... and the Math Basics video series with additional quick references, too.
- SageMath resources:
  - Getting Started with sage.trentu.ca
  - Sage Quick Reference and Sage Quick Reference: Calculus,
    by William Stein, licensed under the GNU Free Documentation License.
  - Sage for Undergraduates (online version), by Gregory Bard.
  - Computational Mathematics with SageMath, by Paul Zimmermann et al.
    Licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.
Assignment # 1, 2, 3, 4, 5, π+e, 6, 7, 8, 9, 10, 11
and Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Final Examination and Solutions to the Final Examination, and the Alternate (Take-Home) Final Examination (written by those unable to attend the the Final Examination in person). Solutions to the Alternate Final Examination will probably not get posted after all due to other commitments.
Lectures and Notes (webm and pdf formats)
Notes from 2022-02-01 on mostly by Megan Dyck and Caden Drover. Thanks to both!
- The Definite Integral - video and notes
  Handout: A Precise Definition of the Definite Integral
- The Fundamental Theorem of Calculus - video and notes
- The (Basic) Substitution Rule - video and notes
  Handout: The Basic Substitution Rule
- Integration by Parts - video and notes
- Integration by Parts II - video and notes
- Integration by Parts III - video and notes
  Handout: Integration by Parts
- Integrating Trigonometric Functions - video and notes
- Integrating Trigonometric Functions II - video and notes
- Trigonometric Substitutions - video and notes
  Handout: Trigonometric Integrals and Substitutions - A Brief Summary
- Trigonometric Substitutions II - video, Megan's notes and Caden's notes
- Trigonometric Substitutions III - video, Megan's notes and Caden's notes
- Integrating Rational Functions - video, Megan's notes and Caden's notes
- Integrating Rational Functions II - video, Megan's notes and Caden's notes
- Integrating Rational Functions III - video, Megan's notes and Caden's notes
- Improper Integrals - video, Megan's notes and Caden's notes
- Areas and Volumes - video and notes
- Volumes of Solids of Revolution - video and notes
- Arc-Length - video and notes
- Arc-Length, Volume, and Surface Area - video, Megan's notes and Caden's notes
- Arc-Length, Volume, and Surface Area II - video, Megan's notes and Caden's notes
- Sequences - video, Megan's notes and Caden's notes
- Series - Definitions and Examples - video, Megan's notes and Caden's notes
- Series II - Divergence and Integral Tests - video, Megan's notes and Caden's notes
- Series III - A Hard Example - video, Megan's notes and Caden's notes
- Series IV - The p-Test and the Comparison Tests - video, Megan's notes and Caden's notes
- Series V - The Generalized p-Test - video, Megan's notes and Caden's notes
- Series VI - The Alternating Series Test and Absolute vs. Conditional Convergence - video, Megan's notes and Caden's notes
- Series VII - Conditional Convergence and the Ratio Test - video, Megan's notes and Caden's notes
- Series VIII - The Root Test - video, Megan's notes and Caden's notes
- Power Series - video, Megan's notes and Caden's notes
- Taylor Series - video, Megan's notes and Caden's notes
- Taylor Series II - video, Megan's notes and Caden's notes
- Taylor Series III - video, Megan's notes and Caden's notes
- Taylor Series IV - video, Megan's notes and Caden's notes

MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, Section C, Fall 2021:

