• No reference on the videos is made to a particular text, although the course is based on the instructor's experience and the text: Calculus (Early Transcendentals version), 8th edition, by Anton, Bivens, and Davis (2005), Wiley.
• Times are approximate.
• There are many internal "Stop Tape" pauses for students to work problems or review.

Unit 0 - FUNCTIONS: A Review of Precalculus
Unit 1 - LIMITS of FUNCTIONS: Approach & Destination
Unit 2 - The DERIVATIVE of a Function
Unit 3 - Some Special DERIVATIVES
Unit 4 - The DERIVATIVE Applied
Unit 5 - The INTEGRAL of a Function
Unit 6 - The DEFINITE INTEGRAL Applied

Tape 1

• Definition of a Function [7.5 min.]
• Visualizing Functions: Graphs [10.5 min.]
• Domain (& Range) of Functions [7.5 min.]
• Some Exercises [11 min.]

• Viewing Windows [3.5 min.]
• Zooming In or Out [2.5 min.]
• Errors in Resolution [5.5 min.]

Tape 2

• Operations on Functions [10 min.]
• How Operations Affect Function Graphs [6.5 min.]
• Functions with Symmetric Graphs [2 min.]
• Some Exercises [8 min.]

• The Power Function Family y = x^p [7 min.]
• The Polynomial Function, and Rational Function Families [4 min.]

Tape 3

• Right Triangle Trigonometry [11.5 min.]
• Trigonometric Graphs [5 min.]
• Handy Trigonometric Identities [5 min.]
• Laws of Sine and Cosine [4 min.]
• Trigonometric Families [4 min.]

• A Function Inverse to Another Function [6 min.]
• When do Inverse Functions (& Their Graphs) Exist? [4 min.]
• Inverse Trigonometric Functions [10 min.]

• The Exponential Function Family [6 min.]
• The Logarithmic Function Family [6.5 min.]
• Solving Exponential & Logarithmic Equations [6 min.]

Tape 4

• A New Tool: The "Limit" [24 min.]
• Some Limit Examples [6.5 min.]
• Two-sided & One-sided Limits [17 min.]
• Limits that Fail to Exist: When f(x) grows without bound [9 min.]
• Limits at Infinity: When x grows without bound [11.5 min.]
• More Limits that Fail to Exist: Infinity & Infinite Indecision [6 min.]
• An Exercise on Limits [5 min.]

Tape 5

• Basic Limits [7.5 min.]
• Limits of Sums, Differences, Products, Quotients, & Roots [11 min.]
• Limits of Polynomial Functions [7 min.]
• Limits of Rational Functions & the Apparent Appearance of 0/0 [17 min.]
• Limits of Piecewise-Defined Functions: When One-sided Limits Matter! [12 min.]
• Some Exercises [11 min.]

Tape 6

• Basic Limits [4.5 min.]
• Limits of Sums, Differences, Products, Quotients, & Roots [10 min.]
• Limits of Polynomial Functions: Two End Behaviors [9 min.]
• Limits of Rational Functions: Three Types of End Behavior [16 min.]
• Limits of Functions with Radicals [9.5 min.]
• Some Exercises [6.5 min.]
• Limits of ln(x), e^x, and More [7 min.]

Tape 7

• Functions Continuous (or not!) at a Single Point x=c [14.5 min.]
• Functions Continuous on an Interval [6 min.]
• Properties & Combinations of Continuous Functions [14 min.]
• The Intermediate Value Theorem & Approximating Roots: f(x) = 0 [13 min.]
• Some Exercises [13.5 min.]

Tape 8

• The 6 Trigonometric Functions: Continuous on Their Domains [4 min.]
• When Inverses are Continuous [3 min.]
• Finding a Limit by "Squeezing" [6 min.]
• Sin(x)/x -> 1 as x -> 0, and Other Limit Tales [11 min.]
• Some Exercises [7.5 min.]

Tape 9

• Slopes of Tangent Lines [14 min.]
• One-Dimensional Motion [7 min.]
• Average Velocity [6.5 min.]
• Instantaneous Velocity [8 min.]
• General Rates of Change [8.5 min.]
• Some Exercises [10.5 min.]

Tape 10

• Definition of the Derived Function: The "Derivative", & Slopes of Tangent Lines [11 min.]
• Instantaneous Velocity [2 min.]
• Functions Differentiable (or not!) at a Single Point [9 min.]
• Functions Differentiable on an Interval [3 min.]
• A Function Differentiable at a point is Continuous at that point [6 min.]
• Other Derivative Notations [4 min.]
• Some Exercises [11 min.]

Tape 11

• The Power Rule [13.5 min.]
• Constant Multiple, Sum, & Difference Rules [5.5 min.]
• Notation for Derivatives of Derivatives [6 min.]
• Some Exercises [7 min.]

• The Product Rule [14.5 min.]
• The Quotient Rule [9 min.]
• Some Exercises [10 min.]

Tape 12

• The Sine Function [5 min.]
• The Other Trigonometric Functions [9 min.]
• Some Applications [11 min.]

• The Chain Rule: Derivatives of Compositions of Functions [14.5 min.]
• Generalized Derivative Formulas [5.5 min.]
• Some Exercises [8 min.]

Tape 13

• Differentiating Equations to "Relate Rates" [10 min.]
• A Strategy [14.5 min.]
• An Exercise [11 min.]

• Local Linear Approximations of Non-Linear Functions [7 min.]
• Defining "dx" and "dy" Alone [5 min.]

Tape 14

• Functions Defined Implicitly [7 min.]
• Derivatives of Functions Defined Implicitly [7.5 min.]
• The Derivative of Rational Powers of x [6 min.]
• Some Exercises [6 min.]

