MAT133Y1

U of T

Course Overview

Lessons & Practice

I. Welcome

1. Functions and Change

1.9hr

1.1.1. Functions7 min

1.1.2. Domain and Range of a Function5 min

1.1.3. Example4 min

1.1.4. Practice (Level 1)56 sec

1.1.5. Practice (Level 2)44 sec

1.1.6. Practice (Level 3)2 min

1.2.1. Function Notation6 min

1.2.2. Example6 min

1.2.3. Practice (Level 1)2 min

1.2.4. Practice (Level 2)1 min

1.2.5. Practice (Level 3)3 min

1.3.1. Equations of Lines6 min

1.3.2. Practice: Equations of Lines3 min

1.4.1. Average Rate of Change & the Secant Line2 min

1.4.3. Practice Level 12 min

1.4.4. Practice Level 2

1.4.5. Practice Level 3

1.5.1. Exponential Functions3 min

1.5.2. Example1 min

1.5.3. Example2 min

1.6.1. Logarithmic Functions4 min

1.6.2. Example3 min

1.6.3. Example:3 min

1.6.4. Practice2 min

1.7.1. Example: Radioactive Decay5 min

1.7.2. Exponential growth and decay

1.7.3. Exponential growth and decay

1.7.4. Exponential growth and decay

1.8.1. Combining Families of Functions2 min

1.8.2. Example2 min

1.8.3. Practice Level 1

1.8.4. Practice Level 21 min

1.8.5. Practice Level 31 min

1.9.1. Composition of Functions2 min

1.9.2. Example2 min

1.9.3. Practice Level 1

1.9.4. Practice Level 2

1.9.5. Practice Level 31 min

1.10.1. Proportionality3 min

1.10.2. Example: Power functions2 min

1.10.3. Proportionality

1.10.4. Practice: Power Functions2 min

1.10.5. Practice: Power Functions2 min

1.11.1. Trigonometric Functions6 min

1.11.2. Example4 min

1.11.3. Trig Identities2 min

1.11.4. Practice3 min

1.11.5. Practice4 min

2. Rate of Change: The Derivative

1.4hr

2.1.1. Derivatives as a Rate of Change2 min

2.1.2. Average Rate of Change46 sec

2.1.3. Example2 min

2.1.4. Practice1 min

2.2.1. The Limit Definition of a Derivative2 min

2.2.2. Example3 min

2.2.3. Practice5 min

2.2.4. When is Function Not Differentiable?

2.3.1. Higher Order Derivatives2 min

2.3.2. Example3 min

2.3.3. Practice2 min

2.3.4. Practice2 min

2.4.1. Cost, Revenue, and Profit2 min

2.4.2. Example3 min

2.4.3. Practice2 min

2.4.4. Practice4 min

3. Shortcuts to Differentiation

1.9hr

3.1.1. Differentiation Laws51 sec

3.2.1. The Power Rule1 min

3.2.2. Example2 min

3.2.3. Practice51 sec

3.3.1. Derivatives of Exponential Functions1 min

3.3.2. Example52 sec

3.3.3. Example3 min

3.3.4. Practice1 min

3.4.1. Derivatives of Logarithmic Functions1 min

3.4.2. Example56 sec

3.4.3. Example2 min

3.4.4. Practice2 min

3.4.5. Practice: Log and Ln2 min

3.5.1. The Chain Rule1 min

3.5.2. Example2 min

3.5.3. Practice3 min

3.6.1. The Product Rule49 sec

3.6.2. Example2 min

3.6.3. Example2 min

3.6.4. Practice2 min

3.7.1. The Quotient Rule1 min

3.7.2. Example2 min

3.7.3. Practice4 min

3.8.1. Derivatives of Trigonometric Functions1 min

3.8.2. Example39 sec

3.8.3. Example3 min

3.8.4. Example1 min

3.8.5. Practice3 min

3.8.6. Practice2 min

3.9.1. Inverse Trig Derivatives1 min

3.9.2. Example1 min

3.9.3. Practice3 min

3.10.1. Tangent Lines1 min

3.10.2. Example3 min

3.10.3. Practice2 min

3.11.1. Normal Lines1 min

3.11.2. Example3 min

