What better way to ace the AP exam than to learn from someone who aced it himself? Professor John Zhu brings together education and teaching experience to Educator's AP Calculus AB course. John explains complicated calculus ideas in easy, understandable terms so that any student can succeed on the exam. In addition, all the topics on the test are covered with many extra examples, as well as a full length practice test at the end of the course. Topics include an Overview of Functions, Derivatives, Integrals, Area between Curves, Revolving Solids, and Differential Equations. Professor Zhu received his B.S. in Electrical Engineering from Michigan State, his MBA from Webster University, and has been teaching AP Calculus for over eight years.
| I. Functions |
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Definitions & Properties of Functions |
11:26 |
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Intro |
0:00 | |
| | |
Definition |
0:28 | |
| | |
Properties: Vertical Line Test |
1:32 | |
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| Domain |
1:38 | |
| | |
| Range |
1:59 | |
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| Vertical Line test |
2:19 | |
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| Example 1 |
2:33 | |
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| Example 2 |
3:10 | |
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Properties: Roots or Zeros |
4:04 | |
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| Finding the Root |
4:16 | |
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Properties: Forms |
5:12 | |
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| Graphically |
5:20 | |
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| List |
5:46 | |
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| Equation |
6:11 | |
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| Function |
6:38 | |
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Properties: Odd & Even |
7:12 | |
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| Even Function |
7:14 | |
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| Odd Function |
8:25 | |
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Properties: Increasing & Decreasing |
9:17 | |
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| Increasing Function |
9:22 | |
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| Decreasing Function |
10:21 | |
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Graphing |
13:58 |
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Intro |
0:00 | |
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Manipulating |
0:10 | |
| | |
| A in the Equation |
0:39 | |
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| B in the Equation |
0:44 | |
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| C & D in the Equation |
0:49 | |
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| Negative values |
0:59 | |
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| Example 1 |
1:17 | |
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Example 2 |
1:51 | |
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Example 3: Absolute Value Functions |
3:43 | |
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| Example 4 |
4:57 | |
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Example 5 |
6:17 | |
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Example 6 |
8:02 | |
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Example 7 |
9:10 | |
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Example 8 |
11:02 | |
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Example 9 |
11:47 | |
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Inverse Functions |
6:47 |
| | |
Intro |
0:00 | |
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Inverse |
0:08 | |
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| Definition |
0:18 | |
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| Example: Finding the Inverse |
1:03 | |
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Example 2 |
2:29 | |
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Example 3 |
3:12 | |
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Example 4 |
4:41 | |
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Polynomial Functions |
5:04 |
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Intro |
0:00 | |
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Types of Functions: Polynomials |
0:07 | |