• Derivatives of Logarithmic Functions [14.5 min.]
• The "Logarithmic Differentiation" Technique [5.5 min.]
• The Derivative of Irrational Powers of x [3.5 min.]
• Some Exercises [5 min.]

Tape 15

• Derivatives of Inverse Functions [10 min.]
• Derivatives of Exponential Functions [7.5 min.]
• Derivatives of Inverse Trigonometric Functions [6 min.]
• Some Exercises [5 min.]

• Limits of Quotients that appear to be "Indeterminate": The Rule of L'Hopital [14 min.]
• Some Examples [11 min.]
• Finding Other "Indeterminate" Limits [16 min.]

Tape 16

• Increasing & Decreasing Functions: The 1^st Derivative Applied [16 min.]
• Functions Concave Up or Concave Down: The 2^nd Derivative Applied [14 min.]
• When Concavity Changes: Inflection Points [19 min.]
• Logistic Growth Curves: A Brief Look [3 min.]
• Some Exercises [14 min.]

Tape 17

• Local Maximums & Minimums [11 min.]
• The 1^st Derivative Test for Local Maximums & Minimums [7.5 min.]
• The 2^nd Derivative Test for Local Maximums & Minimums [9.5 min.]
• Polynomial Function Graphs [15 min.]
• Some Exercises [17.5 min.]

Tape 18

• What to Look For in a Graph [2 min.]
• Rational Function Graphs [19.5 min.]
• Functions Whose Graphs have Vertical Tangents or Cusps [16 min.]
• Some Exercises [18.5 min.]

Tape 19

• Global Maximums & Minimums [4.5 min.]
• Global Extrema on (finite) Closed Intervals [10 min.]
• Global Extrema on (finite or infinite) Open Intervals [13 min.]
• When a Single Local Extremum must be Global [4.5 min.]
• Some Exercises [12 min.]

Tape 20

• Applied Maximum & Minimum Problems [4 min.]
• Optimization over a (finite) Closed Interval:
  Maximizing Area or Volume, Minimizing Cost [21.5 min.]
• Optimization over Other Intervals: Minimizing Materials or Distance [11 min.]
• An Economics Application: Cost, Revenue, Profit, & Marginal Analysis [9 min.]
• Some Exercises [17 min.]

Tape 21

• Development of the Method [12 min.]
• Strength & Weaknesses of the Method [5.5 min.]

• A Special Case of the Mean Value Theorem: Rolle's Theorem [8.5 min.]
• The (Full) Mean Value Theorem for Derivatives [20 min.]
• Direct Consequences of This Mean Value Theorem [13 min.]
• Some Exercises [7 min.]

Tape 22

• Rectilinear Motion Revisited [4.5 min.]
• Velocity, Speed, & Acceleration [12 min.]
• Analyzing a Position Graph [8.5 min.]
• An Exercise [11.5 min.]

Tape 22 (con.)

• Brief History and Overview [17.5 min.]

Tape 23

• "Undo-ing" a Derivative: Antiderivative = Indefinite Integral [16 min.]
• Finding Antiderivatives [22 min.]
• The Graphs of Antiderivatives: Integral Curves & the Slope Field Approximation [16.5 min.]
• The Antiderivative as Solution of a Differential Equation [5 min.]
• Some Exercises [6.5 min.]

Tape 24

• The Substitution Method of Indefinite Integration: A Major Technique [7.5 min.]
• Straightforward Substitutions [10.5 min.]
• More Interesting Substitutions [11.5 min.]
• Some Exercises [7 min.]

Tape 25

• The Sigma Shorthand for Sums [13.5 min.]
• Summation Properties & Handy Formulas [9 min.]
• Definition of Area "Under a Curve" [15 min.]
• Net "Area" [4 min.]
• Approximating Area Numerically [2.5 min.]
• Some Exercises [6.5 min.]

Tape 26

• The Definite Integral Defined [11.5 min.]
• The Definite Integral of a Continuous Function = Net "Area" Under a Curve [6 min.]
• Finding Definite Integrals [10.5 min.]
• A Note on the Definite Integral of a Discontinuous Function [6 min.]
• Some Exercises [6.5 min.]

Tape 27

• The Fundamental Theorem of Calculus, Part 1 [15 min.]
• Definite & Indefinite Integrals Related [7.5 min.]
• The Mean Value Theorem for Integrals [9.5 min.]
• The Fundamental Theorem of Calculus, Part 2 [7 min.]
• Differentiation & Integration are Inverse Processes [2 min.]
• Some Exercises [5 min.]

Tape 28

• Position, Velocity, Distance, & Displacement [16 min.]
• Uniformly Accelerated Motion [12 min.]
• The Free Fall Motion Model [6.5 min.]
• An Exercise [5 min.]

• Extending the Substitution Method of Integration to Definite Integrals [9 min.]
• Some Exercises [4 min.]

Tape 29

• Area Between Two Curves [One Floor, One Ceiling] [11 min.]
• Area Between Two Curves [One Left, One Right] [7.5 min.]
• An Exercise [5.5 min.]

• Volumes by Slicing [12.5 min.]
• Volumes of Solids of Revolution: Disks [15.5 min.]
• Volumes of Solids of Revolution: Washers [12 min.]
• Some Exercises [8.5 min.]

Tape 30

• Volumes of Solids of Revolution: Cylindrical Shells [14.5 min.]
• An Exercise [6 min.]

• Finding Arc Lengths [11.5 min.]
• Finding Arc Lengths of Parametric Curves [6.5 min.]

Tape 31

• Average (Mean) Value of a Continuous Function [13 min.]

• Work Done by a Constant Force [3 min.]
• Work Done by a Variable Force [13.5 min.]
• Do-It-Yourself Integrals: Pumping Fluids [8 min.]
• Work as Change in Kinetic Energy [6 min.]
• An Exercise [5 min.]