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).

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 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: ... 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.

- The textbook: Single Variable Calculus (Early Transcendentals), by David Guichard.
- 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 afrer 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*- video, Megan's notes and Caden's notes*vs.*Conditional Convergence*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: ... 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! :-)

- Single Variable Calculus (Early Transcendentals), by David Guichard.
- 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:

- 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 -*- video & notes*e*Is Irrational*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: ... 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... :-)

- Single Variable Calculus (Early Transcendentals), by David Guichard.
`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!*

`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.

- A very quick start with
*Work and Solutions**Lectures and Notes*[Mostly the same as Fall 2020.]*Introduction to*- video,`Maple``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:
- 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*lecture: video,`Maple``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*- video,`Maple``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:
- 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

- Definite Integrals: 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:
- 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:

`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`.- A very quick start with
- 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!*- A very quick start with
- Assignment # 0,
1,
2,
3,
4,
5,
2
*e*, 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

- 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****MATH 1100Y, 2012-2013****MATH 1100Y, Summer 2012****MATH 1101Y, 2011-2012****MATH 1100Y, Summer 2011****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.

- Assignment # 1,
2,
3,
4,
5,
6,
2π,
7,
8,
9,
10,
11,
12,
4π
**MATH 1100Y, Summer 2010****MATH 1100Y, 2009-2010****MATH 1101Y, 2009-2010****MATH 1100Y (Section A), 2008-2009****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****MATH 110, 2001-2002****MATH 110, 1999-2000****MATH 110, 1998-1999****MATH 110, 1997-1998****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

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

- 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

- 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 2022-06-17.