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| No Domain Restrictions |
0:12 | |
| | |
| No Discontinuities |
0:19 | |
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| Degree Test |
0:31 | |
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Types of Functions: Polynomials |
1:17 | |
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| Leading Coefficient Test |
1:33 | |
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| Leading Coefficient Positive, Even Degree |
1:54 | |
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| Leading Coefficient Positive, Odd Degree |
2:13 | |
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| Leading Coefficient Negative Even Degree |
2:34 | |
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| Leading Coefficient Positive, Odd Degree |
2:46 | |
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Examples: Types of Functions: Polynomials |
3:03 | |
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Examples: Types of Functions: Polynomials |
4:18 | |
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Trigonometric Functions |
6:45 |
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Intro |
0:00 | |
| | |
Types of Functions: Trigonometric |
0:05 | |
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| 6 Functions To Be Familiar With |
0:14 | |
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Example 1: SIN |
1:38 | |
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Example 2: COS |
3:22 | |
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Example 3: TAN |
4:38 | |
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Inverse Trigonometric Functions |
5:58 |
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Intro |
0:00 | |
| | |
Types of Functions: Trigonometric- Inverse Trig Functions |
0:07 | |
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Example: Inverse SIN of X |
0:45 | |
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Example: Inverse Function |
2:30 | |
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Example: Inverse TAN of X |
4:42 | |
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Trigonometric Identities |
17:42 |
| | |
Intro |
0:00 | |
| | |
Types of Functions: Trigonometric- Trig Identities |
0:07 | |
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| 4 Identities |
0:24 | |
| | |
| Pythagorean |
0:28 | |
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| Double Angle |
1:10 | |
| | |
| Power Reducing |
1:28 | |
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| Sum or Difference |
1:42 | |
| | |
Couple More Identities |
1:59 | |
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| Negative Angle |
2:04 | |
| | |
| Product to Sum |
2:39 | |
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Example 1: Prove |
3:00 | |
| | |
Example 2: Simplify Expression |
5:02 | |
| | |
Example 3: Prove |
5:56 | |
| | |
Example 4: Prove |
8:02 | |
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Example 5: Prove With TAN |
12:43 | |
| |
Exponential Functions |
5:53 |
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Intro |
0:00 | |
| | |
Types of Functions: Exponentials |
0:07 | |
| | |
| General Form |
0:10 | |
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| Special Exponential Function |
0:17 | |
| | |
Example 1: Using Exponential Properties |
0:46 | |
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Example 2: Using Exponential Properties |
1:58 | |
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Example 3: Using Trig Identities & Exponential Properties |
3:16 | |
| | |
Example 4: Using Exponential Properties |
4:37 | |
| |
Logarithmic Functions |
7:08 |
| | |
Intro |
0:00 | |
| | |
Types of Functions: Logarithmic |
0:06 | |
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| General Form |
0:10 | |
| | |
| 2 Special Logarithmic Func. |
0:19 | |
| | |
| Euler's # / Natural Log |
0:27 | |
| | |
Logarithmic & Exponential Relationship |
0:45 | |
| | |
| Log form |
1:56 | |
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Properties |
2:09 | |
| | |
Example 1: Apply Basic Principle of Log Func. |
3:05 | |
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Example 2: Use Properties |
3:40 | |
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Example 3: Regular Log |
5:16 | |
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Rational Functions |
15:36 |
| | |
Intro |
0:00 | |
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Types of Functions: Rational - Definition |