Course Information
- MATH 1110H Section C course outline [Unofficial summary of the syllabus.]
- Some useful advice for surviving university math courses: Enjoying Math!
Textbook and Supplementary Materials
- Single Variable Calculus (Early Transcendentals), by David Guichard.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Suggested Homework Exercises from the textbook.
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
  ... and the Math Basics video series with additional quick references, too.
- A Few Useful Bits of Algebra and Trigonometry
- An Alternate Version of the ε-δ Definition of Limits
- A Precise Definition of the Definite Integral - A handout filling in a major gap in the textbook.
- The Basic Substitution Rule - A handout with another take on the integration technique of substitution.
- Integration by Parts - A handout with another take on the technique of integration by parts.
- An Integral Tale - A handout with a tale of working through a difficult integral.
- Trigonometric Identities and Integrals - A handout summarizing the most common trigonometric identities and integral reduction formulas.
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet. Overkill for MATH 1110H, but what the heck! :-)
Assignment # 1, 2, 3, π, 4, 5, 6
Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
and Solutions to Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Take-Home Final Examination
and Solutions to the Take-Home Final Examination
Lectures and Notes [Mostly the same as Fall 2020.]
- Background - video, notes
- Limits - video, notes
  and Limits - an alternate definition - video, notes
- Limits II - non-limits and limits to infinity - video, notes
- Limits III - practical rules for computing limits - video, notes
- Limits IV - examples of computing limits - video, notes
- Limits V - two special limits and a theorem - video, notes
- Derivatives - the limit definition - video, notes
- Derivatives II - rules and examples - video, notes
- Derivatives III - the Chain Rule - video, notes
- Derivatives IV - examples - video, notes
- Derivatives V - implicit differentiation - video, notes
- Derivatives VI - l'Hopital's Rule - video, notes
- Asymptotes - vertical and horizontal - video, notes
- Asymptotes II - some more examples - video, notes
- Maxima and Minima - some basics - video, notes
- Maxima and Minima II - examples - video, notes
- Maxima and Minima III - general procedure - video, notes
- Curve Sketching, i.e. Qualitative Analysis - video, notes
- Curve Sketching II - checklist and example - video, notes
- Curve Sketching III - example - video, notes
- Optimization - applied max/min by example - video, notes
- Optimization II - a distance problem - video, notes
- Related Rates - video, notes
- Related Rates II - Three dimensions home - video, notes
- Related Rates III - Two examples involving angles - video, notes
- Two More Applications - Newton's Method and Average Values - video, notes
- The Definite Integral - an informal look - video, notes
  Supplementary handout: A Precise Definition of the Definite Integral
- The Fundamental Theorem of Calculus - video, notes
- Examples of Substitution - video, notes
  The Basic Substitution Rule - A handout with another take on substitution.
- Examples of Substitution II - video, notes
- Examples of Substitution III - video, notes
- Areas Between Curves - video, notes
- Integration by Parts - video, notes
- Integration by Parts II - video, notes
  Integration by Parts - A handout with another take on integration by parts.
- Integration by Parts III - video, notes
  An Integral Tale - A handout with the story of working through a difficult integral.
  Trigonometric Identities and Integrals - A summary of the most common trigonometric identities and integral reduction formulas.
- Volumes - video, notes
- Volumes II - Solids of Revolution - video, notes
- Why the standard normal density is a valid density (Just for fun! Not on exam!) - video, notes

MATH 1120H - Calculus II: Integrals and Series, Summer 2021:

Course information:
- MATH 1120H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally. [Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.]
- Suggested Homework Exercises
- Handouts:
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet.
General advice and information:
- Some useful advice for surviving university math courses: Enjoying Math!
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
Assignment # 1, 2, 3, 4, 5, π
Solutions to Assignment # 1, 2, 3, 4, 5
Quiz # 1, 2, 3, 4, 5, 6
Solutions to Quiz # 1, 2, 3, 4, 5, 6
Final Examination and Solutions to the Final Examination
Lectures and Notes
- Finding areas and defining the definite integral - video & notes
  Handout: A Precise Definition of the Definite Integral
- The Fundamental Theorem of Calculus - video & notes
- The Substitution Rule - video & notes
  Handout: The Basic Substitution Rule
- Integration by Parts - video & notes
  Handout: Integration by Parts
- Integration by Parts II - video & notes
- Integration by Parts III - video & notes
- Trigonometric Integrals - video & notes
- Trigonometric Integrals II - video & notes
- Trigonometric Integrals III - video & notes
- Trigonometric Substitutions - video & notes
- Trigonometric Substitutions II - video & notes
  Handout: Trigonometric Integrals and Substitutions - A Brief Summary
- Integrating Rational Functions - video & notes
- Improper Integrals - video & notes
- Areas - video & notes
- Volumes - video & notes
- Volumes II - video & notes
- Volumes III - video & notes
- Average Values and Arc-lengths - video & notes
- Areas of Surfaces of Revolution - video & notes
- Sequences and Their Limits - video & notes
- Series - video & notes
- Series II - Easily Summable Series - video & notes
- Series III - The Integral Test - video & notes
- Series IV - The (Basic) Comparison Test - video & notes
- Series V - The Limit Comparison Test - video & notes
- Series VI - The Alternating Series Test - video & notes
- Series VII - Absolute vs. Conditional Convergence - video & notes
- Series VIII - The Ratio and Root Tests - video & notes
- Power Series - video & notes
- Power Series II - Tricks and Techniques - video & notes
- Taylor Series - video & notes
- Taylor Series II - Examples and Shortcuts - video & notes
- Taylor Series III - Taylor Polynomials and Remainders - video & notes
- Taylor Series IV - e Is Irrational - video & notes
- Taylor Series V - A Little Cleanup - video & notes

MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, Winter 2021:

Course Information
- MATH 1110H course outline [Unofficial summary of the syllabus.]
- Some useful advice for surviving university math courses: Enjoying Math!
Textbook and Supplementary Materials
- Single Variable Calculus (Early Transcendentals), by David Guichard.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Suggested Homework Exercises from the textbook.
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
  ... and a video series, too.
- A Few Useful Bits of Algebra and Trigonometry
- An Alternate Version of the ε-δ Definition of Limits
- A Precise Definition of the Definite Integral - A handout filling in a major gap in the textbook.
- The Basic Substitution Rule - A handout with another take on the integration technique of substitution.
- Integration by Parts - A handout with another take on the technique of integration by parts.
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet. It's overkill for MATH 1110H... :-)
Maple and similar software
- A very quick start with Maple
- Getting started with Maple 10 by Gilberto E. Urroz
- A survey of mathematical applications using Maple 10 by Gilberto E. Urroz
  (as a Maple 10 worksheet)
  Thanks to Prof. Urroz for permission to post and use the above documents!
Two alternatives to Maple:
- WolframAlpha makes a good portion of Mathematica accessible for free online.
- SageMath is a free and open source alternative, but is not as slick.
Work and Solutions
- Assignment # 1, 2, 3, π, 4, 5, 6
  and Solutions to Assignment # 1, 2, 3, 4
  and Maple worksheets for Assignment # 1, 2, 3, 4
- Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
  and Solutions to Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
- Final Examination and Solutions to the Final Examination
Lectures and Notes [Mostly the same as Fall 2020.]
- Introduction to Maple - video, Maple worksheet, worksheet (pdf)
- Background - video, notes
- Limits - video, notes
- Limits - an alternate ε-δ definition - video, notes
- Limits II - non-limits and limits to infinity - video, notes
- Limits III - practical rules for computing limits - video, notes
- Limits IV - examples of computing limits - video, notes
- Limits V - two special limits and a theorem - video, notes
- Derivatives - the limit definition - video, notes
- Derivatives II - rules and examples - video, notes
- Derivatives III - the Chain Rule - video, notes
- Derivatives IV - examples - video, notes
- Derivatives V - implicit differentiation - video, notes
- Derivatives VI - l'Hopital's Rule - video, notes
- Asymptotes - vertical and horizontal - video, notes
- Asymptotes II - some more examples - video, notes
- Maxima and Minima - some basics - video, notes
- Maxima and Minima II - examples - video, notes
- Maxima and Minima III - method & example - video, notes
- Curve Sketching, i.e. Qualitative Analysis - video, notes
- Curve Sketching II - checklist and example - video, notes
- Curve Sketching III - example - video, notes
- Optimization - applied max/min by example - video, notes
- Optimization II - a distance problem - video, notes
- Related Rates - video, notes
- Related Rates II - Three dimensions home - video, notes
- Related Rates III - Twice more, with angles - video, notes
- Two more applications - video, notes
- The Definite Integral - an informal look - video, notes
  Supplementary handout: A Precise Definition of the Definite Integral
- The Fundamental Theorem of Calculus - video, notes
- Examples of Substitution - video, notes
- Examples of Substitution II - video, notes
- Areas Between Curves - video, notes
- Integration by Parts - video, notes
- Integration by Parts II - video, notes
- Volumes - video, notes
- Volumes II - Solids of Revolution - video, notes
- Why the standard normal density is a valid density (Just for fun! Not on exam!) - video, notes

MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, Section A, Fall 2020:

Course information:
- MATH 1110H course outline [Unofficial summary of the syllabus.]
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally. [Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.]
- Suggested Homework Exercises
- A Precise Definition of the Definite Integral - A handout filling in a major gap in the textbook.
- The Basic Substitution Rule - A handout with another take on the integration technique of substitution.
- Integration by Parts - A handout with another take on the technique of integration by parts.
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet. It's overkill for MATH 1110H... :-)
General advice and information:
- Some useful advice for surviving university math courses: Enjoying Math!
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet. It's overkill for MATH 1110H... :-)
Maple (and other software) information:
- Introduction to Maple lecture: video, Maple worksheet, worksheet (pdf)
- A very quick start with Maple [Updated 2020-10-31.]
- Getting started with Maple 10 by Gilberto E. Urroz
- A survey of mathematical applications using Maple 10 by Gilberto E. Urroz
  (as a Maple 10 worksheet)
Thanks to Prof. Urroz for permission to post and use the above documents!
Two alternatives to Maple:
- WolframAlpha makes a good portion of Mathematica accessible for free online.
- SageMath is a free and open source alternative, but is not as slick.
Lectures and notes:
- Background - video, notes
- Limits - video, notes
- Limits II - non-limits and limits to infinity - video, notes
- Limits III - practical rules for computing limits - video, notes
- Limits IV - examples of computing limits - video, notes
- Limits V - two special limits and a theorem - video, notes
- Derivatives - The limit definition - video, notes
- Derivatives II - Rules and examples - video, notes
- Derivatives III - The Chain Rule - video, notes
- Derivatives IV - Examples building up a library of derivatives - video, notes
- Derivatives V - Implicit differentiation by example - video, notes
- Derivatives VI - l'Hopital's Rule - video, notes
- Asymptotes - Vertical and horizontal - video, notes
- Asymptotes II - Some more examples - video, notes
- Maxima and Minima - Some basics - video, notes
- Maxima and Minima II - Examples - video, notes
- Maxima and Minima III - A general procedure - video, notes
- Curve Sketching - video, notes
- Curve Sketching II - video, notes
- Curve Sketching III - video, notes
- Introduction to Maple - video, Maple worksheet, worksheet (pdf)
- Optimization - video, notes
- Optimization II - video, notes
- Related Rates - video, notes
- Related Rates II - Three dimensions home - video, notes
- Related Rates III - Twice more, with angles - video, notes
- Two more applications - video, notes
- The Definite Integral - an informal look - video, notes
  Supplementary handout: A Precise Definition of the Definite Integral
- The Fundamental Theorem of Calculus - video, notes
- Examples of Substitution - video, notes
- Examples of Substitution II - video, notes
- Areas Between Curves - video, notes
- Integration by Parts - video, notes
- Integration by Parts II - video, notes
- Volumes - video, notes
- Volumes II - Solids of Revolution - video, notes
- Why the standard normal density is a valid density (Just for fun! Not on exam!) - video, notes
Assignment # 1, 2, 3, π, 4, 5 [corrected], 6
and Solutions to Assignment # 1, 2, 3, 4, 5, 6.
Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
and Solutions to Quiz # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Take-Home Final Examination and Solutions to the Take-Home Final Examination.

MATH 1120H - Calculus II: Integrals and Series, Summer 2020:

