MATH 16B

UCBerkeley

Course Overview

Lessons & Practice

I. Welcome

1. Review: Derivatives

1.3hr

1.1.1. Interpretation of Derivatives8 min

1.1.2. Practice: Definition of Derivative6 min

1.1.3. Practice: Differentiability4 min

1.2.1. Derivative Rules7 min

1.2.2. Example: Derivative Rules4 min

1.2.3. Product, Quotient, and Chain Rule4 min

1.2.4. Example: Product, Quotient, and Chain Rule8 min

1.2.5. Practice: Finding a Derivative4 min

1.2.6. Practice: Finding a Derivative4 min

1.2.7. Practice: Higher Order Derivative6 min

1.2.8. Practice: Product Rule*6 min

1.2.9. Practice: Chain Rule*6 min

1.3.1. Tangent and Normal Lines4 min

1.3.2. Practice: Equation of Tangent Line

1.3.3. Practice: Slope of a Normal Line3 min

1.4.1. Implicit Differentiation1 min

1.4.2. Practice: Implicit differentiation4 min

2. Review: Integration

1.1hr

2.I. What is Integration?

2.1.1. Antiderivatives & Indefinite Integrals6 min

2.1.2. Practice1 min

2.1.3. Practice1 min

2.1.4. Practice (initial condition)2 min

2.2.1. Riemann Sums7 min

2.2.2. Practice (left/right sums)2 min

2.2.3. Practice (area)3 min

2.2.4. Practice (area) *Tricky3 min

2.3.1. Definite Integrals 3 min

2.3.2. Practice1 min

2.3.3. Practice *Tricky3 min

2.3.4. Properties of Definite Integrals5 min

2.3.5. Practice1 min

2.4.1. Fundamental Theorem of Calculus 23 min

2.4.2. Practice2 min

2.4.3. Practice1 min

2.4.4. Practice (absolute values)3 min

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

2.5.2. Practice2 min

2.5.3. Practice3 min

2.5.4. Practice (definite integral)3 min

2.5.5. Short-Cut for U-Substitution3 min

2.Q. Integration Quiz18 Qns

3. Further Techniques of Integration & Applications

46min

3.1.1. Integration by Parts3 min

3.1.2. Example5 min

3.1.3. Example3 min

3.1.4. Example6 min

3.1.5. Practice

3.1.6. Practice

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

3.2.2. Example4 min

3.2.3. Example3 min

3.2.4. Practice

3.2.5. Practice

3.3.1. Average Value of a Function47 sec

3.3.2. Example2 min

3.3.3. Practice2 min

3.4.1. Improper Integrals4 min

3.4.2. Practice (type 1)2 min

3.4.3. Practice (type 1)5 min

3.4.4. Practice (Type 2)5 min

4. Multivariable Calculus

31min

4.1.1. Functions of Several Variables5 min

4.1.2. Practice3 min

4.2.1. Partial derivatives6 min

4.2.2. Practice: First Partial derivatives2 min

4.2.3. Practice: Second Partial Derivatives3 min

4.3.1. Local Max & Min4 min

4.3.2. Absolute Max & Min5 min

4.3.3. Lagrange Multipliers3 min

4.3.4. Practice: Lagrange Multipliers

4.3.5. Practice: Lagrange Multipliers

4.4.1. Double Integration (rectangular)

4.4.2. Practice: Double integration

4.4.3. Practice: Changing the order of integration

4.4.4. Practice: Changing the order of integration

4.4.5. Interpretation of a Double Integral

4.4.6. Practice: Volume under a surface

5. Differential Equations

1.2hr

5.1.1. Differential Equations8 min

5.1.2. Practice Question: DE Solution Graphs3 min

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

5.1.4. Practice

5.2.1. Separable First Order Differential Equations3 min

5.2.2. Practice (separable DE)2 min

5.2.3. Practice (IVP)3 min

5.2.4. Practice (IVP)3 min

5.2.5. Practice (IVP*)5 min