0:06 | |
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Example 1: Graph Rational Func. |
0:36 | |
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Example 2: Find Asymptotes of Func. |
7:02 | |
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Example 3: Find Asymptotes of Func. |
8:59 | |
| | |
Example 4: Graph Rational Func. |
11:08 | |
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Conic Sections |
14:58 |
| | |
Intro |
0:00 | |
| | |
Types of Conic Sections |
0:06 | |
| | |
| Parabolas |
0:19 | |
| | |
| Circles |
1:36 | |
| | |
| Ellipses |
2:40 | |
| | |
| Hyperbolas |
4:42 | |
| | |
Complete the Square |
6:40 | |
| | |
Example: Conic Sections |
9:08 | |
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Example 2: Conic Sections |
10:59 | |
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Example 3: Graph Conic Sections |
12:21 | |
| II. Limits and Continuity |
| |
Limit Definition & Properties |
7:15 |
| | |
Intro |
0:00 | |
| | |
Definition |
0:06 | |
| | |
| Example: Limit |
0:17 | |
| | |
Properties |
1:13 | |
| | |
| 1st Property |
1:21 | |
| | |
| 2nd Property |
1:34 | |
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| Special Property |
1:51 | |
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Limits |
2:36 | |
| | |
| Explain Example |
2:49 | |
| | |
Limits Example |
4:39 | |
| | |
Limits Example |
5:21 | |
| |
Solving Limits with Algebra |
8:01 |
| | |
Intro |
0:00 | |
| | |
Solving Limits with Algebra |
0:07 | |
| | |
| Example 1: Solve Algebraically |
0:30 | |
| | |
Solving Limits with Algebra, Example 2 |
2:28 | |
| | |
Solving Limits with Algebra, Example 3 |
3:18 | |
| | |
Solving Limits with Algebra, Example 4 |
4:56 | |
| | |
Solving Limits with Algebra, Example 5 |
6:26 | |
| |
Rational Limit Rules |
3:16 |
| | |
Intro |
0:00 | |
| | |
Rational Limit Rules |
0:07 | |
| | |
| Review of Solving Problem Algebraically |
0:08 | |
| | |
| Limit Rules |
0:28 | |
| | |
| Rule 1 |
0:35 | |
| | |
| Rule 2 |
0:40 | |
| | |
| Rule 3 |
0:45 | |
| | |
Rational Limit Rules |
1:02 | |
| | |
| Applying 1st Rule |
1:22 | |
| | |
Rational Limit Rules |
1:50 | |
| | |
| Applying 2nd Rule |
2:09 | |
| | |
Rational Limit Rules |
2:26 | |
| | |
| Applying 3rd Rule |
2:40 | |
| |
One Sided Limits |
9:57 |
| | |
Intro |
0:00 | |
| | |
Types of Limits: One-Sided Limit Rules |
0:06 | |
| | |
| Example |
0:19 | |
| | |
| Applying Same Rule |
0:34 | |
| | |
| Rule to Keep In Mind |
0:52 | |
| | |
Types of Limits: One-Sided Limit Example 1 |
1:12 | |
| | |
| Limit of x² From Negative Side |
2:11 | |
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Types of Limits: One-Sided Limit, Example 2 |
2:27 | |
| | |
Types of Limits: One-Sided Limit, Example 3 |
4:26 | |
| | |
Types of Limits: One-Sided Limit, Example 4 |
5:47 | |
| | |
One-Sided Limit Example: X with Even Degree Polynomial |
7:00 | |
| | |
One-Sided Limit Example: Entire Denominator Squared |
8:09 | |
| |
Special Trigonometric Limits |
8:28 |
| | |
Intro |
0:00 | |
| | |
Types of Limits: Special Trig Limits |
0:07 | |
| | |
| Pre-set Rules |
0:35 | |
| | |
Special Trig Limits, Example 1 |
0:58 | |
| | |
Special Trig Limits, Example 2 |
2:50 | |
| | |
Special Trig Limits, Example 3 |
3:55 | |
| | |
Special Trig Limits, Example 4: With More Degrees |
4:57 | |
| | |
Special Trig Limits, Example 5 |
6:21 | |
| |
Limits & Continuity |
10:14 |
| | |
Intro |
0:00 | |
| | |
Definition |
0:06 | |
| | |
| 3 Rules: f(x) Is Continuous
|
0:21 | |
| | |
Example 1: Finding Continuity |
1:06 | |
| | |
Types of Discontinuity |
2:44 | |
| | |
| Jump |
2:52 | |
| | |
| Point |
3:24 | |
| | |
| Essential (Asymptote) |
3:47 | |
| | |
| Removable |
4:17 | |
| | |
Example 2: Continuity Examples |
4:41 | |
| | |
Example 3: Continuity Examples |
6:13 | |
| | |
Example 4: Locate & Identify Type of Discontinuities |
8:00 | |
| |
Limits: Multiple Choice Practice |
6:16 |
| | |
Intro |
0:00 | |
| | |
Problem 1 |
0:08 | |
| | |
Problem 2 |
1:51 | |
| | |
Problem 3 |
2:54 | |
| | |
Problem 4 |
4:31 | |
| III. Derivatives |
| |
Derivative Definition & Properties |
4:11 |
| | |
Intro |
0:00 | |
| | |
Definition |
0:09 | |
| | |
| Formal Definition |
0:45 | |
| | |
| Difference Quotient |
1:12 | |
| | |
Basic Derivatives |
1:16 | |
| | |
Differentiability |
2:54 | |
| |
Basic Rules of Differentiation |
7:07 |
| | |
Intro |
0:00 | |
| | |
Basic Rules of Differentiation |
0:09 | |
