Section 1: Functions |
|
Definitions & Properties of Functions |
11:26 |
| |
Intro |
0:00 | |
| |
Definition |
0:28 | |
| |
Properties: Vertical Line Test |
1:32 | |
| |
| Domain |
1:38 | |
| |
| Range |
1:59 | |
| |
| Vertical Line test |
2:19 | |
| |
| Example 1 |
2:33 | |
| |
| Example 2 |
3:10 | |
| |
Properties: Roots or Zeros |
4:04 | |
| |
| Finding the Root |
4:16 | |
| |
Properties: Forms |
5:12 | |
| |
| Graphically |
5:20 | |
| |
| List |
5:46 | |
| |
| Equation |
6:11 | |
| |
| Function |
6:38 | |
| |
Properties: Odd & Even |
7:12 | |
| |
| Even Function |
7:14 | |
| |
| Odd Function |
8:25 | |
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Properties: Increasing & Decreasing |
9:17 | |
| |
| Increasing Function |
9:22 | |
| |
| Decreasing Function |
10:21 | |
|
Graphing |
13:58 |
| |
Intro |
0:00 | |
| |
Manipulating |
0:10 | |
| |
| A in the Equation |
0:39 | |
| |
| B in the Equation |
0:44 | |
| |
| C & D in the Equation |
0:49 | |
| |
| Negative values |
0:59 | |
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| Example 1 |
1:17 | |
| |
Example 2 |
1:51 | |
| |
Example 3: Absolute Value Functions |
3:43 | |
| |
| Example 4 |
4:57 | |
| |
Example 5 |
6:17 | |
| |
Example 6 |
8:02 | |
| |
Example 7 |
9:10 | |
| |
Example 8 |
11:02 | |
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Example 9 |
11:47 | |
|
Inverse Functions |
6:47 |
| |
Intro |
0:00 | |
| |
Inverse |
0:08 | |
| |
| Definition |
0:18 | |
| |
| Example: Finding the Inverse |
1:03 | |
| |
Example 2 |
2:29 | |
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Example 3 |
3:12 | |
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Example 4 |
4:41 | |
|
Polynomial Functions |
5:04 |
| |
Intro |
0:00 | |
| |
Types of Functions: Polynomials |
0:07 | |
| |
| 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 | |
| |
| Leading Coefficient Test |
1:33 | |
| |
| Leading Coefficient Positive, Even Degree |
1:54 | |
| |
| Leading Coefficient Positive, Odd Degree |
2:13 | |
| |
| Leading Coefficient Negative Even Degree |
2:34 | |
| |
| Leading Coefficient Positive, Odd Degree |
2:46 | |
| |
Examples: Types of Functions: Polynomials |
3:03 | |
| |
Examples: Types of Functions: Polynomials |
4:18 | |
|
Trigonometric Functions |
6:45 |
| |
Intro |
0:00 | |
| |
Types of Functions: Trigonometric |
0:05 | |
| |
| 6 Functions To Be Familiar With |
0:14 | |
| |
Example 1: SIN |
1:38 | |
| |
Example 2: COS |
3:22 | |
| |
Example 3: TAN |
4:38 | |
|
Inverse Trigonometric Functions |
5:58 |
| |
Intro |
0:00 | |
| |
Types of Functions: Trigonometric- Inverse Trig Functions |
0:07 | |
| |
Example: Inverse SIN of X |
0:45 | |
| |
Example: Inverse Function |
2:30 | |
| |
Example: Inverse TAN of X |
4:42 | |
|
Trigonometric Identities |
17:42 |
| |
Intro |
0:00 | |
| |
Types of Functions: Trigonometric- Trig Identities |
0:07 | |
| |
| 4 Identities |
0:24 | |
| |
| Pythagorean |
0:28 | |
| |
| Double Angle |
1:10 | |
| |
| Power Reducing |
1:28 | |
| |
| Sum or Difference |
1:42 | |
| |
Couple More Identities |
1:59 | |
| |
| Negative Angle |
2:04 | |
| |
| Product to Sum |
2:39 | |
| |
Example 1: Prove |
3:00 | |
| |
Example 2: Simplify Expression |
5:02 | |
| |
Example 3: Prove |
5:56 | |
| |
Example 4: Prove |
8:02 | |
| |
Example 5: Prove With TAN |
12:43 | |
|
Exponential Functions |
5:53 |
| |
Intro |
0:00 | |
| |
Types of Functions: Exponentials |
0:07 | |
| |
| General Form |
0:10 | |
| |
| Special Exponential Function |
0:17 | |
| |
Example 1: Using Exponential Properties |
0:46 | |
| |
Example 2: Using Exponential Properties |
1:58 | |
| |
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 | |
| |
| 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 | |
| |
Properties |
2:09 | |
| |
Example 1: Apply Basic Principle of Log Func. |
3:05 | |
| |
Example 2: Use Properties |
3:40 | |
| |
Example 3: Regular Log |
5:16 | |
|
Rational Functions |
15:36 |
| |
Intro |
0:00 | |
| |
Types of Functions: Rational - Definition |
0:06 | |
| |
Example 1: Graph Rational Func. |
0:36 | |
| |
Example 2: Find Asymptotes of Func. |
7:02 | |
| |
Example 3: Find Asymptotes of Func. |
8:59 | |
| |
Example 4: Graph Rational Func. |
11:08 | |
|
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 | |
