CALCULUS 1000A/B

UWO

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

1. Prerequisite Review

1.7hr

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. Operations with Functions3 min

1.2.2. Example2 min

1.2.3. Practice2 min

1.2.4. Practice1 min

1.3.1. Transformation of Graphs2 min

1.3.2. Example1 min

1.3.3. Practice2 min

1.4.1. Basic of Polynomials4 min

1.4.2. Example2 min

1.4.3. Practice3 min

1.4.4. Polynomial Graphs & Characteristics4 min

1.4.5. Example2 min

1.4.6. Practice2 min

1.5.1. Factoring 5 min

1.5.2. Factoring a Difference & Sum of Cubes3 min

1.5.3. Example2 min

1.5.4. Practice46 sec

1.5.5. Practice2 min

1.5.6. Practice2 min

1.6.1. Rational Functions4 min

1.6.2. Solving Rational Equations3 min

1.7.1. Radical Functions59 sec

1.7.2. Solving Radical Equations5 min

1.7.3. Example5 min

1.7.4. Practice8 min

2. Functions and Graphs

1.4hr

2.1.1. Domain2 min

2.1.2. Range2 min

2.1.3. Example2 min

2.1.4. Practice 40 sec

2.1.5. Practice 3 min

2.2.1. Even and Odd Functions3 min

2.2.2. Example2 min

2.3.1. Piecewise Functions4 min

2.3.2. Example5 min

2.3.3. Practice3 min

2.4.1. Absolute Value Function1 min

2.4.2. Example3 min

2.5.1. Trigonometric Functions6 min

2.5.2. Example4 min

2.5.3. Trig Identities2 min

2.5.4. Practice3 min

2.5.5. Practice4 min

2.6.1. Inverse Functions3 min

2.6.2. Example3 min

2.6.3. Practice2 min

2.7.1. Inverse Trigonometric Functions4 min

2.7.2. Example3 min

2.7.3. Practice2 min

2.7.4. Practice2 min

2.8.1. Exponential Functions3 min

2.8.2. Example1 min

2.8.3. Example2 min

2.9.1. Logarithmic Functions4 min

2.9.2. Example3 min

2.9.3. Example:3 min

2.9.4. Practice2 min

3. Limits and Continuity

1.4hr

3.1.1. Limit Basics2 min

3.1.2. Example1 min

3.2.1. One-Sided Limits2 min

3.2.2. Example: One-Sided Limit2 min

3.2.3. Practice: One-Sided Limits3 min

3.3.1. Limit Laws 2 min

3.3.2. Practice1 min

3.4.1. Computing Limits by Factoring1 min

3.4.2. Example1 min

3.4.3. Practice2 min

3.5.1. Computing Limits by Multiplying by the Conjugate3 min

3.5.2. Example3 min

3.5.3. Practice3 min

3.6.1. Computing Limits by Getting a Common Denominator1 min

3.6.2. Example2 min

3.6.3. Practice4 min

3.7.1. The Squeeze Theorem2 min

3.7.2. Example2 min

3.7.3. Practice2 min

3.8.1. Infinite Limits2 min

3.8.2. Example1 min

3.8.3. Example3 min

3.9.1. Indeterminate Forms50 sec

3.10.1. Continuity2 min

3.10.2. Example2 min

3.10.3. Practice4 min

3.11.1. The Intermediate Value Theorem2 min

3.11.2. Example2 min

3.11.3. Practice2 min

4. Derivatives

2.4hr

4.1.1. The Limit Definition of a Derivative2 min

4.1.2. Example3 min

4.1.3. Practice5 min

4.2.1. Differentiation Laws51 sec

4.3.1. The Power Rule1 min

4.3.2. Example2 min

4.3.3. Practice51 sec

4.4.1. The Product Rule49 sec

4.4.2. Example2 min

4.4.3. Example2 min

4.4.4. Practice2 min

4.5.1. The Quotient Rule1 min

4.5.2. Example2 min

4.5.3. Practice4 min

4.6.1. Higher Order Derivatives2 min

4.7.1. Derivatives as a Rate of Change2 min

4.7.2. Average Rate of Change46 sec

4.7.3. Example2 min

4.7.4. Practice1 min

4.8.1. The Chain Rule1 min

4.8.2. Example2 min

4.8.3. Practice3 min

4.9.1. Derivatives of Trigonometric Functions1 min

4.10.1. Inverse Trig Derivatives1 min

4.10.2. Example1 min

4.10.3. Practice3 min

4.11.1. Implicit Differentiation2 min

4.11.2. Example3 min

4.11.3. Example3 min

4.11.4. Practice3 min

4.12.1. Derivatives of Logarithmic Functions1 min

4.12.2. Example56 sec

4.12.3. Example2 min

4.12.4. Practice2 min

4.12.5. Practice: Log and Ln2 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. Tangent Lines1 min

4.14.2. Example3 min

4.14.3. Practice2 min

4.15.1. Logarithmic Differentiation2 min

4.15.2. Example2 min

4.15.3. Practice3 min

5. Applications of Derivatives

4hr

5.1.1. Related Rates1 min

5.2.1. Linear Approximation4 min

5.2.2. Linear approximation2 min

5.2.3. Linear Approximation5 min

5.3.1. Maximum and Minimum on Closed Intervals2 min

5.3.2. Example4 min

5.3.3. Practice3 min

5.3.4. Practice3 min

5.4.1. Mean Value Theorem4 min

5.4.2. Mean Value Theorem Problem4 min

5.4.3. Mean Value Theorem Problem6 min

5.5.1. Intervals of Increase and Decrease1 min

5.5.2. Example2 min