3.11.3. Practice1 min

4. Using The Derivative

2.6hr

4.1.1. Critical Points and Extrema2 min

4.1.3. Practice3 min

4.2.1. Concavity and Inflection Points56 sec

4.2.2. Example6 min

4.2.3. Practice6 min

4.3.1. Maximum and Minimum on Closed Intervals2 min

4.3.2. Example4 min

4.3.3. Practice3 min

4.3.4. Practice3 min

4.4.1. 1st and 2nd Derivative Tests3 min

4.4.2. Example7 min

4.4.4. Practice3 min

4.5.1. Intervals of Increase and Decrease1 min

4.5.2. Example2 min

4.5.3. Practice3 min

4.6.1. Cost, Revenue, and Profit2 min

4.6.2. Example3 min

4.6.3. Practice2 min

4.6.4. Practice4 min

4.7.1. Elasticity of Demand2 min

4.7.2. Example3 min

4.7.3. Practice: Elasticity of Demand4 min

4.8.1. Logistic Growth Model

4.8.2. Example: Logistic Growth Model 5 min

4.9.1. Related Rates

4.9.2. Related Rates5 min

4.9.3. Related Rates5 min

4.9.4. Linear Approximation4 min

4.9.5. Linear Approximation

4.9.6. Taylor Series from Definition7 min

4.9.7. Taylor Polynomials

4.9.8. Maclaurin Polynomial

4.9.9. Newton's Method2 min

4.9.10. Newton's Method

4.9.11. L'Hopital's Rule

4.9.12. L'Hopital's Rule

4.9.13. L'Hopital's Rule

4.9.15. L'Hopital's Rule

4.9.16. L'Hopital's Rule

4.9.19. Extreme Value Theorem

4.9.20. Rolle's Theorem1 min

4.9.21. Rolle's Theorem6 min

4.9.23. MVT2 min

4.9.24. MVT3 min

4.9.26. Intervals of Increase and Decrease

4.9.27. Intervals of Increase and Decrease3 min

4.9.28. Critical Points6 min

4.9.29. Critical Points1 min

4.9.30. Extrema5 min

4.9.31. Extrema6 min

4.9.32. Second Derivative Test10 min

4.9.33. Curve Sketching

4.9.34. Curve Sketching12 min

4.9.35. Curve Sketching

4.9.36. Optimization

4.9.37. Optimization

4.9.38. Optimization

5. Accumulated Change: The Definite Integral

1.5hr

5.1.1. Distance and Displacement (Net Change Theorem)2 min

5.1.2. Example6 min

5.1.3. Practice

5.1.4. Practice

5.2.1. The Definite Integrals & Area Under a Curve2 min

5.2.2. Example7 min

5.2.3. Practice2 min

5.2.4. Practice12 min

5.3.1. Properties of the Definite Integral2 min

5.3.2. Practice2 min

5.3.3. Practice2 min

5.4.1. Computing Definite Integrals Geometrically44 sec

5.4.2. Example1 min

5.4.3. Practice1 min

5.5.1. Fundamental Theorem of Calculus - Part I2 min

5.5.2. Example1 min

5.5.3. Example48 sec

5.5.4. Practice1 min

5.5.5. Practice2 min

5.6.1. Fundamental Theorem of Calculus - Part 21 min

5.6.2. Example2 min

5.6.4. Practice 4 min

5.6.5. Practice3 min

5.6.6. Practice1 min

5.7.1. Average Value of a Function47 sec

5.7.2. Example2 min

5.7.3. Practice2 min

6. Antiderivatives and Application

1.8hr

6.1.1. Antiderivatives (Indefinite Integral)3 min

6.1.2. Example2 min

6.1.3. Practice1 min

6.1.4. Practice1 min

6.1.5. Practice1 min

6.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

6.2.2. Example1 min

6.2.3. Practice1 min

6.2.4. Practice1 min

6.3.1. Antiderivatives (Indefinite Integrals) of Inverse Trig Functions2 min

6.3.2. Example1 min

6.3.3. Practice1 min

6.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

6.4.2. Example42 sec

6.4.3. Practice1 min

6.4.4. Practice2 min

