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.

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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 
    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 
    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 

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.

Additional Features:

  • Free Sample Lessons
  • Closed Captioning (CC)
  • Practice Questions
  • Downloadable Lecture Slides
  • 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:

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