MATH 16A

UCBerkeley

Course Overview

Lessons & Practice

I. Welcome

1. Slopes & Equations of Lines

3hr

1.1.1. Equation of a Line4 min

1.1.2. Horizontal & Vertical Lines4 min

1.1.3. Practice2 min

1.1.4. Slope of a Line8 min

1.1.5. Practice Level 12 min

1.1.6. Finding the Slope of a Line8 min

1.1.7. Practice Level 24 min

1.1.8. Example4 min

1.1.9. Practice Level 33 min

1.2.1. Different Forms of the Equation of a Line4 min

1.2.2. Example9 min

1.2.3. Practice Level 213 min

1.2.4. Practice Level 34 min

1.3.1. Graphing Linear Equations - Table of Values3 min

1.3.2. Graphing Linear Equations - Slope y-Intercept Form5 min

1.3.3. Practice6 min

1.3.4. Graphing Linear Equations - Using Intercepts4 min

1.3.5. Practice5 min

1.3.6. Practice4 min

1.4.1. Parallel & Perpendicular Lines7 min

1.4.2. Practice Level 25 min

1.4.3. Practice Level 24 min

1.5.1. Finding the Equation of a Line4 min

1.5.2. Practice Level 27 min

1.5.3. Practice Level 35 min

1.6.1. Function Notation7 min

1.6.2. Example3 min

1.6.3. Practice (Level 1)2 min

1.6.4. Practice (Level 2)1 min

1.6.5. Practice (Level 3)4 min

1.7.3. Practice

1.7.4. Market Equilibrium1 min

1.7.5. Example: Equilibrium with a Table

1.7.6. Practice: Equilibrium with Equations

1.8.1. Linear Cost Function & Break-Even Analysis

1.9.1. Scatterplots5 min

1.9.2. Practice

1.10.1. Solving for the Regression Line (Least Squares Method)2 min

1.10.2. Example5 min

1.10.3. Practice5 min

1.11.1. Correlation5 min

1.11.2. Practice

1.11.3. Solving for Correlation2 min

1.11.4. Example6 min

1.11.5. Practice4 min

1.11.6. Example3 min

1.11.7. Practice

2. Properties of Functions

4hr

2.1.1. Domain2 min

2.1.2. Range2 min

2.1.3. Example2 min

2.1.4. Practice 40 sec

2.1.5. Practice 3 min

2.2.1. Even and Odd Functions3 min

2.2.2. Example2 min

2.3.1. Quadratic Relations13 min

2.3.2. Example7 min

2.3.3. Practice Level 15 min

2.3.4. Practice Level 25 min

2.3.5. Practice Level 37 min

2.4.1. Factoring Simple Trinomials

y=x^2+bx+c

2.4.2. Example11 min

2.4.3. Practice Level 25 min

2.4.4. Factoring Harder Trinomials

y=ax^2+bx+c

2.4.5. Example5 min

2.4.6. Practice Level 22 min

2.4.7. Practice Level 38 min

2.5.1. Completing the Square (

x^2+bx+c

2.5.2. Example4 min

2.5.3. Practice Level 15 min

2.5.4. Completing the Square (

ax^2+bx+c

2.5.5. Example4 min

2.5.6. Practice Level 14 min

2.5.7. Practice Level 37 min

2.6.1. Quadratic Formula7 min

2.6.2. Example6 min

2.6.3. Practice Level 14 min

2.6.4. Practice Level 23 min

2.6.5. Practice Level 33 min

2.7.1. Vertical Stretches and Reflections7 min

2.7.2. Translations7 min

2.7.3. Example2 min

2.7.4. Practice3 min

2.7.5. Graphing Quadratics in Vertex Form3 min

2.7.6. Example5 min

2.7.7. Practice Level 25 min

2.7.8. Practice Level 33 min

2.8.1. Basic of Polynomials4 min

2.8.2. Example2 min

2.8.3. Practice3 min

2.8.4. Polynomial Graphs & Characteristics4 min

2.8.5. Example2 min

2.8.6. Practice2 min

2.9.1. Rational Functions4 min

2.9.2. Solving Rational Equations3 min

2.9.3. Example5 min

2.9.4. Example3 min

2.9.5. Practice6 min

2.9.6. Practice2 min

2.10.1. Exponential Functions3 min

2.10.2. Example1 min

2.10.3. Example2 min

2.11.1. Logarithmic Functions4 min

2.11.2. Example3 min

2.11.3. Example:3 min

2.11.4. Practice2 min

2.12.1. Trigonometric Functions6 min

2.12.2. Example4 min

2.12.3. Trig Identities2 min

2.12.4. Practice3 min

2.12.5. Practice4 min

3. The Derivatives

1.3hr

3.1.1. Limit Basics2 min

3.1.2. Example1 min

3.1.3. Limit Laws 2 min

3.1.4. Practice1 min

3.1.5. One-Sided Limits2 min

3.1.6. Example: One-Sided Limit2 min

3.1.7. Practice: One-Sided Limits3 min

3.2.1. Infinite Limits2 min

3.2.2. Example1 min

3.2.3. Example3 min

3.3.1. Limits at Infinity3 min

3.3.2. Example60 sec

3.3.3. Example3 min

3.3.4. Example4 min

3.3.5. Practice 3 min

3.3.6. Practice3 min

3.4.1. Indeterminate Forms50 sec

3.4.2. Computing Limits by Factoring1 min

3.4.3. Example1 min

3.4.4. Practice2 min

