MAT 266

ASU

Course Overview

Lessons & Practice

I. Welcome

1. Review: Antiderivatives [4.7]

40min

1.1.1. Antiderivatives (Indefinite Integral)3 min

1.1.2. Example2 min

1.1.3. Practice1 min

1.1.4. Practice1 min

1.1.5. Practice1 min

1.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

1.2.2. Example1 min

1.2.3. Practice1 min

1.2.4. Practice1 min

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

1.3.2. Example1 min

1.3.3. Practice1 min

1.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

1.4.2. Example42 sec

1.4.3. Practice1 min

1.4.4. Practice2 min

1.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

1.5.2. Example2 min

1.5.3. Practice1 min

1.6.1. Initial Conditions2 min

1.6.2. Example2 min

1.6.3. Practice5 min

2. Review: Definite and Indefinite Integrals [5.1-5.4]

1.5hr

2.1.1. Finite Sums & Summation Notation3 min

2.1.2. Example5 min

2.1.3. Practice4 min

2.1.4. Practice4 min

2.2.1. Approximating Areas & Riemann Sums 3 min

2.2.2. Example4 min

2.2.3. Practice3 min

2.3.1. The Definite Integrals & Area Under a Curve2 min

2.3.2. Example7 min

2.3.3. Practice2 min

2.3.4. Practice12 min

2.4.1. Properties of the Definite Integral2 min

2.4.2. Practice2 min

2.4.3. Practice2 min

2.5.1. Fundamental Theorem of Calculus - Part 21 min

2.5.2. Example2 min

2.5.4. Practice 4 min

2.5.5. Practice3 min

2.5.6. Practice1 min

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

2.6.2. Example6 min

2.6.3. Practice

2.6.4. Practice

2.7.1. Fundamental Theorem of Calculus - Part I2 min

2.7.2. Example1 min

2.7.3. Example48 sec

2.7.4. Practice1 min

2.7.5. Practice2 min

2.8.1. Average Value of a Function47 sec

2.8.2. Example2 min

2.8.3. Practice2 min

3. Substitution, Integration by Parts [5.5, 6.1]

39min

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

3.1.2. Practice2 min

3.1.3. Practice3 min

3.1.4. Practice (definite integral)3 min

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

3.1.6. Short-Cut for U-Substitution3 min

3.2.1. Integration by Parts6 min

3.2.2. Practice4 min

3.2.3. Practice (w/

\ln

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

4. Trig Integrals & Substitution [6.2]

1.1hr

4.1.1. Trigonometric Integrals3 min

4.1.2. Practice (odd power of

\cos x

4.1.3. Practice (odd power of

\sin x

4.1.4. Practice (even powers of

\sin x

\cos x

4.1.5. Practice (even power of

\sec x

4.1.6. Practice (w/

\sec x \tan x

4.1.7. Practice (

\sin (mx)

\sin(nx)

