Dr. Jenny Switkes has been teaching mathematics for the past seven years and will help you master the intricacies of calculus from Limits to Derivatives to Integrals. In Educator's Calculus I course, Professor Switkes covers all the important topics with detailed explanations and analysis of common student pitfalls. Jenny understands calculus is not easy but will make it as painless as possible, all the while showing the beauty and importance of math. Each lecture is complete with at least five worked-out video examples that allow you to apply your newfound knowledge and prepare for examinations.
| I. Overview of Functions |
| |
Review of Functions |
26:29 |
| | |
Intro |
0:00 | |
| | |
What is a Function |
0:10 | |
| | |
| Domain and Range |
0:21 | |
| | |
| Vertical Line Test |
0:31 | |
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| Example: Vertical Line Test |
0:47 | |
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Function Examples |
1:57 | |
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| Example: Squared |
2:10 | |
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| Example: Natural Log |
2:41 | |
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| Example: Exponential |
3:21 | |
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| Example: Not Function |
3:54 | |
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Odd and Even Functions |
4:39 | |
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| Example: Even Function |
5:10 | |
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| Example: Odd Function |
5:53 | |
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Odd and Even Examples |
6:48 | |
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| Odd Function |
6:55 | |
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| Even Function |
8:43 | |
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Increasing and Decreasing Functions |
10:15 | |
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| Example: Increasing |
10:42 | |
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| Example: Decreasing |
10:55 | |
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Increasing and Decreasing Examples |
11:41 | |
| | |
| Example: Increasing |
11:48 | |
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| Example: Decreasing |
12:33 | |
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Types of Functions |
13:32 | |
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| Polynomials |
13:45 | |
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| Powers |
14:06 | |
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| Trigonometric |
14:34 | |
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| Rational |
14:50 | |
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| Exponential |
15:13 | |
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| Logarithmic |
15:29 | |
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Lecture Example 1 |
15:55 | |
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Lecture Example 2 |
17:51 | |
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Additional Example 3 |
2:35 | |
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Additional Example 4 |
2:33 | |
| |
Compositions of Functions |
12:29 |
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Intro |
0:00 | |
| | |
Compositions |
0:09 | |
| | |
| Alternative Notation |
0:32 | |
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| Three Functions |
0:47 | |
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Lecture Example 1 |
1:19 | |
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Lecture Example 2 |
3:25 | |
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Lecture Example 3 |
6:45 | |
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Additional Example 4 |
2:02 | |
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Additional Example 5 |
2:35 | |
| II. Limits |
| |
Average and Instantaneous Rates of Change |
20:59 |
| | |
Intro |
0:00 | |
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Rates of Change |
