Math 210: Calculus I
Video Lectures
Displaying all 45 video lectures.
I. Unit 0 - Functions: A Review of Precalculus | |
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Lecture 1 Play Video |
Beginning In this video lecture, UMKC's Professor Richard Delaware discusses: - Definition of a Function - Visualizing Functions: Graphs - Domain (& Range) of Functions - Some Exercises |
Lecture 2 Play Video |
Graphing Technology In this video lecture, UMKC's Professor Richard Delaware discusses: - Viewing Windows - Zooming In or Out - Errors in Resolution |
Lecture 3 Play Video |
New Functions From Old In this video lecture, UMKC's Professor Richard Delaware discusses: - Operations on Functions - How Operations Affect Function Graphs - Functions with Symmetric Graphs - Some Exercisess |
Lecture 4 Play Video |
Families of Functions In this video lecture, UMKC's Professor Richard Delaware discusses: - The Power Function Family y = xp - The Polynomial Function, and Rational Function Families |
Lecture 5 Play Video |
Trigonometry for Calculus In this video lecture, UMKC's Professor Richard Delaware discusses: - Right Triangle Trigonometry - Trigonometric Graphs - Handy Trigonometric Identities - Laws of Sine and Cosine - Trigonometric Families |
Lecture 6 Play Video |
Inverse Functions In this video lecture, UMKC's Professor Richard Delaware discusses: - A Function Inverse to Another Function - When do Inverse Functions (& Their Graphs) Exist? - Inverse Trigonometric Functions |
Lecture 7 Play Video |
Exponential & Logarithmic Functions In this video lecture, UMKC's Professor Richard Delaware discusses: - The Exponential Function Family - The Logarithmic Function Family - Solving Exponential & Logarithmic Equations |
II. Unit 1 - Limits of Functions: Approach & Destination | |
Lecture 8 Play Video |
Intuitive Beginning In this video lecture, UMKC's Professor Richard Delaware discusses: - A New Tool: The "Limit" - Some Limit Examples - Two-sided & One-sided Limits - Limits that Fail to Exist: When f(x) grows without bound - Limits at Infinity: When x grows without bound - More Limits that Fail to Exist: Infinity & Infinite Indecision - An Exercise on Limits |
Lecture 9 Play Video |
The Algebra of Limits as x -> a In this video lecture, UMKC's Professor Richard Delaware discusses: - Basic Limits - Limits of Sums, Differences, Products, Quotients, & Roots - Limits of Polynomial Functions - Limits of Rational Functions & the Apparent Appearance of 0/0 - Limits of Piecewise-Defined Functions: When One-sided Limits Matter! - Some Exercises |
Lecture 10 Play Video |
Continuous Functions In this video lecture, UMKC's Professor Richard Delaware discusses: - Functions Continuous (or not) at a Single Point x=c - Functions Continuous on an Interval - Properties & Combinations of Continuous Functions - The Intermediate Value Theorem & Approximating Roots: f(x) = 0 - Some Exercises |
Lecture 11 Play Video |
Trigonometric Functions In this video lecture, UMKC's Professor Richard Delaware discusses: - The 6 Trigonometric Functions: Continuous on Their Domains - When Inverses are Continuous - Finding a Limit by "Squeezing" - Sin(x)/x -> 1 as x -> 0, and Other Limit Tales - Some Exercises |
III. Unit 2 - The Derivative of a Function | |
Lecture 12 Play Video |
Measuring Rates of Change In this video lecture, UMKC's Professor Richard Delaware discusses: - Slopes of Tangent Lines - One-Dimensional Motion - Average Velocity - Instantaneous Velocity - General Rates of Change - Some Exercises |
Lecture 13 Play Video |
What is a Derivative? In this video lecture, UMKC's Professor Richard Delaware discusses: - Definition of the Derived Function: The "Derivative", & Slopes of Tangent Lines - Instantaneous Velocity - Functions Differentiable (or not!) at a Single Point - Functions Differentiable on an Interval - A Function Differentiable at a point is Continuous at that point - Other Derivative Notations - Some Exercises |
Lecture 14 Play Video |
Finding Derivatives I: Basic Rules In this video lecture, UMKC's Professor Richard Delaware discusses: - The Power Rule - Constant Multiple, Sum, & Difference Rules - Notation for Derivatives of Derivatives - Some Exercises |