| |
Example 2: Conic Sections |
10:59 | |
| |
Example 3: Graph Conic Sections |
12:21 | |
Section 2: 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 | |
| |
| Special Property |
1:51 | |
| |
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 | |
| |
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 | |
Section 3: 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 | |
| |
Example 3 |
3:05 | |
| |
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 | |
| |
Example 4 |
5:24 | |
| |
Example 5 |
6:42 | |
| |
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 | |
| |
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 | |
Section 4: 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 | |
|
Applications of Derivatives: Multiple Choice Practice |
13:21 |
| |
Intro |
0:00 | |
| |
Practice Problem 1 |
0:10 | |
| |
| Answer |
1:57 | |
| |
Practice Problem 2 |
2:08 | |
| |
| Answer |
5:39 | |
| |
Practice Problem 3 |
5:45 | |
| |
| Answer |
9:59 | |
| |
Practice Problem 4 |
10:12 | |
| |
| Answer |
11:49 | |
| |
Practice Problem 5 |
11:52 | |
| |
| Answer |
13:00 | |
|
Applications of Derivatives: Free Response Practice |
10:22 |
| |
Intro |
0:00 | |
| |
Practice Problem 1 |
0:10 | |
| |
| Slope |
1:30 | |
| |
| Tangent Line Equation |
2:17 | |
| |
Absolute Minimum |
2:24 | |
| |
| 2 Possible X Points With Minimums |
3:15 | |
| |
| One Interest Point |
4:14 | |
| |
| Concavity |
4:33 | |
| |
| Positive Value = Positive Concavity |
4:10 | |
| |
| Minimum Point |
5:34 | |
| |
| Absolute Minimum |
6:18 | |
| |
Point(s) of Inflection |
6:31 | |
| |
| Definition |
6:49 | |
| |
| 2 Points Of Inflection |
9:59 | |
Section 5: Integrals |
|
Definition of Integrals |
1:08 |
| |
Intro |
0:00 | |
| |
Definition |
0:09 | |
| |
| Definition |
0:16 | |
| |
| Example |
0:20 | |
|
Integrals of Power Rule |
8:50 |
| |
Intro |
0:00 | |
| |
Power Rule |
0:06 | |
| |
| Example 1 |
0:25 | |
| |
Example 2 |
2:02 | |
| |
Example 3 |
2:54 | |
| |
Example 4 |
3:45 | |
| |
Example 5 |
4:49 | |
| |
Example 6 |
6:47 | |
|
Integrals Basic Rules of Integration |
9:43 |
| |
Intro |
0:00 | |
| |
Basic Rules of Integration |
0:09 | |
| |
| Constant Rule |
0:22 | |
| |
| Example 1 |
0:40 | |
| |
Addition and Difference Rule |
1:40 | |
| |
| Example 2 |
1:58 | |
| |
Example 3: Subtraction/ Difference Rule |
2:47 | |
| |
Example 4 |
3:55 | |
| |
Example 5 |
5:19 | |
| |
Example 6 |
7:37 | |
|
Trigonometric Rules of Integrals |
8:58 |
| |
Intro |
0:00 | |
| |
Trigonometric Rules |
0:09 | |
| |
| Integral of SIN |
0:38 | |
| |
Example 1: Integral of SIN |
1:46 | |
| |
Example 2: Integral of COS |
2:38 | |
| |
Example 3: With 2 terms of X |
3:06 | |
| |
Example 4: Integral of SEC |
4:15 | |
| |
Example 5: Integral of CSC |
5:06 | |
| |
Example 6 |
6:18 | |
|
Chain Rule |
13:59 |
| |
Intro |
0:00 | |
| |
Chain Rule |
0:07 | |
| |
| Example 1 |
0:37 | |
| |
Example 2 |
3:17 | |
| |
Example 3 |
5:09 | |
| |
Example 4 |
7:53 | |
| |
Example 5 |
9:40 | |
| |
Example 6 |
11:39 | |
|
Integrals of Exponential Functions |
12:52 |
| |
Intro |
0:00 | |
| |
Types of Integrals: Exponential Functions |
0:09 | |
| |
| Rule 1 |
0:30 | |
| |
| Rule 2 |
0:49 | |
| |
| Example 1 |
1:11 | |
| |
Example 2 |
2:54 | |
| |
Example 3 |
4:19 | |
| |
Example 4 |
5:19 | |
| |
Example 5 |
7:37 | |
| |
Example 6 |
9:04 | |
|
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 | |
|
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 | |
| |
Example 3 |
4:53 | |
| |
Example 4 |
5:53 | |
|
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 | |
Section 6: Applications of Integrals |
|
Fundamental Theorem of Calculus |
15:55 |
| |
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 | |
| |
Example 3 |
8:48 | |
| |
Example 4 |
10:23 | |
| |
Example 5 |
12:30 | |
| |
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 | |
| |
Example 3 |
7:22 | |
| |
Example 4 |
10:01 | |
|
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 | |
|
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 | |
|
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 | |
|
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 | |
Section 7: 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 | |