MAT135H1

U of T

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

1. Function Review

1.9hr

1.1.1. Interval Notation 4 min

1.1.2. Set Notation3 min

1.1.3. Example4 min

1.1.4. Practice2 min

1.1.5. Practice52 sec

1.1.6. Practice44 sec

1.1.7. Cheatsheet

1.2.1. Domain2 min

1.2.2. Range2 min

1.2.3. Example2 min

1.2.4. Practice 40 sec

1.2.5. Practice 3 min

1.3.1. Operations with Functions3 min

1.3.2. Example2 min

1.3.3. Practice2 min

1.3.4. Practice1 min

1.4.1. Even and Odd Functions3 min

1.4.2. Example2 min

1.5.1. Transformation of Graphs2 min

1.5.2. Example1 min

1.5.3. Practice2 min

1.6.1. Piecewise Functions4 min

1.6.2. Example5 min

1.6.3. Practice3 min

1.7.1. Absolute Value Function1 min

1.7.2. Example3 min

1.8.1. Inverse Functions3 min

1.8.2. Example3 min

1.8.3. Practice2 min

1.9.1. Trigonometric Functions6 min

1.9.2. Example4 min

1.9.3. Trig Identities2 min

1.9.4. Practice3 min

1.9.5. Practice4 min

1.10.1. Inverse Trigonometric Functions4 min

1.10.2. Example3 min

1.10.3. Practice2 min

1.10.4. Practice2 min

1.11.1. Exponential Functions3 min

1.11.2. Example1 min

1.11.3. Example2 min

1.12.1. Logarithmic Functions4 min

1.12.2. Example3 min

1.12.3. Example:3 min

1.12.4. Practice2 min

2. Limits

1.5hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Limit Laws 2 min

2.2.2. Practice1 min

2.3.1. One-Sided Limits2 min

2.3.2. Example: One-Sided Limit2 min

2.3.3. Practice: One-Sided Limits3 min

2.4.1. Infinite Limits2 min

2.4.2. Example1 min

2.4.3. Example3 min

2.5.1. Indeterminate Forms50 sec

2.6.1. The Squeeze Theorem2 min

2.6.2. Example2 min

2.6.3. Practice2 min

2.7.1. Computing Limits by Factoring1 min

2.7.2. Example1 min

2.7.3. Practice2 min

2.8.1. Computing Limits by Multiplying by the Conjugate3 min

2.8.2. Example3 min

2.8.3. Practice3 min

2.9.1. Computing Limits by Getting a Common Denominator1 min

2.9.2. Example2 min

2.9.3. Practice4 min

2.10.1. The Fundamental Trig Limit2 min

2.10.2. Example3 min

2.11.1. Continuity2 min

2.11.2. Example2 min

2.11.3. Practice4 min

2.12.1. The Intermediate Value Theorem2 min

2.12.2. Example2 min

2.12.3. Practice2 min

3. The Derivative

15min

3.1.1. Derivatives as a Rate of Change2 min

3.1.2. Average Rate of Change46 sec

3.1.3. Example2 min

3.1.4. Practice1 min

3.2.1. The Limit Definition of a Derivative2 min

3.2.2. Example3 min

3.2.3. Practice5 min

4. Computing Derivatives

2.4hr

4.1.1. Differentiation Laws51 sec

4.2.1. The Power Rule1 min

4.2.2. Example2 min

4.2.3. Practice51 sec

4.3.1. Tangent Lines1 min

4.3.2. Example3 min

4.3.3. Practice2 min

4.4.1. Normal Lines1 min

4.4.2. Example3 min

4.4.3. Practice

4.4.4. Practice1 min

4.5.1. The Product Rule49 sec

4.5.2. Example2 min

4.5.3. Example2 min

4.5.4. Practice2 min

4.6.1. The Quotient Rule1 min

4.6.2. Example2 min

4.6.3. Practice4 min

4.7.1. The Chain Rule1 min

4.7.2. Example2 min

4.7.3. Practice3 min

4.8.1. Higher Order Derivatives2 min

4.8.2. Example3 min

4.8.3. Practice2 min

4.8.4. Practice

4.8.5. Practice2 min

4.9.1. Derivatives of Trigonometric Functions1 min

4.9.2. Example39 sec

4.9.3. Example3 min

4.9.4. Example1 min

4.9.5. Practice3 min

4.9.6. Practice2 min

4.10.1. Derivatives of Inverse Functions52 sec

4.10.2. Example2 min

4.10.3. Practice3 min

4.11.1. Inverse Trig Derivatives1 min

4.11.2. Example1 min

4.11.3. Practice3 min

4.12.1. Implicit Differentiation2 min