0:11 | |
| | |
| Average Rate of Change |
0:21 | |
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| Instantaneous Rate of Change |
0:33 | |
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| Slope of the Secant Line |
0:46 | |
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| Slope of the Tangent Line |
1:00 | |
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Lecture Example 1 |
1:14 | |
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Lecture Example 2 |
6:36 | |
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Lecture Example 3 |
11:30 | |
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Additional Example 4 |
2:49 | |
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Additional Example 5 |
3:40 | |
| |
Limit Investigations |
22:37 |
| | |
Intro |
0:00 | |
| | |
What is a Limit? |
0:10 | |
| | |
Lecture Example 1 |
0:56 | |
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Lecture Example 2 |
5:28 | |
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Lecture Example 3 |
9:27 | |
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Additional Example 4 |
4:42 | |
| | |
Additional Example 5 |
3:38 | |
| |
Algebraic Evaluation of Limits |
28:19 |
| | |
Intro |
0:00 | |
| | |
Evaluating Limits |
0:09 | |
| | |
Lecture Example 1 |
1:06 | |
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Lecture Example 2 |
5:16 | |
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Lecture Example 3 |
8:15 | |
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Lecture Example 4 |
12:58 | |
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Additional Example 5 |
5:01 | |
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Additional Example 6 |
5:35 | |
| |
Formal Definition of a Limit |
23:39 |
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Intro |
0:00 | |
| | |
Formal Definition |
0:13 | |
| | |
| Template |
0:55 | |
| | |
| Epsilon and Delta |
1:24 | |
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Lecture Example 1 |
1:40 | |
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Lecture Example 2 |
9:20 | |
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Additional Example 3 |
2:52 | |
| | |
Additional Example 4 |
5:49 | |
| |
Continuity and the Intermediate Value Theorem |
19:09 |
| | |
Intro |
0:00 | |
| | |
Continuity |
0:13 | |
| | |
| Continuous |
0:16 | |
| | |
| Discontinuous |
0:37 | |
| | |
Intermediate Value Theorem |
0:52 | |
| | |
| Example |
1:22 | |
| | |
Lecture Example 1 |
2:58 | |
| | |
Lecture Example 2 |
9:02 | |
| | |
Additional Example 3 |
4:12 | |
| | |
Additional Example 4 |
2:23 | |
| III. Derivatives, part 1 |
| |
Limit Definition of the Derivative |
22:52 |
| | |
Intro |
0:00 | |
| | |
Limit Definition of the Derivative |
0:11 | |
| | |
| Three Versions |
0:13 | |
| | |
Lecture Example 1 |
1:02 | |
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Lecture Example 2 |
4:33 | |
| | |
Lecture Example 3 |
6:49 | |
| | |
Lecture Example 4 |
10:11 | |
| | |
Additional Example 5 |
4:41 | |
| | |
Additional Example 6 |
5:18 | |
| |
The Power Rule |
26:01 |
| | |
Intro |
0:00 | |
| | |
Power Rule of Differentiation |
0:14 | |
| | |
| Power Rule with Constant |
0:41 | |
| | |
| Sum/Difference |
1:15 | |
| | |
Lecture Example 1 |
1:59 | |
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Lecture Example 2 |
6:48 | |
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Lecture Example 3 |
11:22 | |
| | |
Additional Example 4 |
4:21 | |
| | |
Additional Example 5 |
3:51 | |
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The Product Rule |
14:54 |
| | |
Intro |
| |
| | |
Statement of the Product Rule |
0:08 | |
| | |
Lecture Example 1 |
0:41 | |
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Lecture Example 2 |
2:27 | |
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Lecture Example 3 |
5:03 | |
| | |
Additional Example 4 |
4:11 | |
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Additional Example 5 |
2:25 | |
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The Quotient Rule |