3.4.5. Computing Limits by Getting a Common Denominator1 min

3.4.6. Example2 min

3.4.7. Practice4 min

3.4.8. Computing Limits by Multiplying by the Conjugate3 min

3.4.9. Example3 min

3.4.10. Practice3 min

3.5.1. Continuity2 min

3.5.2. Example2 min

3.5.3. Practice4 min

3.6.1. Derivatives as a Rate of Change2 min

3.6.2. Average Rate of Change46 sec

3.6.3. Example2 min

3.6.4. Practice1 min

3.7.1. The Limit Definition of a Derivative2 min

3.7.2. Example3 min

3.7.3. Practice5 min

3.7.4. When is Function Not Differentiable?

4. Calculating the Derivative

57min

4.1.1. Differentiation Laws51 sec

4.1.2. The Power Rule1 min

4.1.3. Example2 min

4.1.4. Practice51 sec

4.2.1. The Product Rule49 sec

4.2.2. Example2 min

4.2.3. Example2 min

4.2.4. Practice2 min

4.2.5. The Quotient Rule1 min

4.2.6. Example2 min

4.2.7. Practice4 min

4.3.1. The Chain Rule1 min

4.3.2. Example2 min

4.3.3. Practice3 min

4.4.1. Derivatives of Exponential Functions1 min

4.4.2. Example52 sec

4.4.3. Example3 min

4.4.4. Practice1 min

4.5.1. Derivatives of Logarithmic Functions1 min

4.5.2. Example56 sec

4.5.3. Example2 min

4.5.4. Practice2 min

4.5.5. Practice: Log and Ln2 min

4.6.1. Derivatives of Trigonometric Functions1 min

4.6.2. Example39 sec

4.6.3. Example3 min

4.6.4. Example1 min

4.6.5. Practice3 min

4.6.6. Practice2 min

4.7.1. Tangent Lines1 min

4.7.2. Example3 min

4.7.3. Practice2 min

5. L'Hospital's Rule

20min

5.1.1. L’Hopital’s Rule2 min

5.1.2. Example2 min

5.1.3. Practice5 min

5.2.1. Solving General Indeterminate Forms2 min

5.2.2. Example2 min

5.2.3. Practice5 min

5.2.4. Practice2 min

8. Integration

1.7hr

8.1.1. Antiderivatives (Indefinite Integral)3 min

8.1.2. Example2 min

8.1.3. Practice1 min

8.1.4. Practice1 min

8.1.5. Practice1 min

8.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

8.2.2. Example1 min

8.2.3. Practice1 min

8.2.4. Practice1 min

8.3.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

8.3.2. Example42 sec

8.3.3. Practice1 min

8.3.4. Practice2 min

8.4.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

8.4.2. Example2 min

8.4.3. Practice1 min

8.5.1. Approximating Areas & Riemann Sums 3 min

8.5.2. Example4 min

8.5.3. Practice3 min

8.6.1. The Definite Integrals & Area Under a Curve2 min

8.6.2. Example7 min

8.6.3. Practice2 min

8.6.4. Practice12 min

8.7.1. Fundamental Theorem of Calculus - Part 21 min

8.7.2. Example2 min

8.7.4. Practice 4 min

8.7.5. Practice3 min

8.7.6. Practice1 min

8.8.1. Properties of the Definite Integral2 min

8.8.2. Practice2 min

8.8.3. Practice2 min

8.9.1. Area between curves1 min

8.9.2. Example5 min

8.9.3. Example5 min

8.9.4. Practice

8.10.1. Integration by Substitution2 min

8.10.2. Example4 min

8.10.3. Example3 min

8.10.4. Practice

8.10.5. Practice

8.10.6. Practice

9. Differential Equations

1.2hr

9.1.1. Differential Equations8 min

9.1.2. Direction Fields/Slope Fields5 min

9.1.3. Practice Question: DE Solution Graphs3 min

9.2.1. Separable First Order Differential Equations3 min

9.2.2. Practice (separable DE)2 min

9.2.3. Practice (IVP)3 min

9.2.4. Practice (IVP)3 min

9.2.5. Practice (IVP*)5 min

9.2.6. Practice (separable DE)1 min

9.3.1. Linear First Order Differential Equations7 min

9.3.2. Practice (integrating factor)1 min

9.3.3. Practice (linear DE)3 min

9.3.4. Practice (IVP)3 min

9.3.5. Practice (IVP)4 min

9.4.1. Exponential Growth and Decay3 min

9.4.2. Example4 min

9.4.3. Example5 min

9.4.4. Practice5 min

9.4.5. Practice (population)3 min

9.4.6. Practice (population)4 min

9.5.1. Second-Order Reducible DE

9.5.2. Practice: Dependent Variable Missing

9.5.3. Practice: Independent Variable Missing

9.Q. DE Quiz4 Qns

I Welcome

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Welcome to Wize's Analytic Geometry & Calculus Course!
This course covers most of the concepts you will learn in MATH 16A. 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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