MATH 141

McGill

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

1. Chapter 5: Integrals

1.8hr

1.1.1. The Definite Integrals & Area Under a Curve2 min

1.1.2. Example7 min

1.1.3. Practice2 min

1.1.4. Practice12 min

1.2.1. Properties of the Definite Integral2 min

1.2.2. Practice2 min

1.2.3. Practice2 min

1.3.1. Computing Definite Integrals Geometrically44 sec

1.3.2. Example1 min

1.3.3. Practice1 min

1.4.1. Fundamental Theorem of Calculus - Part I2 min

1.4.2. Example1 min

1.4.3. Example48 sec

1.4.4. Practice1 min

1.4.5. Practice2 min

1.5.1. Fundamental Theorem of Calculus - Part 21 min

1.5.2. Example2 min

1.5.4. Practice 4 min

1.5.5. Practice3 min

1.5.6. Practice1 min

1.6.1. Antiderivatives (Indefinite Integral)3 min

1.6.2. Example2 min

1.6.3. Practice1 min

1.6.4. Practice1 min

1.6.5. Practice1 min

1.7.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

1.7.2. Example1 min

1.7.3. Practice1 min

1.7.4. Practice1 min

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

1.8.2. Example1 min

1.8.3. Practice1 min

1.9.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

1.9.2. Example42 sec

1.9.3. Practice1 min

1.9.4. Practice2 min

1.10.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

1.10.2. Example2 min

1.10.3. Practice1 min

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

1.11.2. Example6 min

1.11.3. Practice

1.11.4. Practice

1.12.1. Integration by Substitution2 min

1.12.2. Example4 min

1.12.3. Example3 min

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

1.12.5. Practice

1.12.6. Practice

1.12.7. Practice

1.12.8. Practice (w/ Back-Substitution)

2. Chapter 6: Applications of Integration

39min

2.1.1. Area between curves1 min

2.1.2. Example5 min

2.1.3. Example5 min

2.1.4. Practice

2.2.1. Volumes of Revolution (Disk/Washer)3 min

2.2.2. Practice (around the x-axis)2 min

2.2.3. Practice (around the y-axis)3 min

2.2.4. Practice (around a line)3 min

2.3.1. Volumes of Revolution (Cylindrical Shells)4 min

2.3.2. Practice2 min

2.4.1. Work2 min

2.4.2. Example3 min

2.4.3. Practice

2.5.1. Average Value of a Function47 sec

2.5.2. Example2 min

2.5.3. Practice2 min

3. Chapter 7: Techniques of Integration

2hr

3.1.1. Trigonometric Integrals5 min

3.1.2. Example3 min

3.1.3. Example: Trigonometric Integrals (Case 1-3)3 min

3.1.4. Example4 min

3.1.5. Example1 min

3.1.6. Example2 min

3.1.7. Practice

3.1.8. Practice

3.1.9. Practice

3.1.10. Practice

3.2.1. Trigonometric Substitution3 min

3.2.2. Example7 min

3.2.3. Practice

3.2.4. Practice

3.3.1. Partial Fractions Decomposition4 min

3.3.2. Example:8 min

3.3.3. Example5 min

3.3.5. Practice

3.3.6. Practice

3.4.1. Strategies for integration5 min

3.5.1. Strategies for Integration3 min

3.5.2. Practice (rationalizing substitution)4 min

3.5.3. Practice: Mixed Integrals4 min

3.5.4. Practic6 min

3.5.5. Practice5 min

3.5.6. Practice7 min

3.5.7. Practice7 min

3.6.1. Improper Integrals4 min

3.6.2. Example: Improper Type 13 min

3.6.3. Example: Improper Type 23 min

3.6.4. Practice (type 1)2 min

3.6.5. Practice (type 1)5 min

3.6.6. Practice (Type 2)5 min

3.7.1. Comparison Theorem for Improper Integrals3 min

3.7.2. Practice (type 1 - converges)3 min

3.7.3. Practice (type 2 - converges)4 min

3.7.4. Practice (type 2 - diverges)

3.Q. Improper Integral Quiz4 Qns

4. Chapter 8: Further Applications of Integration

43min

4.1.1. Arc Length41 sec

4.1.2. Example3 min

4.1.3. Practice4 min

4.2.1. Surface Area of Revolution1 min