19:17 |
| | |
Intro |
0:00 | |
| | |
Statement of the Quotient Rule |
0:07 | |
| | |
| Carrying out the Differentiation |
0:23 | |
| | |
| Quotient Rule in Words |
1:00 | |
| | |
Lecture Example 1 |
1:19 | |
| | |
Lecture Example 2 |
4:23 | |
| | |
Lecture Example 3 |
8:00 | |
| | |
Additional Example 4 |
5:46 | |
| | |
Additional Example 5 |
2:43 | |
| |
Applications of Rates of Change |
17:43 |
| | |
Intro |
0:00 | |
| | |
Rates of Change |
0:11 | |
| | |
Lecture Example 1 |
0:44 | |
| | |
Lecture Example 2 |
5:16 | |
| | |
Lecture Example 3 |
7:38 | |
| | |
Additional Example 4 |
2:18 | |
| | |
Additional Example 5 |
3:54 | |
| |
Trigonometric Derivatives |
26:58 |
| | |
Intro |
0:00 | |
| | |
Six Basic Trigonometric Functions |
0:11 | |
| | |
| Patterns |
0:47 | |
| | |
Lecture Example 1 |
1:18 | |
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Lecture Example 2 |
7:38 | |
| | |
Lecture Example 3 |
12:15 | |
| | |
Lecture Example 4 |
14:25 | |
| | |
Additional Example 5 |
3:37 | |
| | |
Additional Example 6 |
5:27 | |
| |
The Chain Rule |
23:47 |
| | |
Intro |
0:00 | |
| | |
Statement of the Chain Rule |
0:09 | |
| | |
| Chain Rule for Three Functions |
0:27 | |
| | |
Lecture Example 1 |
1:00 | |
| | |
Lecture Example 2 |
4:34 | |
| | |
Lecture Example 3 |
7:23 | |
| | |
Additional Example 4 |
5:05 | |
| | |
Additional Example 5 |
5:38 | |
| |
Inverse Trigonometric Functions |
27:05 |
| | |
Intro |
0:00 | |
| | |
Six Basic Inverse Trigonometric Functions |
0:10 | |
| | |
Lecture Example 1 |
1:11 | |
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Lecture Example 2 |
8:53 | |
| | |
Lecture Example 3 |
12:37 | |
| | |
Additional Example 4 |
7:05 | |
| | |
Additional Example 5 |
4:02 | |
| |
Equation of a Tangent Line |
15:52 |
| | |
Intro |
0:00 | |
| | |
Point Slope Form |
0:10 | |
| | |
Lecture Example 1 |
0:47 | |
| | |
Lecture Example 2 |
3:15 | |
| | |
Lecture Example 3 |
6:10 | |
| | |
Additional Example 4 |
3:27 | |
| | |
Additional Example 5 |
3:01 | |
| IV. Derivatives, part 2 |
| |
Implicit Differentiation |
30:05 |
| | |
Intro |
0:00 | |
| | |
Purpose |
0:09 | |
| | |
| Implicit Function |
0:20 | |
| | |
Lecture Example 1 |
0:32 | |
| | |
Lecture Example 2 |
7:14 | |
| | |
Lecture Example 3 |
11:22 | |
| | |
Lecture Example 4 |
16:43 | |
| | |
Additional Example 5 |
3:55 | |
| | |
Additional Example 6 |
5:04 | |
| |
Higher Derivatives |
13:16 |
| | |
Intro |
0:00 | |
| | |
Notation |
0:08 | |
| | |
| First Type |
0:19 | |
| | |
| Second Type |
0:54 | |
| | |
Lecture Example 1 |
1:41 | |
| | |
Lecture Example 2 |
3:15 | |
| | |
Lecture Example 3 |
4:57 | |
| | |
Additional Example 4 |
4:04 | |
| | |
Additional Example 5 |
1:24 | |
| |
Logarithmic and Exponential Function Derivatives |
17:42 |
| | |
Intro |
0:00 | |
| | |
Essential Equations |
0:12 | |
| | |
Lecture Example 1 |
1:34 | |
| | |
Lecture Example 2 |
2:48 | |
| | |
Lecture Example 3 |
5:54 | |
| | |
Additional Example 4 |
4:18 | |
| | |
Additional Example 5 |
4:51 | |
| |
Hyperbolic Trigonometric Function Derivatives |
14:30 |
| | |
Intro |
0:00 | |
| | |
Essential Equations |
0:15 | |
| | |
| Six Basic Hyperbolic Trigc Functions |
0:32 | |
| | |
| Six Basic Inverse Hyperbolic Trig Functions |
1:21 | |
| | |
Lecture Example 1 |
1:48 | |
| | |
Lecture Example 2 |
3:45 | |
| | |
Lecture Example 3 |
7:09 | |
| | |
Additional Example 4 |
2:12 | |
| | |
Additional Example 5 |
3:03 | |
| |
Related Rates |
29:05 |
| | |
Intro |
0:00 | |
| | |
What Are Related Rates? |
0:08 | |
| | |
Lecture Example 1 |
0:35 | |
| | |
Lecture Example 2 |
5:25 | |
| | |
Lecture Example 3 |
11:54 | |
| | |
Additional Example 4 |
4:04 | |
| | |
Additional Example 5 |
6:52 | |
| |
Linear Approximation |
23:52 |
| | |
Intro |
0:00 | |
| | |
Essential Equations |
0:09 | |
| | |
| Linear Approximation (Tangent Line) |
0:18 | |
| | |
| Example: Graph |
1:18 | |
| | |
| Differential (df) |
2:06 | |
| | |
| Delta F |
5:10 | |
| | |
Lecture Example 1 |
6:38 | |
| | |
Lecture Example 2 |
11:53 | |
