About
Hello! I'm John, your private math and physics tutor. I graduated from the University of Waterloo with degrees in Applied and Pure Mathematics, and studied Civil Engineering Technology at Lakehead University. I have been tutoring highschool, college, and university students online and in person for over 5 years. My academic interests include analysis, and differential geometry. For fun I like to rock climb, play hockey, snowboard, and have just recently taken up cross country skiing.
Academic Expertise
Foundations
Linear Algebra
- Vectors in Euclidean Space
- Systems of Linear Equations
- Matrices and Linear Mappings
- Inverses and Determinants
- Eigenvectors and Diagonalization
- Fundamental Subspaces
- Inner Products
- Singular Value Decomposition, QR Decomposition and Jordan Canonical Form
Calculus
- Limits
- Continuous and Differentiable Functions
- Linear Approximations
- The Product, Quotient and Chain Rule
- Taylor Polynomials
- Partial Derivatives
- Directional Derivatives
- Integrals
- Integration Rules and Techniques
- Double and Triple Integrals
Probability
- Sample Spaces
- Basic Combinatorics
- Mutually Exclusive and Independent Events
- Discrete and Continuous Distributions
- Discrete and Continuous Random Variables
- Joint, Marginal, and Conditional Probability Functions
- Law of Large Numbers
- The Central Limit Theorem
Applied Math
Differential Equations
- First-Order Differential Equations
- Second-Order Differential Equations
- Numerical Methods
- System of Differential Equations
- Laplace Transform Methods
Classical Mechanics
- Newton's Law of Motion
- Momentum and Angular Moment
- Energy Conservation
- Calculus of Variations
- Lagrange and Hamiltonian Mechanics
Electricity and Magnetism
- Electrostatics and Magnetostatics
- Electric Potentials
- Conductors and Currents
- Induction
- Electric and Magnetic Fields in Media
- Electromagnetic Waves
- Maxwell's Equations
Pure Math
Real Analysis
- The Real and Complex Number System
- Basic Topology
- Numerical Sequences and Series
- Continuity, Differentiation and Integration
- Sequences and Series of Functions
- Basic Lebesque Theory
Differential Geometry
- Smooth Manifolds
- Tangent Vectors
- Submersion, Immersions, and Embeddings
- Submanifolds
- Vector Fields
- Differential Forms
- Lie Groups
- Fibre Bundles
- Distributions and Foliations
- Riemannian, Symplectic and Complex Manifolds
I Tutor
High School
Advanced functions, calculus, data management, and physics.
College
Vectors, calculus, statistics, and physics for technologists.
University
Linear algebra, calculus, probability, statistics, differential equations, and physics.
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