Lecture 15 Play Video |
Finding Derivatives II In this video lecture, UMKC's Professor Richard Delaware discusses: - The Product Rule - The Quotient Rule - Some Exercises |
Lecture 16 Play Video |
Finding Derivatives III In this video lecture, UMKC's Professor Richard Delaware discusses: - The Sine Function - The Other Trigonometric Functions - Some Applications |
Lecture 17 Play Video |
Finding Derivatives IV In this video lecture, UMKC's Professor Richard Delaware discusses: - The Chain Rule: Derivatives of Compositions of Functions - Generalized Derivative Formulas - Some Exercises |
Lecture 18 Play Video |
When Rates of Change are Related In this video lecture, UMKC's Professor Richard Delaware discusses: - Differentiating Equations to "Relate Rates" - A Strategy - An Exercise |
Lecture 19 Play Video |
More on Derivatives In this video lecture, UMKC's Professor Richard Delaware discusses: - Local Linear Approximations of Non-Linear Functions - Defining "dx" and "dy" Alone |
IV. Unit 3 - Some Special Derivatives | |
Lecture 20 Play Video |
Implicit Differentiation In this video lecture, UMKC's Professor Richard Delaware discusses: - Functions Defined Implicitly - Derivatives of Functions Defined Implicitly - The Derivative of Rational Powers of x - Some Exercises |
Lecture 21 Play Video |
Derivatives Involving Logarithms In this video lecture, UMKC's Professor Richard Delaware discusses: - Derivatives of Logarithmic Functions - The "Logarithmic Differentiation" Technique - The Derivative of Irrational Powers of x - Some Exercises |
Lecture 22 Play Video |
Derivatives Involving Inverses In this video lecture, UMKC's Professor Richard Delaware discusses: - Derivatives of Inverse Functions - Derivatives of Exponential Functions - Derivatives of Inverse Trigonometric Functions - Some Exercises |
Lecture 23 Play Video |
Finding Limits Using Differentiation In this video lecture, UMKC's Professor Richard Delaware discusses: - Limits of Quotients that appear to be "Indeterminate": The Rule of L'Hopital - Some Examples - Finding Other "Indeterminate" Limits |
V. Unit 4 - The Derivative Applied | |
Lecture 24 Play Video |
Analyzing the Graphs of Functions I In this video lecture, UMKC's Professor Richard Delaware discusses: - Increasing & Decreasing Functions: The 1st Derivative Applied - Functions Concave Up or Concave Down: The 2nd Derivative Applied - When Concavity Changes: Inflection Points - Logistic Growth Curves: A Brief Look - Some Exercises |
Lecture 25 Play Video |
Analyzing the Graphs of Functions II In this video lecture, UMKC's Professor Richard Delaware discusses: - Local Maximums & Minimums - The 1st Derivative Test for Local Maximums & Minimums - The 2nd Derivative Test for Local Maximums & Minimums - Polynomial Function Graphs - Some Exercises |
Lecture 26 Play Video |
Analyzing the Graphs of Functions III In this video lecture, UMKC's Professor Richard Delaware discusses: - What to Look For in a Graph - Rational Function Graphs - Functions Whose Graphs have Vertical Tangents or Cusps - Some Exercises |
Lecture 27 Play Video |
Analyzing the Graphs of Functions IV In this video lecture, UMKC's Professor Richard Delaware discusses: - Global Maximums & Minimums - Global Extrema on (finite) Closed Intervals - Global Extrema on (finite or infinite) Open Intervals - When a Single Local Extremum must be Global - Some Exercises |
Lecture 28 Play Video |
Optimization Problems In this video lecture, UMKC's Professor Richard Delaware discusses: - Applied Maximum & Minimum Problems - Optimization over a (finite) Closed Interval - Maximizing Area or Volume, Minimizing Cost - Optimization over Other Intervals: Minimizing Materials or Distance - An Economics Application: Cost, Revenue, Profit, & Marginal Analysis - Some Exercises |
Lecture 29 Play Video |
Newton's Method for Approximating Roots of Equations In this video lecture, UMKC's Professor Richard Delaware discusses: - Development of the Method - Strength & Weaknesses of the Method |
Lecture 30 Play Video |