| | |
Constant Rule |
0:14 | |
| | |
Constant Multiple Rule |
1:10 | |
| | |
Addition and Difference Rule |
1:40 | |
| | |
Example 1: Constant Rule |
2:25 | |
| | |
Example 2: Constant Multiple Rule |
3:01 | |
| | |
Example 3: Constant Multiple Rule |
3:35 | |
| | |
Example 4: Constant Rule |
4:34 | |
| | |
Example 5: Constant Multiple Rule |
5:03 | |
| | |
Example 6 |
5:33 | |
| |
Power Rule |
7:14 |
| | |
Intro |
0:00 | |
| | |
Power Rule |
0:07 | |
| | |
| Power Rule Definition |
0:30 | |
| | |
Example 1 |
1:11 | |
| | |
Example 2 |
2:25 | |
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Example 3 |
3:05 | |
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Example 4 |
4:18 | |
| | |
Example 5 |
5:13 | |
| |
Trigonometric Rules |
7:53 |
| | |
Intro |
0:00 | |
| | |
Trigonometric Rules |
0:07 | |
| | |
| COS X |
0:38 | |
| | |
| Find Derivative |
1:02 | |
| | |
Example 1 |
2:46 | |
| | |
Example 2: COS Function |
3:09 | |
| | |
Example 3: Composite Expression |
3:54 | |
| | |
Example 4: Sec Function |
5:02 | |
| | |
Example 5: CSC |
5:33 | |
| | |
Example 6L COT |
6:42 | |
| |
Product Rule |
11:11 |
| | |
Intro |
0:00 | |
| | |
Product Rule |
0:07 | |
| | |
| Definition |
0:20 | |
| | |
| Example 1 |
0:43 | |
| | |
Example 2 |
2:11 | |
| | |
Example 3 |
4:24 | |
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Example 4 |
5:24 | |
| | |
Example 5 |
6:42 | |
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Example 6 |
7:51 | |
| |
Quotient Rule |
16:50 |
| | |
Intro |
0:00 | |
| | |
Quotient Rule |
0:07 | |
| | |
| Definition |
0:30 | |
| | |
| Example 1 |
1:17 | |
| | |
Example 2: With No X In Numerator |
2:49 | |
| | |
Example 3 |
4:30 | |
| | |
Example 4: With Decimals |
6:46 | |
| | |
Example 5 |
8:53 | |
| | |
Example 6: With Trig Functions |
12:55 | |
| |
Chain Rule |
19:48 |
| | |
Intro |
0:00 | |
| | |
Chain Rule |
0:07 | |
| | |
| Definition |
0:17 | |
| | |
| Example 1: Applying the Chain Rule |
1:33 | |
| | |
Example 2 |
4:25 | |
| | |
Example 3 |
6:02 | |
| | |
Example 4 |
9:25 | |
| | |
Example 5 |
12:47 | |
| | |
Example 6 |
15:27 | |
| |
Higher Order Derivatives |
15:00 |
| | |
Intro |
0:00 | |
| | |
Types of Derivatives: Higher Order Derivatives |
0:07 | |
| | |
| 1st Derivative / F Prime |
0:19 | |
| | |
| 2nd Derivative |
0:25 | |
| | |
| 3rd Derivative |
0:32 | |
| | |
| Example 1 |
1:48 | |
| | |
Example 2: Find 3rd Derivative |
3:13 | |
| | |
Example 3: Acceleration |
4:25 | |
| | |
Example 4 |
10:20 | |
| | |
Example 5: 2nd Derivative |
12:11 | |
| |
Derivatives of Exponential Functions |
13:14 |
| | |
Intro |
0:00 | |
| | |
Types of Derivatives: Exponential Functions |
0:08 | |
| | |
| Derivatives: Definition/ Formula |
0:28 | |
| | |
| Example 1 |
1:25 | |
| | |
Example 2 |
2:47 | |
| | |
Example 3 |
4:13 | |
| | |
Example 4 |
7:11 | |
| | |
Example 5 |
9:23 | |
| | |
Example 6 |
11:06 | |
| |
Derivatives of Logarithmic Functions |
11:30 |
| | |
Intro |
0:00 | |
| | |
Types of Derivatives: Logarithmic Functions |
0:06 | |
| | |
| Rule for Logarithmic Functions |
0:28 | |
| | |
| Example 1 |
0:58 | |
| | |
Example 2 |
3:10 | |
| | |
Example 3 |
4:38 | |
| | |
Example 4 |
7:18 | |
| | |
Example 5 |
8:48 | |
| | |
Example 6 |
9:38 | |
| |
Derivatives of Inverse Trigonometric Functions |
16:54 |
| | |
Intro |
0:00 | |
| | |
Types of Derivatives: Inverse Trigonometric Functions |
0:06 | |
| | |
| 6 Fundamental Properties of Inverse Trigonometric Functions |
0:38 | |
| | |
Example 1 |
2:17 | |
| | |
Example 2 |
3:41 | |
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Example 3 |
5:37 | |
| | |
Example 4 |
7:24 | |
| | |
Example 5 |
10:08 | |
| |
Implicit Differentiation |
16:53 |
| | |
Intro |
0:00 | |
| | |
Implicit Differentiation: First Order |
0:07 | |
| | |
| Example 1: Setting Up |
0:45 | |
| | |
| Example 1: Solving |
1:41 | |
| | |
Implicit Differentiation: Second Order (Ex. 2) |
4:55 | |
| | |
Example 3: Implicit Differentiation |
9:11 | |
| | |
Example 4: Implicit Differentiation |
9:56 | |
| | |
Example 5: Implicit Differentiation With Double Derivative |
12:46 | |
| |
Multiple Choice Practice: Derivatives |
11:07 |
| | |
Intro |
0:00 | |
| | |
Practice Problem 1 |
0:09 | |
| | |
| Answer |
3:24 | |
| | |
Practice Problem 2 |
3:36 | |
| | |
| Answer |
6:29 | |
| | |
Practice Problem 3 |
6:42 | |
| | |
| Answer |
8:39 | |
| | |
Practice Problem 4 |
8:43 | |
| | |
| Answer |
9:33 | |
| | |
Practice Problem 5 |
9:41 | |