6.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

6.5.2. Example2 min

6.5.3. Practice1 min

6.6.1. Fundamental Theorem of Calculus - Part I2 min

6.6.2. Example1 min

6.6.3. Example48 sec

6.6.4. Practice1 min

6.6.5. Practice2 min

6.7.1. Fundamental Theorem of Calculus - Part 21 min

6.7.2. Example2 min

6.7.4. Practice 4 min

6.7.5. Practice3 min

6.7.6. Practice1 min

6.8.1. Consumer and Producer Surplus [Coming Soon!]

6.8.2. Continuous Income Streams [Coming Soon!]

6.9.1. Integration by Substitution2 min

6.9.2. Example4 min

6.9.3. Example3 min

6.9.4. Example (w/ Back-Substitution)4 min

6.9.5. Practice

6.9.6. Practice

6.9.7. Practice

6.9.8. Practice (w/ Back-Substitution)

6.10.1. Integration by Parts3 min

6.10.2. Example5 min

6.10.3. Example3 min

6.10.4. Example6 min

6.10.5. Practice

6.10.6. Practice

7. Probability

28min

7.1.1. Continuous RV & Probability Density Function4 min

7.1.2. Probability Density Function Line Example #13 min

7.1.3. Example: Probability Density Function2 min

7.1.4. Example: Probability Density Function5 min

7.2.1. Cumulative Distribution Function (CDF)3 min

7.2.2. Example6 min

7.2.3. Practice2 min

7.3.1. Expected Value (Mean)3 min

7.3.2. Expected Value

8. Functions of Several Variables

1.9hr

8.1.1. Functions of Several Variables5 min

8.1.2. Practice3 min

8.2.1. Functions of 2 & 3 Variables and Contour Curves5 min

8.2.2. Contour Diagram3 min

8.2.3. Practice Question1 min

8.2.4. Practice: Match the map with the equation9 min

8.3.1. Partial derivatives6 min

8.3.2. Practice: First Partial derivatives2 min

8.3.3. Practice: Second Partial Derivatives3 min

8.4.1. Chain Rule7 min

8.4.2. Practice: Chain Rule2 min

8.4.3. Practice: Chain Rule2 min

8.4.4. Practice: Chain Rule*3 min

8.4.5. Implicit Differentiation2 min

8.5.1. Differentials4 min

8.5.2. Practice: Differentials

8.5.3. Practice: Differentials

8.6.1. Tangent plane3 min

8.6.2. Practice: Tangent Plane

8.6.3. Linear (Tangent Plane) Approximation3 min

8.6.4. Practice: Linear approximation

8.7.1. Gradient and directional derivative7 min

8.7.2. Practice: Gradient and directional derivative

8.8.1. Maximums, Minimums, and Critical Points5 min

8.8.2. Example5 min

8.8.3. Example5 min

8.8.4. Practice4 min

8.8.5. Practice3 min

8.9.1. Local Max & Min4 min

8.9.2. Absolute Max & Min5 min

8.9.3. Lagrange Multipliers3 min

8.9.4. Practice: Lagrange Multipliers

8.9.5. Practice: Lagrange Multipliers

8.10.1. Lagrange Multipliers3 min

8.10.2. Example3 min

8.10.3. Example

8.10.4. Practice3 min

8.10.5. Practice4 min

9. Mathematical Modeling Using Differential Equations

1.6hr

9.1.1. Differential Equations8 min

9.1.2. Direction Fields/Slope Fields5 min

9.1.3. Practice Question: DE Solution Graphs3 min

9.2.1. Separable First Order Differential Equations3 min

9.2.2. Practice (separable DE)2 min

9.2.3. Practice (IVP)3 min

9.2.4. Practice (IVP)3 min

9.2.5. Practice (IVP*)5 min

9.2.6. Practice (separable DE)1 min

9.3.1. Linear First Order Differential Equations7 min

9.3.2. Practice (integrating factor)1 min

