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Barbara
Forrest (baforres@uwaterloo.ca)
Brian
Forrest (beforres@uwaterloo.ca)
Click on the following link to access
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Calculus 2 for Honours Mathematics: 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.
Beside each lecture link is a link to a PDF file that contains lecture slides that you may download and use to make notes.
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.
Building Power Series
E.
Differentiation of Power Series
F.
Uniqueness of Power Series Representations
G.
Integration of Power Series
H.
Taylor's Polynomials
I.
Taylor's Polynomials : Examples
J.
Taylor's Polynomials : Examples (Part 2)
K.
Taylor's Theorem
L.
Introduction to Taylor Series
M.
Taylor Series for Sine and Cosine
N.
Convergence of Taylor Series
O.
Binomial Series
P.
Additional Examples of Taylor Series
This page is maintained by Barbara Forrest.
Users are encouraged to contact the authors to report any errors.