Calculus I (Math 210)
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Listing of the Videos and Their Contents
Calculus I (Math 210) - Recorded in 2005
Video Professor: Richard Delaware
- 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
PDF copies of all Calculus I pages on the Videos
UNIT 0 - FUNCTIONS: A Review of Precalculus
[2 hr. 33 min.]
Beginning [36.5 min.]
- Definition of a Function [7.5 min.]
- Visualizing Functions: Graphs [10.5 min.]
- Domain (& Range) of Functions [7.5 min.]
- Some Exercises [11 min.]
Graphing Technology [11.5 min.]
- Viewing Windows [3.5 min.]
- Zooming In or Out [2.5 min.]
- Errors in Resolution [5.5 min.]
New Functions From Old [26.5 min.]
- Operations on Functions [10 min.]
- How Operations Affect Function Graphs [6.5 min.]
- Functions with Symmetric Graphs [2 min.]
- Some Exercises [8 min.]
Families of Functions [11 min.]
- The Power Function Family y = xp [7 min.]
- The Polynomial Function, and Rational Function Families [4 min.]
Trigonometry for Calculus [29.5 min.]
- 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.]
Inverse Functions [20 min.]
- A Function Inverse to Another Function [6 min.]
- When do Inverse Functions (& Their Graphs) Exist? [4 min.]
- Inverse Trigonometric Functions [10 min.]
Exponential & Logarithmic Functions [18.5 min.]
- The Exponential Function Family [6 min.]
- The Logarithmic Function Family [6.5 min.]
- Solving Exponential & Logarithmic Equations [6 min.]
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UNIT 1 - LIMITS of Functions: Approach & Destination
[5 hr. 4 min.]
Intuitive Beginning [1 hr. 19 min.]
- 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.]
The Algebra of Limits as x -> a [1 hr. 5.5 min.]
- 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.]
The Algebra of Limits as x -> +/- inf : End Behavior [1 hr. 2.5 min.]
- 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), ex, and More [7 min.]
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Continuous Functions [1 hr. 1 min.]
- 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.]
Trigonometric Functions [31.5 min.]
- 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.]
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UNIT 2 - The DERIVATIVE of a Function
[4 hr. 31 min.]
Measuring Rates of Change [54.5 min.]
- 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.]
What is a Derivative? [46 min.]
- 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.]
Finding Derivatives I: Basic Rules [32 min.]
- 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.]
Finding Derivatives II: [34 min.]
- The Product Rule [14.5 min.]
- The Quotient Rule [9 min.]
- Some Exercises [10 min.]
Finding Derivatives III: [25 min.]
- The Sine Function [5 min.]
- The Other Trigonometric Functions [9 min.]
- Some Applications [11 min.]
Finding Derivatives IV: [31.5 min.]
- The Chain Rule: Derivatives of Compositions of Functions [14.5 min.]
- Generalized Derivative Formulas [5.5 min.]
- Some Exercises [8 min.]
When Rates of Change are Related [35.5 min.]
- Differentiating Equations to "Relate Rates" [10 min.]
- A Strategy [14.5 min.]
- An Exercise [11 min.]
More on Derivatives [12 min.]
- Local Linear Approximations of Non-Linear Functions [7 min.]
- Defining "dx" and "dy" Alone [5 min.]
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UNIT 3 - Some Special DERIVATIVES
[1 hr. 26 min.]
Implicit Differentiation [26.5 min.]
- 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 Involving Logarithms [28.5 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.]
Derivatives Involving Inverses [29.5 min.]
- Derivatives of Inverse Functions [10 min.]
- Derivatives of Exponential Functions [7.5 min.]
- Derivatives of Inverse Trigonometric Functions [6 min.]
- Some Exercises [5 min.]
Finding Limits Using Differentiation [41 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.]
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UNIT 4 - The DERIVATIVE Applied
[6 hr. 53 min.]
Analyzing the Graphs of Functions I [1 hr. 7 min.]
- Increasing & Decreasing Functions: The 1st Derivative Applied [16 min.]
- Functions Concave Up or Concave Down: The 2nd Derivative Applied [14 min.]
- When Concavity Changes: Inflection Points [19 min.]
- Logistic Growth Curves: A Brief Look [3 min.]
- Some Exercises [14 min.]
Analyzing the Graphs of Functions II [1 hr. .5 min.]
- Local Maximums & Minimums [11 min.]
- The 1st Derivative Test for Local Maximums & Minimums [7.5 min.]
- The 2nd Derivative Test for Local Maximums & Minimums [9.5 min.]
- Polynomial Function Graphs [15 min.]
- Some Exercises [17.5 min.]
Analyzing the Graphs of Functions III [56.5 min.]
- 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.]
Analyzing the Graphs of Functions IV [43 min.]
- 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.]
Optimization Problems [1 hr. 2.5 min.]
- 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.]
Newton's Method for Approximating Roots of Equations [17.5 min.]
- Development of the Method [12 min.]
- Strength & Weaknesses of the Method [5.5 min.]
The Mean Value Theorem for Derivatives [48.5 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.]
One-Dimensional Motion & the Derivative [36.5 min.]
- Rectilinear Motion Revisited [4.5 min.]
- Velocity, Speed, & Acceleration [12 min.]
- Analyzing a Position Graph [8.5 min.]
- An Exercise [11.5 min.]
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UNIT 5 - The INTEGRAL of a Function
[4 hr. 55 min.]
The Question of Area [17.5 min.]
- Brief History and Overview [17.5 min.]
The Indefinite Integral [1 hr. 6 min.]
- "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.]
Indefinite Integration by Substitution [36.5 min.]
- 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.]
Area Defined as a Limit [37 min.]
- 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.]
The Definite Integral [39.5 min.]
- 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.]
The Fundamental Theorem of Calculus [45 min.]
- 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.]
One-Dimensional Motion & the Integral [40 min.]
- Position, Velocity, Distance, & Displacement [16 min.]
- Uniformly Accelerated Motion [12 min.]
- The Free Fall Motion Model [6.5 min.]
- An Exercise [5 min.]
Definite Integration by Substitution [13 min.]
- Extending the Substitution Method of Integration to Definite Integrals [9 min.]
- Some Exercises [4 min.]
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UNIT 6 - The DEFINITE INTEGRAL Applied
[2 hr. 40.5 min.]
Plane Area [23.5 min.]
- 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 I [48.5 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.]
Volumes II [20.5 min.]
- Volumes of Solids of Revolution: Cylindrical Shells [14.5 min.]
- An Exercise [6 min.]
Length of a Plane Curve [18 min.]
- Finding Arc Lengths [11.5 min.]
- Finding Arc Lengths of Parametric Curves [6.5 min.]
Average Value of a Function [13 min.]
- Average (Mean) Value of a Continuous Function [13 min.]
Work [37 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.]
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