Course information:
- MATH 1120H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally. [Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.]
- Suggested Homework Exercises
General advice and information:
- Some useful advice for surviving university math courses: Enjoying Math!
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet.
Lectures and Notes:
- Definite Integrals: Video, Notes
  A quick review of the basics of definite integrals and the Fundamental Theorem of Calculus.
- Substitution Video, Notes
  A review of the basic Substitution Rule.
- Integration by Parts: Video, Notes
- Trigonometric Integrals: Video, Notes
- Trigonometric Substitutions: Video, Notes
- Partial Fractions, Part I: Video, Notes
- Partial Fractions, Part II: Video, Notes
- Improper Integrals: Video, Notes
- Applications, Part I: Video, Notes
  Average value, area, volume, and arc-length.
- Applications, Part II: Video, Notes
  Volumes of solids of revolutions and areas of surfaces of revolution.
- Sequences: Video, Notes
  Sequences and their limits.
- The Basics of Series: Video, Notes
  Summing sequences, partial sums, and convergence.
- Integral Test and the p-Tests: Video, Notes
- Alternating Series Test: Video, Notes
  The Alternating Series Test and absolute vs. conditional convergence.
- Comparison Tests: Video, Notes
  The (Basic) Comparison Test and the Limit Comparison Test.
- Ratio and Root Tests: Video, Notes
- Power Series: Video, Notes
  Power series and the radius and interval of convergence of power series.
- Taylor Series: Video, Notes
  Taylor Series and Taylor's formula.
- Why the standard normal density is a valid density, or
  Behold the power of fully operational multivariate calculus! (Just for fun!)
  Video, Notes
Additional notes on various topics:
- A Precise Definition of the Definite Integral - For those interested.
- Trigonometric Integrals and Substitutions - A brief summary.
- An Integral Tale - An example of the computation of a difficult integral, including some false starts.
Assignment # 1, 2, 3, 4, 5,
and Solutions to Assignment # 1, 2, 3, 4, 5.
Quiz # 1, 2, 3, 4, 5, 6,
and Solutions to Quiz # 1, 2, 3, 4, 5, 6.
Final Exam and Solutions to the Final Exam.

MATH 1120H - Calculus II: Integrals and Series, Winter 2020:

Course information:
- MATH 1120H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally. [Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.]
- Suggested Homework Exercises
General advice and information:
- Some useful advice for surviving university math courses: Enjoying Math!
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet.
Supplementary readings:
- A Definition of the Definite Integral (from MATH 1110H, Fall 2019)
- An Integral Tale, the tricky example from the lecture of 9 January.
- Trigonometric Integrals and Substitutions: A Brief Summary
- Post end of in-person classes lecture notes:
Assignment # 1, 2, 3, 4, 5, 5.1, 6, 9.75
and the Solutions to Assignment # 1, 2, 3, 4, 5.1, 6
Quizzes and Solutions to the Quizzes
Test and Solutions to the Test
Final Exam and Solutions to the Final Exam

MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, Section A, Fall 2019:

Course information:
- MATH 1120H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally. [Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.]
- A Definition of the Definite Integral
- Suggested Homework Exercises
General advice and information:
- Some useful advice for surviving university math courses: Enjoying Math!
- Two useful pamphlets from Academic Skills:
  - Formula for Success
  - Lines, Conics, Limits and Derivatives
Maple information:
- A very quick start with Maple
- Getting started with Maple 10 by Gilberto E. Urroz
- A survey of mathematical applications using Maple 10 by Gilberto E. Urroz
  (as a Maple 10 worksheet)
Thanks to Prof. Urroz for permission to post and use the above documents!
SageMath is an open source alternative to Maple and Mathematica.
Assignment # 1, 2, 3, π, 4, 5 6,
and Solutions to Assignment # 2, 3, 4
Quizzes and Solutions to the Quizzes
Test and Solutions to the Test
Final Exam and Solutions to the Final Exam

MATH 1120H, Winter 2019:

Course information:
- MATH 1120H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Homework Exercises
General advice and information:
- Enjoying Math!
- Formula for Success
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet.
Assignment # 1, 2, 3, π, 4, 5, 6
and Solutions to Assignment # 1, 2, 3, 4, 5, 6
Quizzes and Solutions to the Quizzes
Test and Test Solutions
Final Exam and Solutions to the Final Exam

MATH 1110H, Fall 2018 (pdf):

