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.
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)
Click on the following link to access
the course notes.
Foundations of Calculus 2 for Teachers: Course Notes
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
B.
Displacement versus Velocity
C.
Introduction to Riemann Sums
D.
Informal Definition of the Integral
E.
Introduction to Riemann Sums Part II: Lower Sums, Upper Sums, and Refinements
F.
Introduction to Riemann Sums Part III: Refinement Theorem
G.
Formal Definition of the Integral
H.
Two Criteria for Integrability
I.
Uniform Continuity Part I: Introduction
K.
Integrability of Continuous Functions
M.
Geometric Interpretation of the Integral
N.
Average Value of a Function
O.
Differentiation of an Integral Function
P.
Fundamental Theorem of Calculus (Part I)
Q.
Fundamental Theorem of Calculus (Part I) : Examples
S.
Fundamental Theorem of Calculus (Part 2)
T.
Change of Variables for the Indefinite Integral
U.
Method of Substitution: Examples
V.
Change of Variables for the Definite Integral
Chapter 2:
Techniques of Integration
A.
Inverse Trigonometric Substitutions
C.
Examples of Integration by Parts
G.
Introduction to Improper Integrals
H.
Monotone Convergence Theorem for Functions
I.
Comparison Test for Integrals
Chapter 3:
Applications of Integration
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
E.
Graphical and Numerical Solutions of DEs
F.
Exponential Growth and Decay
Chapter 5: Numerical Series
E.
Monotone Convergence Theorem
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
E.
Differentiation of Power Series
F.
Uniqueness of Power Series Representations
G.
Integration of Power Series
H.
Pointwise Convergence of Functions Part I: Pointwise Convergence
I.
Pointwise Convergence of Functions Part II: Flaws
J.
Uniform Convergence of Functions Part I: Definitions
K.
Uniform Convergence of Functions Part II: Continuity
O.
Weierstrass M Test and the Uniform Convergence
of Power Series
P.
Term by Term Integration of Power Series: Part 2
Q.
Term by Term Antidifferentiation
of Power Series
R.
Term by Term Differentiation of Power Series
T.
Taylor's Polynomials : Examples
U.
Taylor's Polynomials : Examples (Part 2)
W.
Introduction to Taylor Series
X.
Taylor Series for Sine and Cosine
Y.
Convergence of Taylor Series
AA.
Additional Examples of Taylor Series
This page is maintained by Barbara Forrest.
Users are encouraged to contact the authors to report any errors.