| | |
| Answer |
10:40 | |
| IV. Applications of Derivatives |
| |
Tangent & Normal Lines |
22:36 |
| | |
Intro |
0:00 | |
| | |
Tangent and Normal Lines |
0:10 | |
| | |
| Definition |
0:22 | |
| | |
| Example 1 |
0:55 | |
| | |
Tangent and Normal Lines: Example 2 |
2:43 | |
| | |
Tangent and Normal Lines |
5:21 | |
| | |
| Example 3 |
5:35 | |
| | |
Tangent and Normal Lines: Example 4 |
9:14 | |
| | |
Tangent and Normal Lines: Example 5 |
12:27 | |
| | |
Tangent and Normal Lines: Example 6 |
15:54 | |
| | |
Tangent and Normal Lines: Example 7 |
19:05 | |
| |
Position Velocity & Acceleration |
18:42 |
| | |
Intro |
0:00 | |
| | |
Position, Velocity, and Acceleration |
0:10 | |
| | |
| Position Function |
0:14 | |
| | |
| Velocity Function |
0:34 | |
| | |
| Acceleration Function |
1:01 | |
| | |
Example 1 |
1:20 | |
| | |
Example 2 |
6:31 | |
| | |
Example Continue: Velocity When Acceleration is Zero |
6:32 | |
| | |
Example 3: Where Is Particle Changing Directions? |
8:16 | |
| | |
Example 4: Total Distance Traveled From 0 to 2 Second |
11:09 | |
| | |
Example 5: Ball Drop Problem |
16:40 | |
| |
Related Rates |
26:22 |
| | |
Intro |
0:00 | |
| | |
Related Rates |
0:06 | |
| | |
| Finding Rate of Change: Organization & Big Picture |
0:23 | |
| | |
Example 2: Area of a Circle |
1:17 | |
| | |
Example 3: Spherical Volume Expanding |
4:19 | |
| | |
Example 4: Traveling Problem |
7:57 | |
| | |
Example 5: Square Increase |
12:37 | |
| | |
Example 6: Standard Related Rates Problem |
16:59 | |
| | |
Example 7: Standard Related Rates Problem |
19:49 | |
| |
Minimum & Maximum |
12:22 |
| | |
Intro |
0:00 | |
| | |
Extrema: First Derivative Test |
0:09 | |
| | |
| Example 1 |
0:46 | |
| | |
Example 2: Real World Application/ Cost Function |
4:05 | |
| | |
Example 3: Minimums & Maximums |
7:10 | |
| | |
Example 4: Find Critical Points |
10:52 | |
| |
Concavity |
11:43 |
| | |
Intro |
0:00 | |
| | |
Concavity: Second Derivative Test |
0:06 | |
| | |
| Definition |
0:34 | |
| | |
| Example 1 |
0:54 | |
| | |
Example 2 |
2:51 | |
| | |
Example 3 |
4:08 | |
| | |
Example 4 |
5:52 | |
| |
Rolles Theorem |
8:28 |
| | |
Intro |
0:00 | |
| | |
Rolle's Theorem |
0:07 | |
| | |
| Conditions |
0:11 | |
| | |
| Summary |
0:41 | |
| | |
Example 1 |
1:09 | |
| | |
Example 2 |
3:08 | |
| | |
Example 3 |
4:48 | |
| |
Mean Value Theorem |
9:39 |
| | |
Intro |
0:00 | |
| | |
Mean Value Theorem |
0:06 | |
| | |
| Rolle's Theorem |
0:07 | |
| | |
| Mean Value Theorem Conditions |
0:24 | |
| | |
| Mean Value Theorem Definition |
0:36 | |
| | |
Example 1 |
0:56 | |
| | |
Example 2 |
2:44 | |
| | |
Example 3 |
5:28 | |
| | |
Example 4 |
7:15 | |
| |
Differentials |
12:25 |
| | |
Intro |
0:00 | |
| | |
Differentials |
0:08 | |
| | |
| 1st Differential Formula |
0:29 | |
| | |
| 2nd Differential Formula |
0:57 | |
| | |
Example 1 |
1:06 | |
| | |
Example 2 |
3:21 | |
| | |
Example 3 |
5:49 | |
| | |
Example 4 |
7:19 | |
| | |
Example 5 |
9:06 | |
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Applications of Derivatives: Multiple Choice Practice |
13:21 |
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Intro |
0:00 | |
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Practice Problem 1 |
0:10 | |
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| Answer |
1:57 | |
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Practice Problem 2 |
2:08 | |
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| Answer |
5:39 | |
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Practice Problem 3 |
5:45 | |
| | |
| Answer |
9:59 | |
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Practice Problem 4 |
10:12 | |
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| Answer |
11:49 | |
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Practice Problem 5 |
11:52 | |
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| Answer |
13:00 | |
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Applications of Derivatives: Free Response Practice |
10:22 |
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Intro |
0:00 | |
| | |
Practice Problem 1 |
0:10 | |
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| Slope |
1:30 | |
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| Tangent Line Equation |
2:17 | |
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Absolute Minimum |
2:24 | |
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| 2 Possible X Points With Minimums |
3:15 | |