4.2.2. Example5 min

4.2.3. Practice

4.3.1. Position, Velocity, and Acceleration1 min

4.3.2. Example2 min

4.3.3. Example4 min

4.3.4. Practice3 min

4.4.1. Mass and Density60 sec

4.4.2. Example3 min

4.4.3. Practice

4.5.1. Center of Mass2 min

4.5.2. Example4 min

4.5.3. Practice3 min

4.6.1. Pressure and Force1 min

4.6.3. Practice3 min

5. Chapter 11: Sequences, Series, & Power Series

5hr

5.1.1. Sequences8 min

5.1.2. Series7 min

5.1.3. Practice (Partial sums)2 min

5.1.4. Practice (Geometric series)2 min

5.1.5. Practice (Geometric series)3 min

5.1.6. Practice: Series Application6 min

5.1.7. How to Test if a Series Converges?

5.2.1. Test of Divergence (nth Term Limit Test)2 min

5.2.2. Practice2 min

5.2.3. Practice1 min

5.2.4. Practice3 min

5.2.5. Practice3 min

5.3.1. Integral Test1 min

5.3.2. Example: Integral Test4 min

5.3.3. Example: Integral Test5 min

5.3.4. Practice: Integral Test6 min

5.3.5. Practice: Integral Test5 min

5.4.1. Series and Limit Comparison Tests5 min

5.4.2. Example: Limit Comparison Test3 min

5.4.3. Example: Limit Comparison Test3 min

5.4.4. Practice (limit comparison test)2 min

5.4.5. Practice (limit comparison test)3 min

5.4.6. Practice (telescoping series*)6 min

5.4.7. Practice (series comparison test)5 min

5.4.8. Practice (series comparison test)2 min

5.4.9. Practice (telescoping series*)3 min

5.5.1. Absolute Convergence Test3 min

5.5.2. Example: Absolute Convergence Test5 min

5.5.3. Practice5 min

5.5.4. Alternating Series Test2 min

5.5.5. Example: Alternating series and conditional convergence50 sec

5.5.6. Example: Alternating series and conditional convergence42 sec

5.5.7. Practice: AST5 min

5.6.1. Ratio Test2 min

5.6.2. Example: Ratio Test6 min

5.6.3. Example: Ratio Test5 min

5.6.4. Practice5 min

5.6.5. Practice2 min

5.6.6. Practice (recursive series*)4 min

5.7.1. Root Test1 min

5.7.2. Example: Root Test2 min

5.7.3. Example: Root Test2 min

5.7.4. Example: Root Test3 min

5.7.5. Practice3 min

5.7.6. Practice: Root Test4 min

5.8.1. How to Pick Which Convergence Test to Use?6 min

5.9.1. Definitions of Power Series9 min

5.9.2. Example: Radius of Convergence5 min

5.9.3. Example: Interval of Convergence10 min

5.9.4. Practice (radius of convergence)2 min

5.9.5. Practice (radius & interval of convergence)7 min

5.9.6. Practice: Radius & Interval of Convergence4 min

5.10.1. Representing Functions as Power Series2 min

5.10.2. Example: Power Series Representation5 min

5.10.3. Practice2 min

5.10.4. Practice2 min

5.10.5. Practice (w/ partial fractions)7 min

5.10.6. Differentiation and Integration of Power Series3 min

5.10.7. Example: Differentiating a Power Series3 min

5.10.8. Example: Integrating a Power Series4 min

5.10.9. Practice (differentiating power series)4 min

5.10.10. Practice (integrating power series)4 min

5.10.11. Practice (integrating power series*)8 min

5.11.1. Taylor and Maclaurin Series6 min

5.11.2. Example: Taylor Series7 min

5.11.3. Practice (Taylor series)7 min

5.11.4. Common Maclaurin Series (Memorize!)*5 min

5.11.5. Example: Maclaurin Series4 min

5.11.6. Practice (Maclaurin series)2 min

5.11.7. Practice (Maclaurin series)3 min

5.11.8. Practice (Maclaurin series of an integral)2 min

5.11.9. Practice (evaluating a series*)3 min

5.Q. Sequences and Series Quiz13 Qns

Mock Exams

ME.1. Midterm Exam - Mock Assessment10 Qns

ME.2. Final Exam - Mock Assessment27 Qns

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