MATH 138

UWaterloo

Course Overview

Lessons & Practice

I. Welcome

1. Integration

1.6hr

1.I. What is Integration?

1.1.1. Review: Sigma Notation6 min

1.1.2. Practice (index

i\neq1

1.1.3. Practice (w/ limits)3 min

1.1.4. Practice (telescoping sum)2 min

1.1.5. Riemann Sums7 min

1.1.6. Practice (left/right sums)2 min

1.1.7. Practice (area)3 min

1.1.8. Practice (area) *Tricky3 min

1.2.1. Definite Integrals 3 min

1.2.2. Practice1 min

1.2.3. Practice *Tricky3 min

1.2.4. Properties of Definite Integrals5 min

1.2.5. Practice1 min

1.3.1. Antiderivatives & Indefinite Integrals6 min

1.3.2. Practice1 min

1.3.3. Practice1 min

1.3.4. Practice (initial condition)2 min

1.4.1. Average value of a function3 min

1.4.2. Example2 min

1.4.3. Practice2 min

1.5.1. Fundamental Theorem of Calculus 13 min

1.5.2. Practice2 min

1.5.3. Practice (w/ limit)2 min

1.5.4. Fundamental Theorem of Calculus 23 min

1.5.5. Practice2 min

1.5.6. Practice1 min

1.5.7. Practice (absolute values)3 min

1.6.1. U-Substitution (Integration by Substitution)6 min

1.6.2. Practice2 min

1.6.3. Practice3 min

1.6.4. Practice (definite integral)3 min

1.6.5. Practice (w/ back-sub)4 min

1.6.6. Short-Cut for U-Substitution3 min

1.Q. Integration Quiz18 Qns

2. Integration Techniques

2.8hr

2.1.1. Trigonometric Integrals3 min

2.1.2. Practice (odd power of

\cos x

2.1.3. Practice (odd power of

\sin x

2.1.4. Practice (even powers of

\sin x

\cos x

2.1.5. Practice (even power of

\sec x

2.1.6. Practice (w/

\sec x \tan x

2.1.7. Practice (

\sin (mx)

\sin(nx)

2.1.8. Practice (special case

\sec x

2.1.9. Practice (special case

\sec^3x

2.1.10. Reduction Formula2 min

2.1.11. Practice5 min

2.1.12. Practice3 min

2.2.1. Trigonometric Substitution10 min

2.2.2. Practice6 min

2.2.3. Practice5 min

2.2.4. Practice (w/ completing the square)6 min

2.3.1. Integration by Parts6 min

2.3.2. Practice4 min

2.3.3. Practice (w/

\ln

2.3.4. Practice (w/ exp & trig)6 min

2.4.1. Partial Fractions Decomposition7 min

2.4.2. Practice (linear factors only)4 min

2.4.3. Practice (w/ quadratic factors)7 min

2.4.4. Practice (w/ long division)6 min

2.5.1. Strategies for Integration3 min

2.5.2. Practice (rationalizing substitution)4 min

2.5.3. Practice: Mixed Integrals4 min

2.5.4. Practic6 min

2.5.5. Practice5 min

2.5.6. Practice7 min

2.5.7. Practice7 min

2.6.1. Improper Integrals4 min

2.6.2. Practice (type 1)2 min

2.6.3. Practice (type 1)5 min

2.6.4. Practice (Type 2)5 min

2.7.1. Comparison Theorem for Improper Integrals3 min

2.7.2. Practice (type 1 - converges)3 min

2.7.3. Practice (type 2 - converges)4 min

2.7.4. Practice (type 2 - diverges)

2.Q. Integration Techniques Quiz18 Qns

3. Applications of Integrals

1hr

3.1.1. Area between Curves3 min

3.1.2. Practice4 min

3.1.3. Practice3 min

3.1.4. Practice (multiple regions)4 min

3.2.1. Volumes - Cross Sections Method3 min

3.2.2. Practice4 min

3.2.3. Practice3 min

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

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

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

3.3.4. Practice (around a line)3 min

3.4.1. Volumes of Revolution (Cylindrical Shells)4 min

3.4.2. Practice2 min

3.5.1. Arc Length of a Curve3 min

3.5.2. Practice6 min

3.5.3. Practice4 min

3.6.1. Surface Area of Revolution1 min

3.6.2. Example5 min

3.6.3. Practice

3.Q. Applications of Integration Quiz7 Qns

4. Differential Equations

1.3hr

4.1.1. Differential Equations8 min

4.1.2. Direction Fields/Slope Fields5 min

4.1.3. Practice Question: DE Solution Graphs3 min

4.1.4. Euler's Method (Approximating Solutions)4 min

4.1.5. Practice

4.2.1. Separable First Order Differential Equations3 min

4.2.2. Practice (separable DE)2 min

4.2.3. Practice (IVP)3 min

4.2.4. Practice (IVP)3 min

4.2.5. Practice (IVP*)5 min

4.2.6. Practice (separable DE)1 min

4.3.1. Linear First Order Differential Equations7 min

4.3.2. Practice (integrating factor)1 min

4.3.3. Practice (linear DE)3 min

4.3.4. Practice (IVP)3 min

4.3.5. Practice (IVP)4 min

4.4.1. Common DE Applications (Word Problems)

4.4.2. Practice (population)3 min

4.4.3. Practice (population)4 min

4.4.4. Practice (cooling & heating)3 min

4.4.5. Practice (mixing tank)6 min

4.4.6. Practice (mixing tank)8 min

4.Q. DE Quiz4 Qns

5. Sequences and Series

2hr

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. Practice: Integral Test6 min

5.3.3. Practice: Integral Test5 min

5.4.1. Series and Limit Comparison Tests5 min

5.4.2. Practice (limit comparison test)2 min

5.4.3. Practice (limit comparison test)3 min

5.4.4. Practice (telescoping series*)6 min

5.4.5. Practice (series comparison test)5 min

5.4.6. Practice (series comparison test)2 min

5.4.7. Practice (telescoping series*)3 min

5.5.1. Absolute Convergence Test3 min

5.5.2. Practice5 min

5.5.3. Alternating Series Test2 min

5.5.4. Practice: AST5 min

5.6.1. Ratio Test2 min

5.6.2. Practice5 min

5.6.3. Practice2 min

5.6.4. Practice (recursive series*)4 min

5.7.1. Root Test1 min

5.7.2. Practice3 min

5.7.3. Practice: Root Test4 min

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

5.Q. Sequences and Series Quiz13 Qns

6. Power Series

1.4hr

6.1.1. Definitions of Power Series9 min

6.1.2. Practice (radius of convergence)2 min

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

6.1.4. Practice: Radius & Interval of Convergence4 min

6.2.1. Representing Functions as Power Series2 min

6.2.2. Practice2 min

6.2.3. Practice2 min

6.2.4. Practice (w/ partial fractions)7 min

6.2.5. Differentiation and Integration of Power Series3 min

6.2.6. Practice (differentiating power series)4 min

6.2.7. Practice (integrating power series)4 min

6.2.8. Practice (integrating power series*)8 min

6.3.1. Taylor and Maclaurin Series6 min

6.3.2. Practice (Taylor series)7 min

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

6.3.4. Practice (Maclaurin series)2 min

6.3.5. Practice (Maclaurin series)3 min

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

6.3.7. Practice (evaluating a series*)3 min

6.Q. Power Series Quiz10 Qns

I Welcome

Free Activity

Welcome to Calculus 2!
My name is Corey and I'm the instructor for this course. Feel free to go through this course at your own pace.
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