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| One Interest Point |
4:14 | |
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| Concavity |
4:33 | |
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| Positive Value = Positive Concavity |
4:10 | |
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| Minimum Point |
5:34 | |
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| Absolute Minimum |
6:18 | |
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Point(s) of Inflection |
6:31 | |
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| Definition |
6:49 | |
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| 2 Points Of Inflection |
9:59 | |
| V. Integrals |
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Definition of Integrals |
1:08 |
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Intro |
0:00 | |
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Definition |
0:09 | |
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| Definition |
0:16 | |
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| Example |
0:20 | |
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Integrals of Power Rule |
8:50 |
| | |
Intro |
0:00 | |
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Power Rule |
0:06 | |
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| Example 1 |
0:25 | |
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Example 2 |
2:02 | |
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Example 3 |
2:54 | |
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Example 4 |
3:45 | |
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Example 5 |
4:49 | |
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Example 6 |
6:47 | |
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Integrals Basic Rules of Integration |
9:43 |
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Intro |
0:00 | |
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Basic Rules of Integration |
0:09 | |
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| Constant Rule |
0:22 | |
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| Example 1 |
0:40 | |
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Addition and Difference Rule |
1:40 | |
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| Example 2 |
1:58 | |
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Example 3: Subtraction/ Difference Rule |
2:47 | |
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Example 4 |
3:55 | |
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Example 5 |
5:19 | |
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Example 6 |
7:37 | |
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Trigonometric Rules of Integrals |
8:58 |
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Intro |
0:00 | |
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Trigonometric Rules |
0:09 | |
| | |
| Integral of SIN |
0:38 | |
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Example 1: Integral of SIN |
1:46 | |
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Example 2: Integral of COS |
2:38 | |
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Example 3: With 2 terms of X |
3:06 | |
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Example 4: Integral of SEC |
4:15 | |
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Example 5: Integral of CSC |
5:06 | |
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Example 6 |
6:18 | |
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Chain Rule |
13:59 |
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Intro |
0:00 | |
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Chain Rule |
0:07 | |
| | |
| Example 1 |
0:37 | |
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Example 2 |
3:17 | |
| | |
Example 3 |
5:09 | |
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Example 4 |
7:53 | |
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Example 5 |
9:40 | |
| | |
Example 6 |
11:39 | |
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Integrals of Exponential Functions |
12:52 |
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Intro |
0:00 | |
| | |
Types of Integrals: Exponential Functions |
0:09 | |
| | |
| Rule 1 |
0:30 | |
| | |
| Rule 2 |
0:49 | |
| | |
| Example 1 |
1:11 | |
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Example 2 |
2:54 | |
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Example 3 |
4:19 | |
| | |
Example 4 |
5:19 | |
| | |
Example 5 |