5.5.3. Practice3 min

5.6.1. Critical Points and Extrema2 min

5.6.2. Example

5.6.3. Practice3 min

5.7.1. 1st and 2nd Derivative Tests3 min

5.7.2. Example7 min

5.7.3. Example

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. Curve Sketching2 min

5.9.2. Example7 min

5.9.3. Practice9 min

5.10.1. Limits at Infinity3 min

5.10.2. Example60 sec

5.10.3. Example3 min

5.10.4. Example4 min

5.10.5. Practice 3 min

5.10.6. Practice3 min

5.11.1. Optimization1 min

5.11.2. Example4 min

5.11.3. Example4 min

5.11.4. Practice6 min

5.11.5. Practice4 min

5.12.1. Position, Velocity, and Acceleration1 min

5.12.2. Example3 min

5.12.3. Practice2 min

5.13.1. L’Hopital’s Rule2 min

5.13.2. Example2 min

5.13.3. Practice5 min

5.14.1. Solving General Indeterminate Forms2 min

5.14.2. Example2 min

5.14.3. Practice5 min

5.14.4. Practice2 min

5.15.1. Newton's Method1 min

5.15.2. Theory: Linear Approximation and Newton's method10 min

5.16.1. Related Rates

5.16.2. Related Rates5 min

5.16.3. Related Rates5 min

5.16.4. Linear Approximation4 min

5.16.5. Linear Approximation

5.16.6. Newton's Method2 min

5.16.7. Newton's Method

5.16.8. L'Hopital's Rule

5.16.9. L'Hopital's Rule

5.16.10. L'Hopital's Rule

5.16.11. Limits

5.16.12. L'Hopital's Rule

5.16.13. L'Hopital's Rule

5.16.14. Limits

5.16.15. Limits

5.16.16. Extreme Value Theorem

5.16.17. Rolle's Theorem1 min

5.16.18. Rolle's Theorem6 min

5.16.23. Intervals of Increase and Decrease

5.16.24. Intervals of Increase and Decrease3 min

5.16.25. Critical Points6 min

5.16.26. Critical Points1 min

5.16.27. Extrema5 min

5.16.28. Extrema6 min

5.16.29. Second Derivative Test10 min

5.16.30. Curve Sketching

5.16.31. Curve Sketching12 min

5.16.32. Curve Sketching

5.16.33. Optimization

5.16.34. Optimization

5.16.35. Optimization

6. Integration

2.7hr

6.1.1. Antiderivatives (Indefinite Integral)3 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}

2 min

6.5.2. Example2 min

6.5.3. Practice1 min

6.6.1. Initial Conditions2 min

6.6.2. Example2 min

6.6.3. Practice5 min

6.7.1. Finite Sums & Summation Notation3 min

6.7.2. Example5 min

6.7.3. Practice4 min

6.7.4. Practice4 min

6.8.1. Approximating Areas & Riemann Sums 3 min

6.8.2. Example4 min

6.8.3. Practice3 min

6.9.1. The Definite Integrals & Area Under a Curve2 min

6.9.2. Example7 min

6.9.3. Practice2 min

6.9.4. Practice12 min

6.10.1. Properties of the Definite Integral2 min

6.10.2. Practice2 min

6.10.3. Practice2 min

6.11.1. Computing Definite Integrals Geometrically44 sec

6.11.2. Example1 min

6.11.3. Practice1 min

6.12.1. Fundamental Theorem of Calculus - Part I2 min

6.12.2. Example1 min

6.12.3. Example48 sec

6.12.4. Practice1 min

6.12.5. Practice2 min

6.13.1. Fundamental Theorem of Calculus - Part 21 min

6.13.2. Example2 min

6.13.3. Example

6.13.4. Practice 4 min

6.13.5. Practice3 min

6.13.6. Practice1 min

6.14.1. Integration by Substitution2 min

6.14.2. Example4 min

6.14.3. Example3 min

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

6.14.5. Practice

6.14.6. Practice

6.14.7. Practice

6.14.8. Practice (w/ Back-Substitution)

6.15.1. Integrating Even and Odd Functions2 min

6.15.2. Example2 min

6.15.3. Practice2 min

7. Applications of Integration

1.1hr

7.I. Chapter Intro23 sec

7.1.1. Area between curves1 min

7.2.1. Volumes of Revolution by Cylindrical Shells2 min

7.2.2. Practice

7.2.3. Practice

7.2.4. Practice

7.3.1. Volumes of Revolution by Cross Sections (Washers)3 min

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

7.4.2. Example6 min

7.4.3. Practice

7.4.4. Practice

7.5.1. Position, Velocity, and Acceleration1 min

7.5.2. Example2 min

7.5.3. Example4 min

7.5.4. Practice3 min

7.6.1. Displacement, Velocity, and Acceleration3 min

7.6.2. Position, Velocity and Acceleration 2 min

7.6.3. Position, Velocity and Acceleration 3 min

7.6.4. Area Between Curves

7.6.5. Area Between Curves4 min

7.6.6. Area Between Curves

7.6.7. Area Between Curves

7.6.8. Volumes of Revolution, Cylindrical Shells

7.6.9. Volumes of Revolution, Disc/Washer4 min

7.6.10. Volumes of Revolution, Cylindrical Shells

7.6.11. Volumes of Revolution9 min

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