Calculus 2 for Honours Mathematics

Instructor: Barbara Forrest

 

Access to the course notes and online lectures are available according to the following terms of use. The course notes are available as a PDF file. The lectures are available as MP4 files. These files are being made available so that students may view the course notes and lectures on their mobile devices. No technical support is available.


Terms of Use


IMPORTANT:

 

All rights, including copyright, images, slides, audio, and video components, of the content of this course are owned by the course authors Barbara Forrest and Brian Forrest.

 

By accessing these web pages, you agree that you may only download the content for your own personal, non-commercial use.

 

You are not permitted to copy, broadcast, download, store (in any medium), transmit, show or play in public, adapt, or change in any way the content of these web pages for any other purpose whatsoever without the prior written permission of the course authors.

 

Author Contact Information:

 

Barbara Forrest (baforres@uwaterloo.ca)

Brian Forrest (beforres@uwaterloo.ca)

 

 

 

 


Course Notes


 

Click on the following link to access the course notes.

 

Calculus 2 for Honours Mathematics: Course Notes

 

 

 

 

Supplementary Notes:

Curves


Lectures


 

Click on any of the following links to access the lectures that accompany the course notes for this course.

 

All lectures are available as MP4 files. You must have an MP4 player installed on your device in order to view the files.

 

 

 

Chapter 1: Integration

 

A.    Areas under Curves

B.    Displacement versus Velocity

C.    Introduction to Riemann Sums

D.    Definition of the Integral

E.    Properties of the Integral

F.     Geometric Interpretation of the Integral

G.    Average Value of a Function

H.    Differentiation of an Integral Function

I.       Fundamental Theorem of Calculus (Part I)

J.      Fundamental Theorem of Calculus (Part I) : Examples

K.    Antiderivatives

L.      Fundamental Theorem of Calculus (Part 2)

M.   Change of Variables for the Indefinite Integral

N.    Method of Substitution: Examples

O.    Change of Variables for the Definite Integral

 

Chapter 2: Techniques of Integration

 

A.    Inverse Trigonometric Substitutions

B.    Integration by Parts

C.    Examples of Integration by Parts

D.    Partial Fractions

E.    Partial Fractions (Part 2)

F.     Partial Fractions (Part 3)

G.    Introduction to Improper Integrals

H.    Monotone Convergence Theorem for Functions

I.       Comparison Test for Integrals

J.      The Gamma Function

K.    Type II Improper Integrals

 

Chapter 3: Applications of Integration

 

A.    Areas Between Curves

B.    Areas Between Curves: Examples

C.    Volumes of Revolution: Disk Method (Part 1)

D.    Volumes of Revolution: Disk Method (Part 2)

E.    Volumes of Revolution: Shell Method

F.     Arc Length

 

Chapter 4: Differential Equations

 

A.    Introduction to Differential Equations

B.    Separable Differential Equations

C.    Linear Differential Equations

D.    Initial Value Problems

E.    Graphical and Numerical Solutions of DEs

F.    Exponential Growth and Decay

G.    Newton's Law of Cooling

H.    Logistic Growth

 

 

Chapter 5: Numerical Series

 

 

A.    Introduction to Series

B.    Geometric Series

C.    Divergence Test

D.    Arithmetic for Series

E.    Monotone Convergence Theorem

F.    Positive Series

G.    Comparison Test

H.    Limit Comparison Test

I.     Integral Test Part I: Introduction

J.    Integral Test Part II: p-Series Test

K.    Integral Test Part III: Estimation of Sums and Errors

L.    Alternating Series Part I: Introduction

M.    Alternating Series Part 2: Error Estimation

N.     Absolute vs Conditional Convergence

O.    Ratio Test

P.    Root Test

 

 

Chapter 6: Power Series

 

 

A.    Introduction to Power Series

B.    Finding the Radius of Convergence

C.    Functions Represented by Power Series

D.    Differentiation of Power Series

E.    Uniqueness of Power Series Representations

F.    Integration of Power Series

G.    Taylor's Polynomials

H.    Taylor's Polynomials : Examples

I.     Taylor's Polynomials : Examples (Part 2)

J.    Taylor's Theorem

K.    Introduction to Taylor Series

L.    Taylor Series for Sine and Cosine

M.    Convergence of Taylor Series

N.     Binomial Series

O.    Additional Examples of Taylor Series

 


This page is maintained by Barbara Forrest.

Users are encouraged to contact the authors to report any errors.