Course information:
- MATH 1110H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Homework Exercises
General advice and information:
- Enjoying Math!
- Formula for Success
- Dale Landry's Calculus Aid Sheet
  Thanks to Dale for permission to post his MATH 1120H aid sheet.
Maple information:
- A very quick start with Maple
- Getting started with Maple 10 by Gilberto E. Urroz
- A survey of mathematical applications using Maple 10 by Gilberto E. Urroz
  (as a Maple 10 worksheet)
- Worksheets and slides from the Maple labs (mostly as pdfs):
  Week 1 worksheet [Maple file],
  Week 2 worksheet and slides
Thanks to Prof. Urroz and our Maple TA, Francis Quinby, for permission to use the above documents!
Assignment # 0, 1, 2, 3, 4, 5, 2e, 6, 7, 8, 9, 10, 11,
and Solutions to Assignment # 0, 1, 2, 3, 4, 5, 6, 7, 8
Test and Solutions to the Test
Final Exam and Solutions to the Final Exam

MATH 1120H, Summer 2018 (pdf):

Course information:
- MATH 1120H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Homework Exercises
Assignment # 1, 2, 3, 4, 5, 2π
and Solutions to Assignment # 1, 2
Quizzes and Solutions to the Quizzes
Practice Test and Practice Test Solutions
Test and Test Solutions
Practice Final Exam and Solutions to the Practice Final Exam
Final Exam and Solutions to the Final Exam

MATH 1110H, Summer 2018 (pdf):

Course information:
- MATH 1110H course outline
- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard. May be downloaded for free from communitycalculus.org or locally.
  Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License.
- Homework Exercises
Assignment # 1, 2, 3, 4, 5, 6
and Solutions to Assignment # 1, 2, 3 & 4
Quizzes and Solutions to the Quizzes
Test and Solutions to the Test
Practice Final Exam and Solutions to the Practice Final Exam
Final Exam and Solutions to the Final Exam