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Lecture Example 3 |
15:54 | |
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Additional Example 4 |
2:56 | |
| | |
Additional Example 5 |
2:38 | |
| V. Application of Derivatives |
| |
Absolute Minima and Maxima |
18:57 |
| | |
Intro |
0:00 | |
| | |
Minimums and Maximums |
0:09 | |
| | |
| Absolute Minima and Maxima (Extrema) |
0:53 | |
| | |
| Critical Points |
1:25 | |
| | |
Lecture Example 1 |
2:58 | |
| | |
Lecture Example 2 |
6:57 | |
| | |
Lecture Example 3 |
10:02 | |
| | |
Additional Example 4 |
3:19 | |
| | |
Additional Example 5 |
2:34 | |
| |
Mean Value Theorem and Rolle's Theorem |
20:00 |
| | |
Intro |
0:00 | |
| | |
Theorems |
0:09 | |
| | |
| Mean Value Theorem |
0:13 | |
| | |
| Graphical Explanation |
0:36 | |
| | |
| Rolle's Theorem |
2:06 | |
| | |
| Graphical Explanation |
2:28 | |
| | |
Lecture Example 1 |
3:36 | |
| | |
Lecture Example 2 |
6:33 | |
| | |
Lecture Example 3 |
9:32 | |
| | |
Additional Example 4 |
2:27 | |
| | |
Additional Example 5 |
2:52 | |
| |
First Derivative Test, Second Derivative Test |
27:11 |
| | |
Intro |
0:00 | |
| | |
Local Minimum and Local Maximum |
0:14 | |
| | |
| Example |
1:01 | |
| | |
First and Second Derivative Test |
1:26 | |
| | |
| First Derivative Test |
1:36 | |
| | |
| Example |
2:00 | |
| | |
| Second Derivative Test (Concavity) |
2:58 | |
| | |
| Example: Concave Down |
3:15 | |
| | |
| Example: Concave Up |
3:54 | |
| | |
| Inconclusive |
4:19 | |
| | |
Lecture Example 1 |
5:23 | |
| | |
Lecture Example 2 |
12:03 | |
| | |
Lecture Example 3 |
15:54 | |
| | |
Additional Example 4 |
4:34 | |
| | |
Additional Example 5 |
2:52 | |
| |
L'Hopital's Rule |
23:09 |
| | |
Intro |
0:00 | |
| | |
Using L'Hopital's Rule |
0:09 | |
| | |
| Informal Definition |
0:34 | |
| | |
Lecture Example 1 |
1:27 | |
| | |
Lecture Example 2 |
4:00 | |
| | |
Lecture Example 3 |
5:40 | |
| | |
Lecture Example 4 |
9:38 | |
| | |
Additional Example 5 |
4:50 | |
| | |
Additional Example 6 |
6:32 | |
| |
Curve Sketching |
40:16 |
| | |
Intro |
0:00 | |
| | |
Collecting Information |
0:15 | |
| | |
| Domain and Range |
0:17 | |
| | |
| Intercepts |
0:21 | |
| | |
| Symmetry Properties (Even/Odd/Periodic) |
0:33 | |
| | |
| Asymptotes (Vertical/Horizontal/Slant) |
0:45 | |
| | |
| Critical Points |
1:15 | |
| | |
| Increasing/Decreasing Intervals |
1:24 | |
| | |
| Inflection Points |
1:38 | |
| | |
| Concave Up/Down |
1:52 | |
| | |
| Maxima/Minima |
2:03 | |
| | |
Lecture Example 1 |
2:58 | |
| | |
Lecture Example 2 |
10:52 | |
| | |
Lecture Example 3 |
17:55 | |
| | |
Additional Example 4 |
12:57 | |
| | |
Additional Example 5 |
4:38 | |
| |
Applied Optimization |
25:37 |
| | |
Intro |
0:00 | |
| | |
Real World Problems |
0:08 | |
| | |
| Sketch |
0:11 | |
| | |
| Interval |
0:20 | |
| | |
| Rewrite in One Variable |
0:26 | |
| | |
| Maximum or Minimum |
0:34 | |
| | |
| Critical Points |
0:42 | |
| | |
| Optimal Result |
0:52 | |
| | |
Lecture Example 1 |
1:05 | |
| | |
Lecture Example 2 |
6:12 | |
| | |
Lecture Example 3 |
13:31 | |
| | |
Additional Example 4 |
2:37 | |
| | |
Additional Example 5 |
4:03 | |
| |
Newton's Method |
25:13 |
| | |
Intro |
0:00 | |
| | |
Approximating Using Newton's Method |
0:10 | |
| | |
| Good Guesses for Convergence |
0:32 | |
| | |
Lecture Example 1 |
0:49 | |
| | |
Lecture Example 2 |
4:21 | |
| | |
Lecture Example 3 |
7:59 | |
| | |
Additional Example 4 |
5:13 | |
| | |
Additional Example 5 |
7:06 | |
| VI. Integrals |
| |
Approximating Areas and Distances |
36:50 |
| | |
Intro |
0:00 | |
| | |
Three Approximations |
0:12 | |
| | |
| Right Endpoint, Left Endpoint, Midpoint |
0:22 | |
| | |
| Formulas |
1:05 | |
| | |
| Velocity and Distance |
1:35 | |
| | |
Lecture Example 1 |
2:28 | |
| | |
Lecture Example 2 |
12:10 | |
| | |
Lecture Example 3 |
19:43 | |
| | |
Additional Example 4 |
5:43 | |
| | |
Additional Example 5 |
4:08 | |
| |
Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus |
22:02 |
| | |
Intro |
0:00 | |
| | |
Important Equations |
0:22 | |
| | |
| Riemann Sum |
