Home » Mathematics » College Calculus: Level I
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15:13

# College Calculus 1 Online CourseDr. Jenny Switkes, Ph.D. Facebook Twitter More

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376 ratings • 34 reviews
• 39 Lessons (15hr : 13min)
• Audio: English

Join Dr. Jennifer Switkes in her College Calculus 1 online course where she covers all the important topics with clear explanations, tons of step-by-step examples, and analysis of common student pitfalls.

## Section 1: 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
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

## Section 2: 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
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
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
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
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

## Section 3: 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
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
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
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
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
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
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
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
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

## Section 4: 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
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
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
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
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
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

## Section 5: 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
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
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
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
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
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
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

## Section 6: 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
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
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

## Section 7: 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
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
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
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

## Section 8: 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
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
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

Duration: 15 hours, 13 minutes

Number of Lessons: 39

Ideal for college students taking their first course in Calculus, or for high schoolers who want to see what Calculus is all about. Dr. Switkes will show you how to reap the rewards of your hard work while demonstrating the beauty and importance of math. Complete the rest of your journey with Dr. Murray’s Calculus 2 course also on Educator.

• Free Sample Lessons
• Closed Captioning (CC)
• Practice Questions
• Study Guides

Topics Include:

• Limits
• Power & Product Rule
• Implicit Differentiation
• First & Second Derivative Test
• L’Hopital’s Rule
• Integrals
• Riemann Sums
• Area Between Curves
• Volume Method of Cylindrical Shells

Dr. Jennifer Switkes has taught mathematics for 15+ years in the university setting and has garnered top review scores from her students.

### Student Testimonials:

“Very smooth teaching — no stuttering and pauses so easy to follow the train of thought. Very well done!!!!” — John D.

“Thank you so much for your ultra-detailed explanation.” — Eric N.

"This material in this video was very well explained. Thank you, Professor! keep up the good work." — Wayne P.

"Very clear lecture on this complicated topic. I liked the schema she presented as an aid in organizing your thinking in solving these kinds of problems." — John P.

“Very nice lecture. Great examples. This is what my instructor went over in class today and this explained it the same or better. I understand the concepts better now.” — Scott J.

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#### Student Feedback

4.4

34 Reviews

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By Joyce FerreiraOctober 27, 2017
Dear Prof. Switkes,

It has been a while that I took a calculus class and I need to review partial differentiation, so I can be able to follow the lectures on my physical chemistry class. Please, I would liek to ask you what calculus lecture should I watch? Thank you. Best regards.
By Zhe YangNovember 3, 2014
you did a wonderful job explaining it, thanks!
By edder villegasOctober 26, 2014
on example 2, can you explain please how did we get 0 and 4 as the values for the other two second travel options, thank you
By Kevin GoldenSeptember 30, 2014
Great lecture!!!
very cool! you do a great jobâ€¦i've never taken calculus before and just happened to be browsing..kind of want to take the actual course now!

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