The Mean Value Theorem for Derivatives In this video lecture, UMKC's Professor Richard Delaware discusses: - A Special Case of the Mean Value Theorem: Rolle's Theorem - The (Full) Mean Value Theorem for Derivatives - Direct Consequences of This Mean Value Theorem - Some Exercises |
Lecture 31 Play Video |
One-Dimensional Motion & the Derivative In this video lecture, UMKC's Professor Richard Delaware discusses: - Rectilinear Motion Revisited - Velocity, Speed, & Acceleration - Analyzing a Position Graph - An Exercise |
VI. Unit 5 - The Integral of a Function | |
Lecture 32 Play Video |
The Question of Area In this video lecture, UMKC's Professor Richard Delaware discusses: - Brief History and Overview |
Lecture 33 Play Video |
The Indefinite Integral In this video lecture, UMKC's Professor Richard Delaware discusses: - "Undo-ing" a Derivative: Antiderivative = Indefinite Integral - Finding Antiderivatives - The Graphs of Antiderivatives: Integral Curves & the Slope Field Approximation - The Antiderivative as Solution of a Differential Equation - Some Exercises |
Lecture 34 Play Video |
Indefinite Integration by Substitution In this video lecture, UMKC's Professor Richard Delaware discusses: - The Substitution Method of Indefinite Integration: A Major Technique - Straightforward Substitutions - More Interesting Substitutions - Some Exercises |
Lecture 35 Play Video |
Area Defined as a Limit In this video lecture, UMKC's Professor Richard Delaware discusses: - The Sigma Shorthand for Sums - Summation Properties & Handy Formulas - Definition of Area "Under a Curve" - Net "Area" - Approximating Area Numerically - Some Exercises |
Lecture 36 Play Video |
The Definite Integral In this video lecture, UMKC's Professor Richard Delaware discusses: - The Definite Integral Defined - The Definite Integral of a Continuous Function = Net "Area" Under a Curve - Finding Definite Integrals - A Note on the Definite Integral of a Discontinuous Function - Some Exercises |
Lecture 37 Play Video |
The Fundamental Theorem of Calculus In this video lecture, UMKC's Professor Richard Delaware discusses: - The Fundamental Theorem of Calculus, Part 1 - Definite & Indefinite Integrals Related - The Mean Value Theorem for Integrals - The Fundamental Theorem of Calculus, Part 2 - Differentiation & Integration are Inverse Processes - Some Exercises |
Lecture 38 Play Video |
One-Dimensional Motion & the Integral In this video lecture, UMKC's Professor Richard Delaware discusses: - Position, Velocity, Distance, & Displacement - Uniformly Accelerated Motion - The Free Fall Motion Model - An Exercise |
Lecture 39 Play Video |
Definite Integration by Substitution In this video lecture, UMKC's Professor Richard Delaware discusses: - Extending the Substitution Method of Integration to Definite Integrals - Some Exercises |
VII. Unit 6 - The Definite Integral Applied | |
Lecture 40 Play Video |
Plane Area In this video lecture, UMKC's Professor Richard Delaware discusses: - Area Between Two Curves [One Floor, One Ceiling] - Area Between Two Curves [One Left, One Right] - An Exercise |
Lecture 41 Play Video |
Volumes I In this video lecture, UMKC's Professor Richard Delaware discusses: - Volumes by Slicing - Volumes of Solids of Revolution: Disks - Volumes of Solids of Revolution: Washers - Some Exercises *Please note the correction that appears on screen at 10:53. |
Lecture 42 Play Video |
Volumes II In this video lecture, UMKC's Professor Richard Delaware discusses: - Volumes of Solids of Revolution: Cylindrical Shells - An Exercise |
Lecture 43 Play Video |
Length of a Plane Curve In this video lecture, UMKC's Professor Richard Delaware discusses: - Finding Arc Lengths - Finding Arc Lengths of Parametric Curves |
Lecture 44 Play Video |
Average Value of a Function In this video lecture, UMKC's Professor Richard Delaware discusses: - Average (Mean) Value of a Continuous Function |
Lecture 45 Play Video |
Work In this video lecture, UMKC's Professor Richard Delaware discusses: - Work Done by a Constant Force - Work Done by a Variable Force - Do-It-Yourself Integrals: Pumping Fluids - Work as Change in Kinetic Energy - An Exercise |