4.1.8. Practice (special case

\sec x

4.1.9. Practice (special case

\sec^3x

4.1.10. Reduction Formula2 min

4.1.11. Practice5 min

4.1.12. Practice3 min

4.2.1. Trigonometric Substitution10 min

4.2.2. Practice6 min

4.2.3. Practice5 min

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

5. Partial Fractions [ 6.3]

24min

5.1.1. Partial Fractions Decomposition7 min

5.1.2. Practice (linear factors only)4 min

5.1.3. Practice (w/ quadratic factors)7 min

5.1.4. Practice (w/ long division)6 min

6. Summary: All Integration Techniques [5.5, 6.1-6.3]

37min

6.1.1. Strategies for Integration3 min

6.1.2. Practice (rationalizing substitution)4 min

6.1.3. Practice: Mixed Integrals4 min

6.1.4. Practic6 min

6.1.5. Practice5 min

6.1.6. Practice7 min

6.1.7. Practice7 min

6.Q. Integration Techniques Quiz18 Qns

7. Numerical Integration, Improper Integrals [6.5-6.6]

38min

7.1.1. The Midpoint Rule1 min

7.1.2. Example2 min

7.1.3. The Trapezoid Rule 1 min

7.1.4. Example2 min

7.1.5. Practice

7.1.6. Simpson's Rule1 min

7.1.7. Example2 min

7.1.8. Practice

7.1.9. Error Bounds for Approximations2 min

7.1.10. Practice

7.1.11. Numerical Integration (Summary)

7.2.1. Improper Integrals4 min

7.2.2. Practice (type 1)2 min

7.2.3. Practice (type 1)5 min

7.2.4. Practice (Type 2)5 min

7.3.1. Comparison Theorem for Improper Integrals3 min

7.3.2. Practice (type 1 - converges)3 min

7.3.3. Practice (type 2 - converges)4 min

7.3.4. Practice (type 2 - diverges)

8. Area Between Curves [7.1]

15min

8.1.1. Area between Curves3 min

8.1.2. Practice4 min

8.1.3. Practice3 min

8.1.4. Practice (multiple regions)4 min

9. Volumes (Slicking, Disks, Washers, Shells) [7.2-7.3]

28min

9.1.1. Volumes - Cross Sections Method3 min

9.1.2. Practice4 min

9.1.3. Practice3 min

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

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

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

9.2.4. Practice (around a line)3 min

9.3.1. Volumes of Revolution (Cylindrical Shells)4 min

9.3.2. Practice2 min

10. Arc Length, Work [7.4, 7.6]

37min

10.1.1. Arc Length of a Curve3 min

10.1.2. Practice6 min

10.1.3. Practice4 min

10.2.1. Work2 min

10.2.2. Example3 min

10.2.3. Practice

10.3.1. Pressure and Force1 min

10.3.2. Example

10.3.3. Practice3 min

10.4.1. Mass and Density60 sec

10.4.2. Example3 min

10.4.3. Practice

10.5.1. Center of Mass2 min

10.5.2. Example4 min

10.5.3. Practice3 min

11. Sequences, Series [8.1, 8.2]

39min

11.1.1. Sequences8 min

11.1.2. Series7 min

11.1.3. Practice (Partial sums)2 min

11.1.4. Practice (Geometric series)2 min

11.1.5. Practice (Geometric series)3 min

11.1.6. Practice: Series Application6 min

11.1.7. How to Test if a Series Converges?

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

11.2.2. Practice2 min

11.2.3. Practice1 min

11.2.4. Practice3 min

11.2.5. Practice3 min

12. Convergence Tests [8.3-8.4]

1.3hr

12.1.1. Integral Test1 min

12.1.2. Practice: Integral Test6 min

12.1.3. Practice: Integral Test5 min

12.2.1. Series and Limit Comparison Tests5 min

12.2.2. Practice (limit comparison test)2 min

12.2.3. Practice (limit comparison test)3 min

12.2.4. Practice (telescoping series*)6 min

12.2.5. Practice (series comparison test)5 min

12.2.6. Practice (series comparison test)2 min

12.2.7. Practice (telescoping series*)3 min

12.3.1. Absolute Convergence Test3 min

12.3.2. Practice5 min

12.3.3. Alternating Series Test2 min

12.3.4. Practice: AST5 min

12.4.1. Ratio Test2 min

12.4.2. Practice5 min

12.4.3. Practice2 min

12.4.4. Practice (recursive series*)4 min

12.5.1. Root Test1 min

12.5.2. Practice3 min

12.5.3. Practice: Root Test4 min

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

12.Q. Sequences and Series Quiz13 Qns

13. Power Series, Rep. Functions as Power Series, Taylor & Maclaurin Series [8.5-8.7]

1.4hr

13.1.1. Definitions of Power Series9 min

13.1.2. Practice (radius of convergence)2 min

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

13.1.4. Practice: Radius & Interval of Convergence4 min

13.2.1. Representing Functions as Power Series2 min

13.2.2. Practice2 min

13.2.3. Practice2 min

13.2.4. Practice (w/ partial fractions)7 min

13.2.5. Differentiation and Integration of Power Series3 min

13.2.6. Practice (differentiating power series)4 min

13.2.7. Practice (integrating power series)4 min

13.2.8. Practice (integrating power series*)8 min

13.3.1. Taylor and Maclaurin Series6 min

13.3.2. Practice (Taylor series)7 min

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

13.3.4. Practice (Maclaurin series)2 min

13.3.5. Practice (Maclaurin series)3 min

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

13.3.7. Practice (evaluating a series*)3 min

13.Q. Power Series Quiz10 Qns

14. Parametric & Polar Curves [9.1-9.4]

1.8hr

14.1.1. Parametric Curves6 min

14.1.2. Practice (Cartesian equations)2 min

14.1.3. Practice (graphs)4 min

14.1.4. Practice (graphs)3 min

14.2.1. Tangents/Derivatives of Parametric Curves2 min

14.2.2. Practice (derivatives)2 min

14.2.3. Practice (horizontal/vertical tangents)5 min

14.2.4. Practice (horizontal/vertical tangents*)6 min

14.2.5. Arc Length, Area, and Surface Area2 min

14.2.6. Practice (arc length)3 min

14.2.7. Practice (area)3 min

14.2.8. Practice (surface area)6 min

14.2.9. Practice (surface area)5 min

14.3.1. Polar Coordinates7 min

14.3.2. Graphing Polar Curves6 min

14.3.3. Practice (graphs)6 min

14.3.4. Practice (polar coordinates)2 min

14.3.5. Practice (matching graphs)4 min

14.4.1. Tangents/Derivatives of Polar Curves2 min

14.4.2. Practice (derivative)4 min

14.4.3. Practice (horizontal/vertical tangents)7 min

14.4.4. Arc Length, Area Under & Between Curves2 min

14.4.5. Practice (arc length)3 min

14.4.6. Practice (area inside curve)2 min

14.4.7. Practice (area inside curve)4 min

14.4.8. Practice (area between curves)8 min

14.Q. Parametric and polar curves Quiz6 Qns

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