Course Information

Course

Subject:	Mathematics
Topic:	Calculus
Views:	126,982

Educator

Name:	University of Missouri-Kansas City (UMKC)
Type:	University

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Instructor

Name

Richard Delaware

Math 210: Calculus I

Video Lectures

Displaying all 45 video lectures.

I. Unit 0 - Functions: A Review of Precalculus
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