7:37 | |
| | |
Example 6 |
9:04 | |
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Integrals of Natural Logarithmic Functions |
13:00 |
| | |
Intro |
0:00 | |
| | |
Types of Integrals: Natural Log Functions |
0:09 | |
| | |
| Example 1 |
0:49 | |
| | |
Example 2 |
2:06 | |
| | |
Example 3 |
4:01 | |
| | |
Example 4 |
5:37 | |
| | |
Example 5 |
7:30 | |
| | |
Example 6 |
9:05 | |
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Integrals of Inverse Trigonometric Functions |
8:29 |
| | |
Intro |
0:00 | |
| | |
Types of Integrals: Inverse Trig Functions |
0:09 | |
| | |
| One Property |
0:40 | |
| | |
Example 1 |
1:19 | |
| | |
Example 2 |
3:44 | |
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Example 3 |
4:53 | |
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Example 4 |
5:53 | |
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Integrals: Multiple Choice Practice |
15:37 |
| | |
Intro |
0:00 | |
| | |
Problem 1 |
0:09 | |
| | |
| Answer |
4:09 | |
| | |
Problem 2 |
4:33 | |
| | |
| Answer |
5:54 | |
| | |
Problem 3 |
5:59 | |
| | |
| Answer |
8:02 | |
| | |
Problem 4 |
8:06 | |
| | |
| Answer |
10:27 | |
| | |
Problem 5 |
10:43 | |
| | |
| Answer |
14:46 | |
| VI. Applications of Integrals |
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Fundamental Theorem of Calculus |
15:55 |
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Intro |
0:00 | |
| | |
Fundamental Theorem of Calculus: Properties |
0:10 | |
| | |
| Definition of Integral |
0:49 | |
| | |
| Example 1 |
1:14 | |
| | |
Fundamental Theorem of Calculus: Properties |
2:40 | |
| | |
| Rule 1 |
2:50 | |
| | |
| Rule 2 |
3:14 | |
| | |
| Rule 3 |
3:33 | |
| | |
| Rule 4 |
3:52 | |
| | |
Example 2 |
4:07 | |
| | |
Example 3 |
6:17 | |
| | |
Example 4 |
9:31 | |
| | |
Example 5 |
10:52 | |
| | |
Example 6 |
13:34 | |
| |
Area Under A Curve |
18:34 |
| | |
Intro |
0:00 | |
| | |
Area Under Curve |
0:07 | |
| | |
| Definition of Integral |
0:09 | |
| | |
| Left Endpoint |
1:17 | |
| | |
| Right Endpoint |
1:47 | |
| | |
| Midpoints |
2:09 | |
| | |
Example 1 |
2:40 | |
| | |
Example 2 |
4:59 | |
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Example 3 |
8:48 | |
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Example 4 |
10:23 | |
| | |
Example 5 |
12:30 | |
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Example 6 |
15:32 | |
| |
Reimann Sums |
10:35 |
| | |
Intro |
0:00 | |
| | |
Reimann Sums |
0:08 | |
| | |
| Definition |
1:07 | |
| | |
Example 1 |
2:48 | |
| | |
Example 2 |
5:38 | |
| | |
Example 3 |
7:21 | |
| | |
Example 4 |
9:14 | |
| |
Trapezoid Rule |
12:46 |
| | |
Intro |
0:00 | |
| | |
The Trapezoid Rule |
0:09 | |
| | |
| Definition: Area Of A Trapezoid |
0:26 | |
| | |
| Terms of Formula |
1:35 | |
| | |
Example 1 |
2:11 | |
| | |
Example 2 |
4:29 | |
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Example 3 |
7:22 | |
| | |
Example 4 |
10:01 | |
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Mean Value Theorem |
11:22 |
| | |
Intro |
0:00 | |
| | |
Mean Value Theorem of Integration |
0:06 | |
| | |
| Example 1 |
0:53 | |
| | |
Example 2 |
2:29 | |
| | |
Example 3 |
3:48 | |
| | |
Example 4 |
6:02 | |
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Second Fundamental Theorem of Calculus |
4:44 |
| | |
Intro |
0:00 | |
| | |
Second Fundamental Theorem of Calculus |
0:07 | |
| | |
| Definition |
0:39 | |
| | |
Example 1 |
1:08 | |
| | |
Example 2 |
2:07 | |
| | |
Example 3 |
2:48 | |
| | |
Example 4 |
3:23 | |
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Area Between Curves |
16:39 |
| | |
Intro |
0:00 | |
| | |
Example 1 |
0:10 | |
| | |
Example 2 |
3:00 | |
| | |
Example 3 |
4:46 | |
| | |
Example 4 |
8:22 | |
| | |
Example 5 |
11:04 | |
| | |
Example 6 |
13:09 | |
| |
Revolving Solids Washer Disk Methods |
21:09 |
| | |
Intro |
0:00 | |
| | |
Revolving Solids Washer Disk Methods |
0:11 | |
| | |
| Explanation |
0:33 | |
| | |
| Formula |
3:12 | |
| | |
Example 1 |
3:42 | |
| | |
Example 2 |
6:54 | |
| | |
Example 3 |
9:29 | |
| | |
Example 4 |
12:16 | |
| | |
Example 5 |
15:35 | |
| |
Revolving Solids Cylindrical Shells Method |
26:46 |
| | |
Intro |
0:00 | |
| | |
Revolving Solids: Cylindrical Shells Method |
0:09 | |
| | |
| Volume Of A Solid |
0:25 | |
| | |
| Formula |
2:51 | |
| | |
Example 1 |
2:56 | |
| | |
Example 2 |
7:28 | |
| | |
Example 3 |
11:39 | |
| | |
Example 4 |
17:36 | |
| | |
Example 5 |
21:45 | |
