# Math 210: Calculus I

## Video Lectures

Displaying all 45 video lectures.
I. Unit 0 - Functions: A Review of Precalculus
Lecture 1

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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

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Graphing Technology

In this video lecture, UMKC's Professor Richard Delaware discusses:

- Viewing Windows

- Zooming In or Out

- Errors in Resolution
Lecture 3

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Finding Derivatives II

In this video lecture, UMKC's Professor Richard Delaware discusses:

- The Product Rule

- The Quotient Rule

- Some Exercises
Lecture 16

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Finding Derivatives III

In this video lecture, UMKC's Professor Richard Delaware discusses:

- The Sine Function

- The Other Trigonometric Functions

- Some Applications
Lecture 17

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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The Question of Area

In this video lecture, UMKC's Professor Richard Delaware discusses:

- Brief History and Overview
Lecture 33

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Volumes II

In this video lecture, UMKC's Professor Richard Delaware discusses:

- Volumes of Solids of Revolution: Cylindrical Shells

- An Exercise
Lecture 43

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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

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Average Value of a Function

In this video lecture, UMKC's Professor Richard Delaware discusses:

- Average (Mean) Value of a Continuous Function
Lecture 45

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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