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2025
MATA36 Winter 2025
Tutorial Week 2
Basic Integration Rules
Integration Methods
Practice Questions
Practice Questions
Tutorial Week 3
Integration Methods Review
Trigonometric Substitution (Trig Sub)
Partial Fraction Decomposition (PFD)
Tutorial Week 4
Partial Fraction Decomposition (PFD)
Riemann Sums and Sigma Notation
Tutorial Week 5
Numerical Integration
Improper Integrals
Tutorial Week 6
Volumes of Revolution
Volumes by Cylindrical Shells
Tutorial Week 7
Arc Length
Initial Value Problems (Differential Equations)
Tutorial Week 8
Separable Differential Equations
Linear Differential Equations
Tutorial Week 9
Sequences
Recurrence Relations
Monotonic Sequences
Bounded Monotone Convergence Theorem (MCT)
Tutorial Week 10
Term Test Review
Tutorial Week 11
Series Definitions
Geometric Series
Comparison Test
Alternating Series Test
Tutorial Week 12
Absolute Convergence
Ratio Test
Root Test
Taylor Series
2024
MATA36 Winter 2024
Tutorial Week 2
Basic Integration Rules
Integration Methods
Practice Questions
Challenge Questions
Tutorial Week 3
Trigonometric Substitution (Trig Sub)
Practice Questions
Tutorial Week 4
Partial Fraction Decomposition (PFD)
Riemann Sums and Sigma Notation
Tutorial Week 5
Riemann Sums (Again)
Numerical Integration
Improper Integrals
Tutorial Week 6
Volumes of Revolution
Volumes by Cylindrical Shells
Tutorial Week 7
Arc Length
Complex Numbers
Tutorial Week 8
Initial Value Problems
Separable Differential Equations
Linear Differential Equations
Tutorial Week 9
Sequences
Recurrence Relations
Monotonic Sequences
Bounded Monotone Convergence Theorem (MCT)
Tutorial Week 10
Series Definitions
Geometric Series
Tutorial Week 11
Comparison Test
Alternating Series Test
Tutorial Week 12
Ratio Test
Root Test
MATA30 Fall 2024
Tutorial Week 2
2023
MATA30 Fall 2023
Tutorial Week 2
What are tutorials?
Expectations when showing your work
Sets
Quantifiers and shorthands
Functions and graphs
Some terminology for functions
Solving inequalities
Exponentials and Logarithms
Tutorial Week 3
Trigonometric and inverse trigonometric functions
Inverse trigonometric practice
Finite Limits
Tutorial Week 4
Indeterminate Form
Limit Identities
Squeeze Theorem
Absolute Values
More examples
Tutorial Week 5
Continuity
Intermediate Value Theorem
Limit definition of a derivative
Tutorial Week 6
Midterm Rundown
Midterm Review
Tutorial Week 7
Derivative Notation
Derivative Rules
Common derivatives
Derivative Practice
Logarithmic Differentiation
Implicit Differentiation
Tutorial Week 8
Curve Sketching
Derivatives of inverse functions
Applications of derivatives and related rates
Tutorial Week 9
L’Hopital’s Rule
Mean Value Theorem
Linearization
Tutorial Week 10
Initial Value Problems
Newton’s Law of Cooling
Optimization
Tutorial Week 11
Definitions
Intermediate Value Theorem
Limit Definition of a Derivative
Computing Deriviatives
Related Rates
Maximums and Minimums within Intervals
Curve Sketching
Slope of Tangent Lines
Tutorial Week 12
Sigma Notation
Riemann Sums
Integrals
Integral Properties and Formulas
Fundamental Theorem of Calculus 2 (FTC 2)
MATA33 Winter 2023
Tutorial Week 2
Graphing Linear Inequalities
FTLP and Feasable regions
Finding optimal solutions to Linear Programming problems
Tutorial Week 3
Unbounded Regions
Numbers of Solutions
Matrices
Tutorial Week 4
Proving with Matrices
Gaussian Elimination and Systems of Equations
Tutorial Week 5
Gaussian Elimination and Number of Solutions
Homogeneous Systems
Midterm Review
Tutorial Week 6
Inverting Matrices
Solving System of Equations with Inverse Matrices
Equations with Inverse Matrices
Determinants
Tutorial Week 7
Cramer’s Rule
Domains of multivariable functions
Level sets
Tutorial Week 8
Partial Derivatives
Marginal Costs
Tutorial Week 9
Higher order Partial Derivatives
Implicit functions and Higher order Partial Derivatives
Tutorial Week 10
Chain Rule
Tangent Planes
Critical Points
Tutorial Week 11
Hessian Matrix and Local Extrema
Multivariable Optimization and Lagrange Multipliers
Tutorial Week 12
Changing Order of Integration
MATA36 Winter 2023
Tutorial Week 2
\(\rule{0pt}{0ex}\)
Tutorial Week 3
Assignment Review
Integral Practice
Tutorial Week 4
Integral Practice
Partial Fraction Decomposition
Tutorial Week 5
Trigonometric Substitution
Area Between Functions
Midterm Review
Tutorial Week 6
Volumes using Cross-Sectional Areas
Volumes of Revolution
Volumes by Cylindrical Shells
Tutorial Week 7
Arc length of curves
Simpson’s Rule
Tutorial Week 8
Improper Integrals
Comparison Test
Tutorial Week 9
Limits, convergence, and divergence of Sequences
Monotone Convergence Theorem (MCT) and Convergence
Limits of Monotonic Sequences
Tutorial Week 10
Recursively defined Functions
Conditions for convergent series
Geometric Series
Tutorial Week 11
Integral Test
Comparison Test
Telescoping Series
Tutorial Week 12
Alternating Series
Ratio Test
2022
MATA30 Fall 2022
Tutorial Week 2
Writing Math
Factoring
Lines
Functions
Sketching functions
Function inverses
Absolute values
Inequalities
Logarithms and exponents
Function composition
Tutorial Week 3
Inverse Trig
Inverse Trig Functions
Inverse Trig Cancellation Rules
Graphs of Limits
Calculating Limits
Tutorial Week 4
Proof of Trigonometric Limit Identities
Squeeze Theorem
Indeterminant Forms
Conjugates
Finding Limits
Trigonometric Limits
Tutorial Week 5
Continuity
Finding Derivatives using the Limit Definition of a Derivative
Differentiability using the Limit Definition of a Derivative
Intermediate Value Theorem
Tutorial Week 6
Graphing differentiability
Derivative Notation
Derivatives with absolute values
Computing derivatives
Derivative tables
Piecewise function differentiability
Tutorial Week 7
Implicit Differentiation
Exponential Derivatives
Inverse Trigonometric Derivatives
Logarithmitic Differentiation
Related Rates
Inverse Function Derivatives
Tutorial Week 8
Curve Sketching
Sinusodial Function Derivatives
Test for Absolute Extrema
Drawing Functions
Term Test 2 Supplementary Practice
Q1: Definitions
Q2: Continuity & IVT
Q3: Limit Definition of a Derivative
Q4/5: Computing Derivatives
Q6: Related Rates
Q7: Absolute Extrema
Q8: Curve Sketching
Q9: Tangent Lines
Tutorial Week 9
L’Hopital’s Rule
L’Hopital’s Rule with Logs
Mean Value Theorem
Linearization
Tutorial Week 10
Exponential Modelling
Newton’s Law of Cooling
Optimization
Tutorial Week 11
Computing Integrals
Riemann Sums
Approximating Integrals using Riemann Sums
Tutorial Week 12
Integral Theorems
Fundamental Theorem Of Calculus I
Subtitution Method (aka u-substitution)
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