My online video lessons for MATH 119 and MATH 207 are publicly available on my YouTube channel, Mathemation.

I am interested in linear algebra, matrix analysis, operator theory, and operator algebras.

I am an academic advisor for the Faculty of Mathematics. If you are a Waterloo math student, the following links may be helpful to you.

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Below are my notes for MATH 138.

Riemann Sums and the Definite Integral
Properties of the Integral
Average Values
The Fundamental Theorem of Calculus - Part 1
The Fundamental Theorem of Calculus - Part 2
Integration by Substitution
Trigonometric Substitution
Integration by Parts
Partial Fractions
Improper Integrals
Area Between Curves
Volumes by Disks and Washers
Volumes by Cylindrical Shells

Introduction to Differential Equations
Separable DEs
First Order Linear DEs
Applications of DEs

Introduction to Infinite Series
Geometric Series
The Divergence Test
Integral Test
Comparison and Limit Comparison Tests
Alternating Series
Absolute vs. Conditional Convergence
Rearrangements
Ratio and Root Tests
Appendix: Series Convergence Tests Reference Sheet

Power Series
Representing Functions as Power Series
Differentiating and Integrating Power Series
Review of Taylor Polynomials
Taylor and Maclaurin Series
Binomial Series
Applications of Taylor Series

Below are my notes for MATH 118.

Substitution Rule and Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions
Numerical Integration
Improper Integrals

Introduction to Differential Equations
Separable Differential Equations
Linear Differential Equations
Applications of Differential Equations
Reducible Second-Order DEs (Not covered in W24)

Sequences and their Limits
Recursive Sequences and the Monotone Sequence Theorem

Introduction to Infinite Series
Geometric Series; the Divergence Test
The Integral and p-Series Tests
The Comparison and Limit Comparison Tests
The Alternating Series Test
Absolute vs. Conditional Convergence
The Ratio and Root Tests
Rearrangements
Approximating Sums
Appendix: Series Tests Reference Sheet

Power Series
Taylor Polynomials
Taylor's Inequality
Taylor Series
Manipulating Taylor Series
Applications of Taylor Series

Parametric Curves
Calculus with Parametric Curves
Polar Coordinates and Polar Curves
Calculus with Polar Curves

Below are my notes for MATH 116.

Functions, Domain, Range
Compositions and Inverses
Transformations
Even and Odd Functions
Absolute Values
Piecewise and Heaviside Functions
Trigonometry
Inverse Trigonometric Functions
Generalized Sine Function
Exponential and Logarithmic Functions
Hyperbolic Trigonometric Functions

Limits and the Squeeze Theorem
Infinite Limits and Asymptotes
Continuity

Definition of the Derivative
Derivative Rules
Derivatives of Trigonometric Functions
Implicit Differentiation
Derivatives of Log and Exponential Functions
Derivatives of Inverse Trig Functions
Logarithmic Differentiation

The Intermediate Value Theorem
Newton's Method
The Mean Value Theorem
Increasing and Decreasing Functions
Local Maxima and Minima
Concavity
Curve Sketching with Calculus
Global Extrema and Optimization
Related Rates
L'Hopital's Rule
Linear Approximation and Differentials

The Definite Integral
The Fundamental Theorem of Calculus Part 1
The Fundamental Theorem of Calculus Part 2
Substitution Rule
Integration by Parts
Average Values, Areas Between Curves
Volumes by Disks and Washers
Volumes by Cylindrical Shells
Work

Below are my notes for PMATH 336.

Course Outline

Introduction to Groups
Subgroups
Cyclic Groups
Symmetric Groups
Cosets and Lagrange's Theorem
Quotients and Normal Subgroups
Homomorphisms and Isomorphisms
Group Actions
Finite Abelian Groups

Practice Problems

Course Outline

Vectors and Lines
Length, Dot Product, Orthogonality
Planes and Hyperplanes
Projections
Cross Products
Subspaces of Rⁿ
Spanning Sets, Linear Independence

Gaussian Elimination
Gauss-Jordan Elimination
Applications to Spanning Sets and Linear Independence

Operations on Matrices
Matrix Mappings and Linear Mappings
Geometrical Transformations
Special Subspaces of Systems and Mappings
Inverse Matrices and Mappings

Determinants by Cofactors
Determinants by Row Operations

Intro to Eigenvalues and Eigenvectors
Diagonalization

Course Outline

Algebra Review

Lines and Linear Functions
Properties of Functions
Quadratic Functions, Translations and Reflections
Polynomial and Rational Functions

Exponential Functions
Logarithmic Functions
Growth and Decay
Trigonometric Functions

Limits
Continuity
Rates of Change
Definition of the Derivative
Graphical Differentiation

Preliminary Derivative Methods
Derivatives of Products and Quotients
The Chain Rule
Derivatives of Exponential Functions
Derivatives of Logarithmic Functions
Derivatives of Trigonometric Functions
Implicit Differentiation

Increasing, Decreasing Functions
Relative Extrema
Optimization
Related Rates
Higher Derivatives, Concavity
Curve Sketching

Antiderivatives
Substitution Rule
Area and the Definite Integral
The Fundamental Theorem of Calculus
Area Between Curves
Applications of Integration

Numerical Integration

Vectors and Lines in R² and R³
Length, Dot Product, Planes
Projections and Minimum Distance
Vector Cross Product in R³

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