MATH 20B

UCSD

Course Overview

Lessons & Practice

I. Welcome

1. Integration

1.3hr

1.1.1. Definite Integrals 3 min

1.1.2. Practice1 min

1.1.3. Practice *Tricky3 min

1.1.4. Properties of Definite Integrals5 min

1.1.5. Practice1 min

1.2.1. Antiderivatives & Indefinite Integrals6 min

1.2.2. Practice1 min

1.2.3. Practice1 min

1.2.4. Practice (initial condition)2 min

1.3.1. Fundamental Theorem of Calculus 13 min

1.3.2. Practice2 min

1.3.3. Practice (w/ limit)2 min

1.3.4. Fundamental Theorem of Calculus 23 min

1.3.5. Practice2 min

1.3.6. Practice1 min

1.3.7. Practice (absolute values)3 min

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

1.4.2. Example6 min

1.4.3. Practice

1.4.4. Practice

1.5.1. Integration by Substitution4 min

1.5.2. Example: Indefinite with Trig2 min

1.5.3. Example: Indefinite with Polynomials2 min

1.5.4. Practice: Definite with Exponential3 min

1.5.5. Example: Indefinite with Roots2 min

1.5.6. Practice: Definite with Roots5 min

1.5.7. Practice: Indefinite with Power3 min

1.5.8. Example: Indefinite with Fraction3 min

1.5.9. Practice: Indefinite with Exponentials2 min

1.5.10. Practice: Indefinite with Trig3 min

2. Applications of Integrals

37min

2.1.1. Area between Curves3 min

2.1.2. Practice4 min

2.1.3. Practice3 min

2.1.4. Practice (multiple regions)4 min

2.2.1. Volumes - Cross Sections Method3 min

2.2.2. Practice4 min

2.2.3. Practice3 min

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

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

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

2.3.4. Practice (around a line)3 min

3. Techniques of Integration

18min

3.1.1. Integration by Parts6 min

3.1.2. Practice4 min

3.1.3. Practice (w/

\ln

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

4. Parametric & Polar Curves

58min

4.1.1. Polar Coordinates7 min

4.1.2. Graphing Polar Curves6 min

4.1.3. Practice (graphs)6 min

4.1.4. Practice (polar coordinates)2 min

4.1.5. Practice (matching graphs)4 min

4.2.1. Tangents/Derivatives of Polar Curves2 min

4.2.2. Practice (derivative)4 min

4.2.3. Practice (horizontal/vertical tangents)7 min

4.2.4. Arc Length, Area Under & Between Curves2 min

4.2.5. Practice (arc length)3 min

4.2.6. Practice (area inside curve)2 min

4.2.7. Practice (area inside curve)4 min

4.2.8. Practice (area between curves)8 min

5. Complex Numbers

1.4hr

5.I. Chapter Overview1 min

5.1.1. Basics of Complex Numbers10 min

5.1.2. Operations With Complex Numbers16 min

5.1.3. Example: Operations With Complex Numbers10 min

5.1.4. Practice: Operations With Complex Numbers

5.2.1. Powers of Complex Numbers3 min

5.2.2. Example: Powers of Complex Numbers6 min

5.2.3. Roots of Complex Numbers9 min

5.2.4. Example: Roots of Complex Numbers9 min

5.2.5. Practice: Powers and Roots of Complex Numbers

5.3.1. Polar Form of Complex Numbers10 min

5.3.2. Example: Polar Form of Complex Numbers12 min

5.3.3. Practice: Polar Form of Complex Numbers

5.3.4. Practice: Polar Form of Complex Numbers

5.Q. Complex Numbers Checkpoint Quiz6 Qns

6. Techniques of Integration Cont.

3hr

6.1.1. Trigonometric Integrals3 min

6.1.2. Practice (odd power of

\cos x

6.1.3. Practice (odd power of

\sin x

6.1.4. Practice (even powers of

\sin x

\cos x

6.1.5. Practice (even power of

\sec x

6.1.6. Practice (w/

\sec x \tan x

6.1.7. Practice (

\sin (mx)

\sin(nx)

6.1.8. Practice (special case

\sec x

6.1.9. Practice (special case

\sec^3x

6.1.10. Reduction Formula2 min

6.1.11. Practice5 min

6.1.12. Practice3 min

6.2.1. Trigonometric Substitution10 min

6.2.2. Practice6 min

6.2.3. Practice5 min

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

6.3.1. Partial Fractions Decomposition7 min

6.3.2. Example: Partial Fraction4 min

6.3.3. Example: Partial Fractions w/ repeated factors (~2019 Test A7, B3)7 min

6.3.4. Example: Partial Fractions w/ Long Division6 min

6.4.1. Partial Fraction Breakdown11 min

6.4.2. Partial Fraction Breakdown45 sec

6.4.3. Partial Fraction Breakdown7 min

6.4.4. Partial Fraction Breakdown25 sec

6.4.5. Partial Fraction Breakdown2 min

6.4.6. Partial Fraction Breakdown2 min

6.4.7. Partial Fraction Breakdown6 min

6.4.8. Partial Fraction Breakdown2 min

6.4.9. Partial Fraction Breakdown (Using Complex Numbers)22 min

6.4.10. Partial Fraction Breakdown5 min

6.4.11. Partial Fraction Breakdown3 min

6.4.12. Partial Fraction Breakdown3 min

6.4.13. Partial Fraction24 min

6.4.14. Partial Fraction8 min

6.4.15. Partial Fractions: Solving for Coefficients

6.5.1. Strategies for integration5 min

7. Improper Integrals

40min

7.1.1. L'Hospital's Rule5 min

7.1.2. Practice2 min

7.1.3. Practice4 min

7.1.4. Practice4 min

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)