0:28 | |
| | |
| Integral |
1:58 | |
| | |
| Integrand |
2:35 | |
| | |
| Limits of Integration (Upper Limit, Lower Limit) |
2:43 | |
| | |
| Other Equations |
3:05 | |
| | |
| Fundamental Theorem of Calculus |
4:00 | |
| | |
Lecture Example 1 |
5:04 | |
| | |
Lecture Example 2 |
10:43 | |
| | |
Lecture Example 3 |
13:52 | |
| | |
Additional Example 4 |
2:59 | |
| | |
Additional Example 5 |
3:20 | |
| |
Substitution Method for Integration |
23:19 |
| | |
Intro |
0:00 | |
| | |
| U-Substitution |
0:13 | |
| | |
Important Equations |
0:30 | |
| | |
| Purpose |
0:36 | |
| | |
Lecture Example 1 |
1:30 | |
| | |
Lecture Example 2 |
6:17 | |
| | |
Lecture Example 3 |
9:00 | |
| | |
Lecture Example 4 |
11:24 | |
| | |
Additional Example 5 |
2:10 | |
| | |
Additional Example 6 |
3:48 | |
| VII. Application of Integrals, part 1 |
| |
Area Between Curves |
19:59 |
| | |
Intro |
0:00 | |
| | |
Area Between Two Curves |
0:12 | |
| | |
| Graphic Description |
0:34 | |
| | |
Lecture Example 1 |
1:44 | |
| | |
Lecture Example 2 |
5:39 | |
| | |
Lecture Example 3 |
8:45 | |
| | |
Additional Example 4 |
3:37 | |
| | |
Additional Example 5 |
3:01 | |
| |
Volume by Method of Disks and Washers |
24:22 |
| | |
Intro |
0:00 | |
| | |
Important Equations |
0:16 | |
| | |
| Equation 1: Rotation about x-axis (disks) |
0:27 | |
| | |
| Equation 2: Two curves about x-axis (washers) |
3:38 | |
| | |
| Equation 3: Rotation about y-axis |
5:31 | |
| | |
Lecture Example 1 |
6:05 | |
| | |
Lecture Example 2 |
8:28 | |
| | |
Lecture Example 3 |
11:55 | |
| | |
Additional Example 4 |
4:12 | |
| | |
Additional Example 5 |
2:46 | |
| |
Volume by Method of Cylindrical Shells |
30:29 |
| | |
Intro |
0:00 | |
| | |
Important Equations |
0:50 | |
| | |
| Equation 1: Rotation about y-axis |
1:04 | |
| | |
| Equation 2: Rotation about y-axis (2 curves) |
7:34 | |
| | |
| Equation 3: Rotation about x-axis |
8:15 | |
| | |
Lecture Example 1 |
8:57 | |
| | |
Lecture Example 2 |
14:26 | |
| | |
Lecture Example 3 |
18:15 | |
| | |
Additional Example 4 |
4:45 | |
| | |
Additional Example 5 |
3:45 | |
| |
Average Value of a Function |
16:31 |
| | |
Intro |
0:00 | |
| | |
Important Equations |
0:11 | |
| | |
| Origin of Formula |
0:34 | |
| | |
Lecture Example 1 |
2:51 | |
| | |
Lecture Example 2 |
5:30 | |
| | |
Lecture Example 3 |
8:13 | |
| | |
Additional Example 4 |
2:40 | |
| | |
Additional Example 5 |
3:23 | |
| VIII. Extra |
| |
Graphs of f, f', f'' |
23:58 |
| | |
Intro |
0:00 | |
| | |
Slope Function of f(x) |
0:41 | |
| | |
| Slope is Zero |
0:53 | |
| | |
| Slope is Positive |
1:03 | |
| | |
| Slope is Negative |
1:13 | |
| | |
Slope Function of f'(x) |
1:31 | |
| | |
| Slope is Zero |
1:42 | |
| | |
| Slope is Positive |
1:48 | |
| | |
| Slope is Negative |
1:54 | |
| | |
Lecture Example 1 |
2:23 | |
| | |
Lecture Example 2 |
8:06 | |
| | |
Lecture Example 3 |
12:36 | |
| | |
Additional Example 4 |
3:11 | |
| | |
Additional Example 5 |
3:31 | |
| |
Slope Fields for Differential Equations |
18:32 |
| | |
Intro |
0:00 | |
| | |
Things to Remember |
0:13 | |
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| Graphic Description |
0:42 | |
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Lecture Example 1 |
1:44 | |
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Lecture Example 2 |
6:59 | |
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Lecture Example 3 |
9:46 | |
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Additional Example 4 |
3:09 | |
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Additional Example 5 |
2:01 | |
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Separable Differential Equations |
17:04 |
| | |
Intro |
0:00 | |
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Differential Equations |
0:10 | |
| | |
| Focus on Exponential Growth/Decay |
0:27 | |
| | |
| Separating Variables |
0:47 | |
| | |
Lecture Example 1 |
1:35 | |
| | |
Lecture Example 2 |
6:41 | |
| | |
Lecture Example 3 |
9:36 | |
| | |
Additional Example 4 |
2:56 | |
| | |
Additional Example 5 |
2:10 | |