5.2.6. Practice (separable DE)1 min

5.3.1. Linear First Order Differential Equations7 min

5.3.2. Practice (integrating factor)1 min

5.3.3. Practice (linear DE)3 min

5.3.4. Practice (IVP)3 min

5.3.5. Practice (IVP)4 min

5.4.1. Common DE Applications (Word Problems)

5.4.2. Practice (population)3 min

5.4.3. Practice (population)4 min

5.4.4. Practice (cooling & heating)3 min

5.4.5. Practice (mixing tank)6 min

5.4.6. Practice (mixing tank)8 min

6. Probability & Calculus

1.5hr

6.1.1. Distribution Functions4 min

6.1.2. Practice: PDF3 min

6.1.3. Practice: CDF2 min

6.2.1. Mean, Median, and Variance3 min

6.2.2. Practice2 min

6.2.3. Practice: Median1 min

6.3.1. Uniform Distribution1 min

6.3.2. Practice3 min

6.3.3. Exponential Experiment3 min

6.3.4. Exponential Distribution7 min

6.3.5. Practice7 min

6.3.6. Normal Distribution11 min

6.3.7. Practice5 min

6.3.8. Standard Normal Distribution (Z-Scores)11 min

6.3.9. Standardizing a Normal Random Variable4 min

6.3.10. Example10 min

6.3.11. Practice6 min

6.3.12. Practice3 min

7. Sequences & Series

1.9hr

7.1.1. Geometric Sequences8 min

7.1.2. Example3 min

7.1.3. Practice Level 13 min

7.1.4. Practice Level 24 min

7.1.5. Practice Level 37 min

7.1.6. Summary - Geometric Sequence

7.2.1. Geometric Series6 min

7.2.2. Example5 min

7.2.3. Practice Level 13 min

7.2.4. Practice Level 27 min

7.2.5. Practice Level 34 min

7.2.6. Summary - Geometric Series

7.3.1. Investments and Loans with Regular Payments8 min

7.3.2. Example5 min

7.3.3. Example5 min

7.3.4. Practice Level 14 min

7.3.5. Practice Level 1 (Spreadsheets)

7.3.6. Practice Level 24 min

7.3.7. Practice Level 38 min

7.4.1. Series7 min

7.4.2. Practice (Partial sums)2 min

7.4.3. Practice (Geometric series)2 min

7.4.4. Practice (Geometric series)3 min

7.4.5. Practice: Series Application6 min

7.4.6. How to Test if a Series Converges?

7.5.1. Newton's Method1 min

7.5.3. Example4 min

7.5.4. Practice

7.5.5. Practice2 min

8. Differential Equations

1.2hr

8.1.1. Differential Equations8 min

8.1.2. Direction Fields/Slope Fields5 min

8.1.3. Practice Question: DE Solution Graphs3 min

8.2.1. Separable First Order Differential Equations3 min

8.2.2. Practice (separable DE)2 min

8.2.3. Practice (IVP)3 min

8.2.4. Practice (IVP)3 min

8.2.5. Practice (IVP*)5 min

8.2.6. Practice (separable DE)1 min

8.3.1. Linear First Order Differential Equations7 min

8.3.2. Practice (integrating factor)1 min

8.3.3. Practice (linear DE)3 min

8.3.4. Practice (IVP)3 min

8.3.5. Practice (IVP)4 min

8.4.1. Exponential Growth and Decay3 min

8.4.2. Example4 min

8.4.3. Example5 min

8.4.4. Practice5 min

8.4.5. Practice (population)3 min

8.4.6. Practice (population)4 min

8.5.1. Second-Order Reducible DE

8.5.2. Practice: Dependent Variable Missing

8.5.3. Practice: Independent Variable Missing

8.Q. DE Quiz4 Qns

I Welcome

Free Activity

Welcome to Wize's Analytic Geometry & Calculus Course!
This course covers most of the concepts you will learn in MATH 16B. Feel free to go through the video tutorials and practice questions as your own pace, and let me know if you have any questions.

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