7.Q. Improper Integral Quiz4 Qns

8. Sequences and Series

2hr

8.1.1. Sequences8 min

8.1.2. Series7 min

8.1.3. Practice (Partial sums)2 min

8.1.4. Practice (Geometric series)2 min

8.1.5. Practice (Geometric series)3 min

8.1.6. Practice: Series Application6 min

8.1.7. How to Test if a Series Converges?

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

8.2.2. Practice2 min

8.2.3. Practice1 min

8.2.4. Practice3 min

8.2.5. Practice3 min

8.3.1. Integral Test1 min

8.3.2. Practice: Integral Test6 min

8.3.3. Practice: Integral Test5 min

8.4.1. Series and Limit Comparison Tests5 min

8.4.2. Practice (limit comparison test)2 min

8.4.3. Practice (limit comparison test)3 min

8.4.4. Practice (telescoping series*)6 min

8.4.5. Practice (series comparison test)5 min

8.4.6. Practice (series comparison test)2 min

8.4.7. Practice (telescoping series*)3 min

8.5.1. Absolute Convergence Test3 min

8.5.2. Practice5 min

8.5.3. Alternating Series Test2 min

8.5.4. Practice: AST5 min

8.6.1. Ratio Test2 min

8.6.2. Practice5 min

8.6.3. Practice2 min

8.6.4. Practice (recursive series*)4 min

8.7.1. Root Test1 min

8.7.2. Practice3 min

8.7.3. Practice: Root Test4 min

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

8.Q. Sequences and Series Quiz13 Qns

9. Power Series

1.4hr

9.1.1. Definitions of Power Series9 min

9.1.2. Practice (radius of convergence)2 min

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

9.1.4. Practice: Radius & Interval of Convergence4 min

9.2.1. Representing Functions as Power Series2 min

9.2.2. Practice2 min

9.2.3. Practice2 min

9.2.4. Practice (w/ partial fractions)7 min

9.2.5. Differentiation and Integration of Power Series3 min

9.2.6. Practice (differentiating power series)4 min

9.2.7. Practice (integrating power series)4 min

9.2.8. Practice (integrating power series*)8 min

9.3.1. Taylor and Maclaurin Series6 min

9.3.2. Practice (Taylor series)7 min

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

9.3.4. Practice (Maclaurin series)2 min

9.3.5. Practice (Maclaurin series)3 min

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

9.3.7. Practice (evaluating a series*)3 min

9.Q. Power Series Quiz10 Qns

10. Applications of Integration

59min

11. Differential Equations

1.2hr

11.1.1. Differential Equations8 min

11.1.2. Direction Fields/Slope Fields5 min

11.1.3. Practice Question: DE Solution Graphs3 min

11.2.1. Separable First Order Differential Equations3 min

11.2.2. Practice (separable DE)2 min

11.2.3. Practice (IVP)3 min

11.2.4. Practice (IVP)3 min

11.2.5. Practice (IVP*)5 min

11.2.6. Practice (separable DE)1 min

11.3.1. Linear First Order Differential Equations7 min

11.3.2. Practice (integrating factor)1 min

11.3.3. Practice (linear DE)3 min

11.3.4. Practice (IVP)3 min

11.3.5. Practice (IVP)4 min

11.4.1. Exponential Growth and Decay3 min

11.4.2. Example4 min

11.4.3. Example5 min

11.4.4. Practice5 min

11.4.5. Practice (population)3 min

11.4.6. Practice (population)4 min

11.5.1. Second-Order Reducible DE

11.5.2. Practice: Dependent Variable Missing

11.5.3. Practice: Independent Variable Missing

11.Q. DE Quiz4 Qns

I Welcome

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Welcome to Calculus!
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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Answered

Anonymous

What are the conecpts to focus on for midterm 1 at western 

C

Corey M

Instructor

Likely limits and differentiation techniques through the chain rule, but double-check with your instructor to see exactly what will be covered.

Unanswered

L

Layan E

Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.
sin(x)=x2−x, x∈(1,2)

C

Corey M

Instructor

While this isn't quite the place for this question (please refer to the IVT section in the course), and we can't really just solve random problems for you, I can give you a bit of a hint:  You could try moving everything to one side of the equation and treating it like a function, and then see if you can't find function values within your specified range that return a positive value and a negative value (another hint: try the endpoints of your interval first).  If you're able to do that, then the IVT tells us that there should exist a function input between those two points that returns 0 or, in other words, that is a root.

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