9.3.3. Practice (linear DE)3 min

9.3.4. Practice (IVP)3 min

9.3.5. Practice (IVP)4 min

9.4.1. Exponential Growth and Decay3 min

9.4.2. Example4 min

9.4.3. Example5 min

9.4.4. Practice5 min

9.4.5. Practice (population)3 min

9.4.6. Practice (population)4 min

9.5.1. Common DE Applications (Word Problems)

9.5.2. Practice (population)3 min

9.5.3. Practice (population)4 min

9.5.4. Practice (cooling & heating)3 min

9.5.5. Practice (mixing tank)6 min

9.5.6. Practice (mixing tank)8 min

10. Geometric Series and Compound Interest

4hr

10.1.1. Sequence5 min

10.1.2. Arithmetic Sequence6 min

10.1.3. Practice Level 13 min

10.1.4. Practice Level 13 min

10.1.5. Practice Level 22 min

10.1.6. Practice Level 37 min

10.1.7. Summary - Arithmetic Sequence

10.2.1. Arithmetic Series9 min

10.2.2. Example3 min

10.2.3. Practice Level 13 min

10.2.4. Practice Level 25 min

10.2.5. Practice Level 34 min

10.2.6. Summary - Arithmetic Series

10.3.1. Geometric Sequences8 min

10.3.2. Example3 min

10.3.3. Practice Level 13 min

10.3.4. Practice Level 24 min

10.3.5. Practice Level 37 min

10.3.6. Summary - Geometric Sequence

10.4.1. Geometric Series6 min

10.4.2. Example5 min

10.4.3. Practice Level 13 min

10.4.4. Practice Level 27 min

10.4.5. Practice Level 34 min

10.4.6. Summary - Geometric Series

10.5.1. Simple Interest8 min

10.5.2. Example3 min

10.5.3. Practice Level 13 min

10.5.4. Practice Level 23 min

10.5.5. Practice Level 34 min

10.6.1. Compound Interest9 min

10.6.2. Example5 min

10.6.3. Example4 min

10.6.4. Practice Level 13 min

10.6.5. Practice Level 23 min

10.6.6. Practice Level 36 min

10.7.1. Present Value3 min

10.7.2. Example: Net Present Value6 min

10.7.3. Concept Clarifier: Net Present Value (NPV) 5 min

10.7.4. Practice: Present Value1 min

10.8.1. Time Value of Money27 min

10.8.2. Concept Clarifier: Annuity Due (Future Value)8 min

10.9.1. Investments and Loans with Regular Payments8 min

10.9.2. Example5 min

10.9.3. Example5 min

10.9.4. Practice Level 14 min

10.9.5. Practice Level 1 (Spreadsheets)

10.9.6. Practice Level 24 min

10.9.7. Practice Level 38 min

10.10.1. Pascal's Triangle3 min

10.10.2. Binomial Expansion

10.10.3. Example6 min

10.10.4. Practice Level 12 min

10.10.5. Practice Level 28 min

10.10.6. Practice Level 34 min

11. Systems of Linear Equations and Matrices

4hr

11.1.1. Basics of Systems of Linear Equations8 min

11.1.2. Example3 min

11.1.3. Practice2 min

11.1.4. Practice3 min

11.2.1. Basics of Matrices3 min

11.2.2. Matrix Arithmetic3 min

11.2.3. Example1 min

11.2.4. Practice2 min

11.3.1. Augmented Matrix3 min

11.3.2. Example3 min

11.3.3. Example1 min

11.3.4. Practice2 min

11.3.5. Practice2 min

11.4.1. Echelon Forms5 min

11.4.2. Example2 min

11.4.3. Example2 min

11.4.4. Practice

11.4.5. Practice

11.4.6. Practice

11.5.1. Reducing a Matrix5 min

11.5.2. Example3 min

11.5.3. Example7 min

11.5.4. Practice2 min

11.5.5. Practice3 min

11.5.6. Practice

11.6.1. Rank of a Matrix5 min

11.6.2. Example3 min

11.6.3. Practice38 sec

11.6.4. Practice1 min

11.7.1. Matrix Multiplication6 min

