### Lecture Description

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

### Course Index

- Beginning
- Graphing Technology
- New Functions From Old
- Families of Functions
- Trigonometry for Calculus
- Inverse Functions
- Exponential & Logarithmic Functions
- Intuitive Beginning
- The Algebra of Limits as x -> a
- Continuous Functions
- Trigonometric Functions
- Measuring Rates of Change
- What is a Derivative?
- Finding Derivatives I: Basic Rules
- Finding Derivatives II
- Finding Derivatives III
- Finding Derivatives IV
- When Rates of Change are Related
- More on Derivatives
- Implicit Differentiation
- Derivatives Involving Logarithms
- Derivatives Involving Inverses
- Finding Limits Using Differentiation
- Analyzing the Graphs of Functions I
- Analyzing the Graphs of Functions II
- Analyzing the Graphs of Functions III
- Analyzing the Graphs of Functions IV
- Optimization Problems
- Newton's Method for Approximating Roots of Equations
- The Mean Value Theorem for Derivatives
- One-Dimensional Motion & the Derivative
- The Question of Area
- The Indefinite Integral
- Indefinite Integration by Substitution
- Area Defined as a Limit
- The Definite Integral
- The Fundamental Theorem of Calculus
- One-Dimensional Motion & the Integral
- Definite Integration by Substitution
- Plane Area
- Volumes I
- Volumes II
- Length of a Plane Curve
- Average Value of a Function
- Work

### Course Description

In this course, UMKC's Professor Richard Delaware gives 45 video lectures on Calculus, in association with UMKC's Video Based Supplemental Instruction Program. **Topics **covered in this course are:

**Unit 0 - Functions: A Review of Precalculus**

- Beginning

- Graphing Technology

- New Functions From Old

- Families of Functions

- Trigonometry for Calculus

- Inverse Functions

- Exponential & Logarithmic Functions

**Unit 1 - Limits of Functions: Approach & Destination**

- Intuitive Beginning

- The Algebra of Limits as x -> a

- The Algebra of Limits as x -> +/- inf : End Behavior

- < Continuous Functions

- Trigonometric Functions

**Unit 2 - The Derivative of a Function**

- Measuring Rates of Change

- What is a Derivative?

- Finding Derivatives I:

- Finding Derivatives II:

- Finding Derivatives II:

- Finding Derivatives IV:

- When Rates of Change are Related

- More on Derivatives

**Unit 3 - Some Special Derivatives**

- Implicit Differentiation

- Derivatives Involving Logarithms

- Derivatives Involving Inverses

- Finding Limits Using Differentiation

**Unit 4 - The Derivative Applied**

- Analyzing the Graphs of Functions I

- Analyzing the Graphs of Functions II

- Analyzing the Graphs of Functions III

- Analyzing the Graphs of Functions IV

- Optimization Problems

- Newton's Method for Approximating Roots of Equations

- The Mean Value Theorem for Derivatives

- One-Dimensional Motion & the Derivative

**Unit 5 - The Integral of a Function**

- The Question of Area

- The Indefinite Integral

- Indefinite Integration by Substitution

- Area Defined as a Limit

- The Definite Integral

- The Fundamental Theorem of Calculus

- One-Dimensional Motion & the Integral

- Definite Integration by Substitution

**Unit 6 - The Definite Integral Applied**

- Plane Area

- Volumes I

- Volumes II

- Length of a Plane Curve

- Average Value of a Function

- Work

**Original Course Name: **VSI Calculus I (Math 210) Video Course

**Links:**

- Listing of the Calculus I Videos and Their Contents

**Textbook: ***Calculus *(Early Transcendentals version), 8th edition, by Anton, Bivens, and Davis (2005), Wiley.

**Brief History of this Video Course**

- In 2005, Richard Delaware spent 8 months recording a Calculus I course on video for the **VSI **(Video-based Supplemental Instruction) program at UMKC. "Supplemental Instruction" in this sense does not indicate a remedial course, and no content or conceptual richness has been sacrificed. College Algebra was the first mathematics VSI course to be recorded, but the VSI concept which has been in place at UMKC since 1992 has attracted national attention because of its success in 3 other video courses taken by students at UMKC and at 30 other institutions in Missouri.

- Although video technology is commonplace, the pedagogy is fresh. Students view the tapes in the presence of a trained **facilitator**, and have control over the flow of information; lectures are stopped, started, and replayed as needed. When the facilitator pushes the stop button, as cued on the video, students have time to work problems, ask questions, make observations, resolve confusions, collect their thoughts, and more.

- This VSI course has been offered since **Fall 2005** off the UMKC campus to advanced students at rural high schools, and on the UMKC campus to students requiring more time and assistance to succeed in Calculus I.

- The course was recorded in a UMKC video studio by the Multimedia Technology Services division of Instructional Technologies.