4.12.2. Example3 min

4.12.3. Practice3 min

4.12.4. Example3 min

4.13.1. Derivatives of Exponential Functions1 min

4.13.2. Example52 sec

4.13.3. Example3 min

4.13.4. Practice1 min

4.14.1. Derivatives of Logarithmic Functions1 min

4.14.2. Example56 sec

4.14.3. Example2 min

4.14.4. Practice2 min

4.14.5. Practice: Log and Ln2 min

4.15.1. Logarithmic Differentiation2 min

4.15.2. Example2 min

4.15.3. Practice3 min

5. Using Derivatives/Applications

3hr

5.1.1. Related Rates1 min

5.1.2. Example5 min

5.1.3. Example4 min

5.1.4. Practice2 min

5.1.5. Practice4 min

5.1.6. Practice4 min

5.2.1. L’Hopital’s Rule2 min

5.2.2. Example2 min

5.2.3. Practice5 min

5.2.4. Solving General Indeterminate Forms2 min

5.2.5. Example2 min

5.2.6. Practice5 min

5.2.7. Practice2 min

5.3.1. Critical Points and Extrema2 min

5.3.3. Practice3 min

5.4.1. Extreme Value Theorem1 min

5.5.1. Maximum and Minimum on Closed Intervals2 min

5.5.2. Example4 min

5.5.3. Practice3 min

5.5.4. Practice3 min

5.6.1. Intervals of Increase and Decrease1 min

5.6.2. Example2 min

5.6.3. Practice3 min

5.7.1. 1st and 2nd Derivative Tests3 min

5.7.2. Example7 min

5.7.4. Practice3 min

5.8.1. Concavity and Inflection Points56 sec

5.8.2. Example6 min

5.8.3. Practice6 min

5.9.1. Limits at Infinity3 min

5.9.2. Example60 sec

5.9.3. Example3 min

5.9.4. Example4 min

5.9.5. Practice 3 min

5.9.6. Practice3 min

5.10.1. Curve Sketching2 min

5.10.2. Example7 min

5.10.3. Practice9 min

5.10.4. Practice

5.11.1. Related Rates

5.11.2. Related Rates5 min

5.11.3. Related Rates5 min

5.11.4. Linear Approximation4 min

5.11.5. Linear Approximation

5.11.6. Newton's Method2 min

5.11.7. Newton's Method

5.11.8. L'Hopital's Rule

5.11.9. L'Hopital's Rule

5.11.10. L'Hopital's Rule

5.11.11. Limits

5.11.12. L'Hopital's Rule

5.11.13. L'Hopital's Rule

5.11.14. Limits

5.11.15. Limits

5.11.16. Extreme Value Theorem

5.11.17. Rolle's Theorem1 min

5.11.18. Rolle's Theorem6 min

5.11.20. MVT2 min

5.11.21. MVT3 min

5.11.23. Intervals of Increase and Decrease

5.11.24. Intervals of Increase and Decrease3 min

5.11.25. Critical Points6 min

5.11.26. Critical Points1 min

5.11.27. Extrema5 min

5.11.28. Extrema6 min

5.11.29. Second Derivative Test10 min

5.11.30. Curve Sketching

5.11.31. Curve Sketching12 min

5.11.32. Curve Sketching

5.11.33. Optimization

5.11.34. Optimization

5.11.35. Optimization

6. Differential Equations

1.2hr

6.1.1. Differential Equations8 min

6.1.2. Direction Fields/Slope Fields5 min

6.1.3. Practice Question: DE Solution Graphs3 min

6.2.1. Separable First Order Differential Equations3 min

6.2.2. Practice (separable DE)2 min

6.2.3. Practice (IVP)3 min

6.2.4. Practice (IVP)3 min

6.2.5. Practice (IVP*)5 min

6.2.6. Practice (separable DE)1 min

6.3.1. Linear First Order Differential Equations7 min

6.3.2. Practice (integrating factor)1 min

6.3.3. Practice (linear DE)3 min

6.3.4. Practice (IVP)3 min

6.3.5. Practice (IVP)4 min

6.4.1. Exponential Growth and Decay3 min

6.4.2. Example4 min

6.4.3. Example5 min

6.4.4. Practice5 min

6.4.5. Practice (population)3 min

6.4.6. Practice (population)4 min

6.5.1. Second-Order Reducible DE

6.5.2. Practice: Dependent Variable Missing

6.5.3. Practice: Independent Variable Missing

6.Q. Exam-Like Practice Questions4 Qns

Mock Exam

ME.1. Term Test - Mock Assessment27 Qns

ME.1 Term Test - Mock Assessment

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