Older stuff

Single-variable Calculus Problems (and some solutions, too!) [pdf, ~5.1mb], by Stefan Bilaniuk.
This is a compilation of a lot of quizzes, tests, and exams, and many of their solutions, from first-year calculus courses I taught over a decade or so. Typos and other errors have been lovingly preserved! You can also find all these items individually, plus a lot of assignments and many of their solutions, plus material from more recent courses, below.
MATH 1101Y, 2013-2014
- Quizzes and Solutions to the Quizzes
- Assignment # 1, 2, e, 3, π, 4, 5, ♥, 6
  and Solutions to Assignment # 1, 2, 5, ♥
- Test 1, 2 and Solutions to Test 1, 2
- Final Exam Max-imum Fun, the Final Exam proper, and the Solutions to the Final Exam
MATH 1100Y, 2012-2013
- Assignment # 1, 2, 3, π, 4, 5, γ, 6
  and Solutions to Assignment # 1, 2, 3, 4
- Quizzes and Solutions to the Quizzes
- Tests 1 & 2 and Solutions to Tests 1 & 2
- Final Exam and the Solutions to the Final Exam
MATH 1100Y, Summer 2012
- Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
  and Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Quizzes and Solutions to the Quizzes
- Tests 1 & 2 and Solutions to Tests 1 & 2
- Final Exam and the Solutions to the Final Exam
MATH 1101Y, 2011-2012
- Assignment # 1, 2, 3, π, 4, 5, 2e, 6
  Solutions to Assignment # 1, 2, 3, 4, 5
- Quizzes and Solutions to the Quizzes
- Tests 1 & 2 and Solutions to Tests 1 & 2
- Final Exam and the Solutions to the Final Exam
MATH 1100Y, Summer 2011
- Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
  Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
- Quizzes and Quiz Solutions
  Take-Home Quiz and Take-Home Quiz Solution
- Tests 1 and 2 and Solutions to Tests 1 and 2
- Final Exam and the Solutions to the Final Exam
MATH 1101Y, 2010-2011
- Assignment # 1, 2, 3, 4, 5, 6, 2π, 7, 8, 9, 10, 11, 12, 4π
  Solutions to Assignment # 1, 2, 3, 4, 5, 6, 10
- Quizzes and Quiz Solutions
- Tests 1 and 2 and Solutions to Tests 1 and 2
- Final Exam and the Solutions to the Final Exam
- David Merritt, a MATH 1101Y student who uses his laptop to take notes, has kindly agreed to share them:
  Epsilon-Delta Definition of Limits
  Week 1, 2, 3, 7, 8, 9, 10, 11
  Thanks, David!
  Note that these notes are not complete and may have errors. (In particular, they preserve the errors made by the instructor...) You will need a fairly recent version of Microsoft Word to read them.
MATH 1100Y, Summer 2010
- Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
  Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9
- Quizzes and Quiz Solutions
- Test 1, 2 and Solutions to Test 1, 2
- Final Exam and the Solutions to the Final Exam
MATH 1100Y, 2009-2010
- Assignments & Solutions: 1, 2, 3, 4
- Quizzes & Solutions: 1a, 1b, 2a, 2b, 3a, 3b, 4a, 4b, 5a, 5b, 6a, 6b, 7a, 7b, 8a, 8b, 9a, 9b, 10a, 10b, 11a, 11b, 12a, 12b, 13a, 13b, 14a, 14b, 15a, 15b, 16a, 16b, 17a, 17b, 18a, 18b,
- Test Solutions: 1, 2
- Final Exam Solutions
MATH 1101Y, 2009-2010
- Assignments & Solutions: 1, 2, 3, 4
- Quizzes & Solutions: 1a, 1b, 2a, 2b, 3a, 3b, 4a, 4b, 5a, 5b, 6a, 6b, 7a, 7b, 8a, 8b, 9a, 9b, 10a, 10b, 11a, 11b, 12a, 12b, 13a, 13b, 14a, 14b, 15a, 15b, 16a, 16b, 17a, 17b, 18a, 18b, 19a, 19b
- Test Solutions: 1, 2
MATH 1100Y (Section A), 2008-2009
- Final Examination
MATH 110, 2003-2004
- Second Annual Equation Limerick Competition (pdf)
- Assignment # 1, 2, 3, 4, 5, 6 (pdf: 1, 2, 3, 4, 5, 6)
  Solutions to Assignment # 1, 2, 3, 4, 5 (pdf: 1, 2, 3, 4, 5)
  Matt Connell's solution to Assignment #3.
- §A Quizzes (pdf) and Solutions (pdf)
- §A Test # 1, 2 (pdf: 1, 2)
  Solutions to §A Test # 1, 2 (pdf: 1, 2)
- §B Review exercises (pdf)
- §A Final Exam (pdf)
MATH 110, 2002-2003
- Equation Limerick Competition
  - Results!
- Assignment # 1 2 3 4 5 6 7 8 9 10
- Quizzes & Solutions:
  - Quizzes & Solutions for 110A
  - Quizzes & Solutions for 110B
- Tests:
- Final Exam:
MATH 110, 2001-2002
- Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Bonus
  - Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Bonus
- Quizzes
  - Quiz Solutions
- Test 1, 2
  - Solutions to Test 1, 2
- Final Exam
MATH 110, 1999-2000
- Assignment 1
- Quizzes (with solutions) 1, 2, 3, 4, 5, 6, 7, 8
- Test 1
  - Solutions to Test 1
MATH 110, 1998-1999
- Assignment 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Quizzes
- Test 1, 2
- Final Exam
MATH 110, 1997-1998
- Assignment 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
  - Solutions to Assignment 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Quizzes
- Test 1, 2
  - Solutions to Test 1, 2
- Final Exam
MATH 110, 1996-1997
- Test 1, 2
- Final Exam
MATH 110, 1993-1994
- Test 2
- Final Exam
MATH 110, 1992-1993
- Test 1, 2
- Final Exam
MATH 110, 1991-1992
- Test 1, 2
- Final Exam

Other sources

There is fair bit of material available online about calculus; a brief selection follows:

Some calculus notes and texts available online

The Calculus Bible by G. S. Gill
Understanding Calculus by Faraz Hussain
Elementary Calculus: An Approach Using Infinitesimals by H. Jerome Keisler
Calculus by Gilbert Strang at MIT OpenCourseWare
The mooculus textbook by Jim Fowler and Bart Snapp

Some other calculus references and resources online

Calculus at The Math Forum
Single Variable Calculus, Fall 2006 at MIT OpenCourseWare
Calculus at Wikipedia
Calculus at Wolfram MathWorld

Maintained by Stefan Bilaniuk. Last updated 2024-04-30.