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  
 
 Example: Vertical Line Test 
0:47  
 
Function Examples 
1:57  
 
 Example: Squared 
2:10  
 
 Example: Natural Log 
2:41  
 
 Example: Exponential 
3:21  
 
 Example: Not Function 
3:54  
 
Odd and Even Functions 
4:39  
 
 Example: Even Function 
5:10  
 
 Example: Odd Function 
5:53  
 
Odd and Even Examples 
6:48  
 
 Odd Function 
6:55  
 
 Even Function 
8:43  
 
Increasing and Decreasing Functions 
10:15  
 
 Example: Increasing 
10:42  
 
 Example: Decreasing 
10:55  
 
Increasing and Decreasing Examples 
11:41  
 
 Example: Increasing 
11:48  
 
 Example: Decreasing 
12:33  
 
Types of Functions 
13:32  
 
 Polynomials 
13:45  
 
 Powers 
14:06  
 
 Trigonometric 
14:34  
 
 Rational 
14:50  
 
 Exponential 
15:13  
 
 Logarithmic 
15:29  
 
Lecture Example 1 
15:55  
 
Lecture Example 2 
17:51  
 
Additional Example 3 
2:35  
 
Additional Example 4 
2:33  

Compositions of Functions 
12:29 
 
Intro 
0:00  
 
Compositions 
0:09  
 
 Alternative Notation 
0:32  
 
 Three Functions 
0:47  
 
Lecture Example 1 
1:19  
 
Lecture Example 2 
3:25  
 
Lecture Example 3 
6:45  
 
Additional Example 4 
2:02  
 
Additional Example 5 
2:35  
II. Limits 

Average and Instantaneous Rates of Change 
20:59 
 
Intro 
0:00  
 
Rates of Change 
0:11  
 
 Average Rate of Change 
0:21  
 
 Instantaneous Rate of Change 
0:33  
 
 Slope of the Secant Line 
0:46  
 
 Slope of the Tangent Line 
1:00  
 
Lecture Example 1 
1:14  
 
Lecture Example 2 
6:36  
 
Lecture Example 3 
11:30  
 
Additional Example 4 
2:49  
 
Additional Example 5 
3:40  

Limit Investigations 
22:37 
 
Intro 
0:00  
 
What is a Limit? 
0:10  
 
Lecture Example 1 
0:56  
 
Lecture Example 2 
5:28  
 
Lecture Example 3 
9:27  
 
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  
 
Lecture Example 2 
5:16  
 
Lecture Example 3 
8:15  
 
Lecture Example 4 
12:58  
 
Additional Example 5 
5:01  
 
Additional Example 6 
5:35  

Formal Definition of a Limit 
23:39 
 
Intro 
0:00  
 
Formal Definition 
0:13  
 
 Template 
0:55  
 
 Epsilon and Delta 
1:24  
 
Lecture Example 1 
1:40  
 
Lecture Example 2 
9:20  
 
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  
 
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  
 
Lecture Example 2 
6:48  
 
Lecture Example 3 
11:22  
 
Additional Example 4 
4:21  
 
Additional Example 5 
3:51  

The Product Rule 
14:54 
 
Intro 
 
 
Statement of the Product Rule 
0:08  
 
Lecture Example 1 
0:41  
 
Lecture Example 2 
2:27  
 
Lecture Example 3 
5:03  
 
Additional Example 4 
4:11  
 
Additional Example 5 
2:25  

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  
 
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  
 
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  
 
Lecture Example 3 
15:54  
 
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  
 
 USubstitution 
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 xaxis (disks) 
0:27  
 
 Equation 2: Two curves about xaxis (washers) 
3:38  
 
 Equation 3: Rotation about yaxis 
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 yaxis 
1:04  
 
 Equation 2: Rotation about yaxis (2 curves) 
7:34  
 
 Equation 3: Rotation about xaxis 
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  
 
 Graphic Description 
0:42  
 
Lecture Example 1 
1:44  
 
Lecture Example 2 
6:59  
 
Lecture Example 3 
9:46  
 
Additional Example 4 
3:09  
 
Additional Example 5 
2:01  

Separable Differential Equations 
17:04 
 
Intro 
0:00  
 
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  