11.7.2. Example1 min

11.7.3. Example4 min

11.7.4. Practice3 min

11.7.5. Practice2 min

11.7.6. Practice

11.8.1. Matrix Transpose3 min

11.8.2. Symmetric Matrices3 min

11.8.3. Example3 min

11.8.4. Practice60 sec

11.8.5. Practice2 min

11.9.1. Matrix Inverse4 min

11.9.2. Example3 min

11.9.3. Practice32 sec

11.9.4. Practice2 min

11.10.1. Matrix Inverse Algorithm3 min

11.10.2. Example2 min

11.10.3. Example2 min

11.10.4. Practice2 min

11.11.1. Elementary Matrices7 min

11.11.2. Example2 min

11.11.3. Example4 min

11.11.4. Practice2 min

11.11.5. Practice3 min

11.12.1. Solving Linear Systems5 min

11.12.2. Homogeneous Systems2 min

11.12.3. Example3 min

11.12.4. Example5 min

11.12.5. Practice2 min

11.12.6. Practice5 min

11.13.1. Solving Matrix Equations2 min

11.13.2. Example52 sec

11.13.3. Example4 min

11.13.4. Practice2 min

11.13.5. Practice54 sec

11.13.6. Practice2 min

11.14.1. Cramer's Rule3 min

11.14.2. Example2 min

11.14.3. Practice3 min

11.15.1. Invertible Matrix Theorem2 min

11.15.2. Example1 min

11.15.3. Practice1 min

11.16.1. Linear Transformations6 min

11.16.2. Example2 min

11.16.3. Example3 min

11.16.4. Practice2 min

11.16.5. Practice8 min

11.17.1. Composition and Inverse3 min

11.17.2. Example4 min

11.17.3. Practice3 min

11.18.1. Special Linear Transformations in

\reals^2

11.18.2. Example3 min

11.18.3. Practice3 min

11.18.4. Practice4 min

12. Applications of Linear Algebra

1.4hr

12.1.1. Eigenvalues and Eigenvectors6 min

12.1.2. Example7 min

12.1.3. Practice8 min

12.1.4. Practice4 min

12.2.1. Markov Chains (Random Walks)7 min

12.2.2. Example6 min

12.2.3. Practice5 min

12.3.1. Linear Dynamical Systems and Recurrence Relations9 min

12.3.2. Example7 min

12.3.3. Practice8 min

12.4.1. Systems of Linear Differential Equations3 min

12.4.2. Solving a System of Linear DEs2 min

12.4.3. Example4 min

12.4.4. Practice

12.4.5. Practice

12.5.1. Higher Order Linear DEs

12.5.2. Example

12.5.3. Practice

12.5.4. Practice

12.6.1. Least Squares Approximation6 min

12.6.2. Example4 min

12.6.3. Example: Least Squares for Polynomials

12.6.4. Practice

13. Differential Equations

1.2hr

13.1.1. Differential Equations8 min

13.1.2. Direction Fields/Slope Fields5 min

13.1.3. Practice Question: DE Solution Graphs3 min

13.2.1. Separable First Order Differential Equations3 min

13.2.2. Practice (separable DE)2 min

13.2.3. Practice (IVP)3 min

13.2.4. Practice (IVP)3 min

13.2.5. Practice (IVP*)5 min

13.2.6. Practice (separable DE)1 min

13.3.1. Linear First Order Differential Equations7 min

13.3.2. Practice (integrating factor)1 min

13.3.3. Practice (linear DE)3 min

13.3.4. Practice (IVP)3 min

13.3.5. Practice (IVP)4 min

13.4.1. Exponential Growth and Decay3 min

13.4.2. Example4 min

13.4.3. Example5 min

13.4.4. Practice5 min

13.4.5. Practice (population)3 min

13.4.6. Practice (population)4 min

13.5.1. Second-Order Reducible DE

13.5.2. Practice: Dependent Variable Missing

13.5.3. Practice: Independent Variable Missing

13.Q. DE Quiz4 Qns

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