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Revolving Solids Known Cross Sections |
27:41 |
| | |
Intro |
0:00 | |
| | |
Revolving Solids Known Cross Sections |
0:08 | |
| | |
| Example 1 |
0:35 | |
| | |
Example 2 |
6:01 | |
| | |
Example 3 |
11:03 | |
| | |
Example 4 |
17:29 | |
| | |
Example 5 |
22:19 | |
| |
Differential Equations Eulers Method |
17:54 |
| | |
Intro |
0:00 | |
| | |
Differential Equations |
0:08 | |
| | |
| Example 1 |
0:30 | |
| | |
Differential Equations: Euler's Method |
2:33 | |
| | |
| Rules |
2:39 | |
| | |
| Example 2 |
3:00 | |
| | |
Example 3 |
5:42 | |
| | |
Example 4 |
9:44 | |
| | |
Example 5 |
14:14 | |
| |
Differential Equations Slope Fields |
16:30 |
| | |
Intro |
0:00 | |
| | |
Slope Fields |
0:08 | |
| | |
| What Are Slope Fields |
0:21 | |
| | |
| Example 1 |
0:42 | |
| | |
Example 2 |
6:30 | |
| | |
Example 3 |
11:17 | |
| |
Application of Integrals: Multiple Choice Practice |
14:19 |
| | |
Intro |
0:00 | |
| | |
Practice Problem 1 |
0:10 | |
| | |
| Answer |
3:46 | |
| | |
Practice Problem 2 |
3:49 | |
| | |
| Answer |
6:20 | |
| | |
Practice Problem 3 |
6:26 | |
| | |
| Answer |
8:02 | |
| | |
Practice Problem 4 |
8:07 | |
| | |
| Answer |
10:58 | |
| | |
Practice Problem 5 |
11:05 | |
| | |
| Answer |
14:06 | |
| |
Application of Integrals: Free Response Practice |
9:14 |
| | |
Intro |
0:00 | |
| | |
Problem 1 |
0:10 | |
| | |
| Part A |
0:24 | |
| | |
| Part A: Solution |
2:04 | |
| | |
| Part B |
2:10 | |
| | |
Problem 1, Part B Continue |
2:23 | |
| | |
| Part B: Solution |
6:15 | |
| | |
Problem 1, Part C |
6:58 | |
| | |
| Part C: Solution |
12:40 | |
| | |
Problem 2 |
12:52 | |
| | |
| Part A |
13:02 | |
| | |
| Part A: Solution |
15:34 | |
| | |
| Part B |
16:03 | |
| | |
| Part B: Solution |
18:48 | |
| VII. Sample AP Test |
| |
AP Calculus AB Practice test: Section 1: Multiple Choice Part 1 |
17:50 |
| | |
Intro |
0:00 | |
| | |
Problem 1 |
0:20 | |
| | |
Problem 2 |
1:24 | |
| | |
Problem 3 |
2:53 | |
| | |
Problem 4 |
3:56 | |
| | |
Problem 5 |
8:18 | |
| | |
Problem 6 |
9:06 | |
| | |
Problem 7 |
10:14 | |
| | |
Problem 8 |
12:16 | |
| | |
Problem 9 |
14:13 | |
| |
AP Calculus AB Practice test: Section 1: Multiple Choice Part 2 |
17:32 |
| | |
Intro |
0:00 | |
| | |
Problem 10 |
0:18 | |
| | |
Problem 11 |
2:26 | |
| | |
Problem 12 |
6:11 | |
| | |
Problem 13 |
7:04 | |
| | |
Problem 14 |
8:06 | |
| | |
Problem 15 |
10:32 | |
| | |
Problem 16 |
11:40 | |
| | |
Problem 17 |
13:00 | |
| | |
Problem 18 |
14:43 | |
| |
AP Calculus AB Practice test: Section 1: Multiple Choice Part 3 |
22:14 |
| | |
Intro |
0:00 | |
| | |
Problem 19 |
0:21 | |
| | |
Problem 20 |
2:33 | |
| | |
Problem 21 |
7:23 | |
| | |
Problem 22 |
10:24 | |
| | |
Problem 23 |
12:18 | |
| | |
Problem 24 |
13:13 | |
| | |
Problem 25 |
15:52 | |
| | |
Problem 26 |
17:03 | |
| | |
Problem 27 |
19:44 | |
| |
AP Calculus AB Practice test: Section 1: Multiple Choice Part 4 |
19:35 |
| | |
Intro |
0:00 | |
| | |
Problem 28 |
0:23 | |
| | |
Problem 29 |
3:50 | |
| | |
Problem 30 |
5:31 | |
| | |
Problem 31 |
9:02 | |
| | |
Problem 32 |
10:07 | |
| | |
Problem 33 |
11:27 | |
| | |
Problem 34 |
13:47 | |
| | |
Problem 35 |
15:21 | |
| | |
Problem 36 |
16:53 | |
| |
AP Calculus AB Practice test: Section 1: Multiple Choice Part 5 |
25:43 |
| | |
Intro |
0:00 | |
| | |
Problem 37 |
0:22 | |
| | |
Problem 38 |
2:27 | |
| | |
Problem 39 |
5:36 | |
| | |
Problem 40 |
7:21 | |
| | |
Problem 41 |
10:08 | |
| | |
Problem 42 |
11:29 | |
| | |
Problem 43 |
13:07 | |
| | |
Problem 44 |
18:18 | |
| | |
Problem 45 |
21:08 | |
| |
AP Calculus AB Practice Test: Section 2: Free Response Part 1 |
16:50 |
| | |
Intro |
0:00 | |
| | |
Problem 1, Part A |
0:20 | |
| | |
Problem 1, Part B |
3:03 | |
| | |
Problem 1, Part C |
4:11 | |
| | |
Problem 1, Part D |
5:36 | |
| | |
Problem 2, Part A |
7:37 | |
| | |
Problem 2, Part B |
9:02 | |
| | |
Problem 2, Part C |
12:31 | |
| |
AP Calculus AB Practice Test: Section 2: Free Response Part 2 |
21:36 |
| | |
Intro |
0:00 | |
| | |
Problem 3, Part A |
0:18 | |
| | |
Problem 3, Part B |
5:57 | |
| | |
Problem 4, Part A |
11:26 | |
| | |
Problem 4, Part B |
12:28 | |
| | |
Problem 4, Part C |
15:35 | |
| | |
Problem 4, Part D |
18:56 | |
| |
AP Calculus AB Practice Test: Section 2: Free Response Part 3 |
13:39 |
| | |
Intro |
0:00 | |
| | |
Problem 5, Part A |
0:21 | |
| | |
Problem 5, Part B |
3:07 | |
| | |
Problem 5, Part C |
6:43 | |
| | |
Problem 6 |
8:24 | |