# Math 210: Calculus I

### 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

- 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.

UMKC's Professor Richard Delaware in Lecture 1: A Review of Precalculus.
16 ratings

### Video Lectures & Study Materials

Visit the official course website for more study materials: http://cas.umkc.edu/math/VSI/RDvsiCalc.htm

# Lecture Play Lecture
I. Unit 0 - Functions: A Review of Precalculus
1 Beginning Play Video
2 Graphing Technology Play Video
3 New Functions From Old Play Video
4 Families of Functions Play Video
5 Trigonometry for Calculus Play Video
6 Inverse Functions Play Video
7 Exponential & Logarithmic Functions Play Video
II. Unit 1 - Limits of Functions: Approach & Destination
8 Intuitive Beginning Play Video
9 The Algebra of Limits as x -> a Play Video
10 Continuous Functions Play Video
11 Trigonometric Functions Play Video
III. Unit 2 - The Derivative of a Function
12 Measuring Rates of Change Play Video
13 What is a Derivative? Play Video
14 Finding Derivatives I: Basic Rules Play Video
15 Finding Derivatives II Play Video
16 Finding Derivatives III Play Video
17 Finding Derivatives IV Play Video
18 When Rates of Change are Related Play Video
19 More on Derivatives Play Video
IV. Unit 3 - Some Special Derivatives
20 Implicit Differentiation Play Video
21 Derivatives Involving Logarithms Play Video
22 Derivatives Involving Inverses Play Video
23 Finding Limits Using Differentiation Play Video
V. Unit 4 - The Derivative Applied
24 Analyzing the Graphs of Functions I Play Video
25 Analyzing the Graphs of Functions II Play Video
26 Analyzing the Graphs of Functions III Play Video
27 Analyzing the Graphs of Functions IV Play Video
28 Optimization Problems Play Video
29 Newton's Method for Approximating Roots of Equations Play Video
30 The Mean Value Theorem for Derivatives Play Video
31 One-Dimensional Motion & the Derivative Play Video
VI. Unit 5 - The Integral of a Function
32 The Question of Area Play Video
33 The Indefinite Integral Play Video
34 Indefinite Integration by Substitution Play Video
35 Area Defined as a Limit Play Video
36 The Definite Integral Play Video
37 The Fundamental Theorem of Calculus Play Video
38 One-Dimensional Motion & the Integral Play Video
39 Definite Integration by Substitution Play Video
VII. Unit 6 - The Definite Integral Applied
40 Plane Area Play Video
41 Volumes I Play Video
42 Volumes II Play Video
43 Length of a Plane Curve Play Video
44 Average Value of a Function Play Video
45 Work Play Video

Matt Smith wrote 9 years ago.
These videos have been posted on YouTube by UMKC (The Uni of
Missouri at Kansas City)

richy wrote 10 years ago.
this guy is a genuis, even if u have no pre knowledge u can
understand everything

Syd Dogonniuck wrote 11 years ago.
The last example you did with the absolute value was very

pratik wrote 11 years ago.
thanks! really useful and very well explanations

idiado esosa wrote 11 years ago.
how do i get your calculus lecture on a cd

ZRROBHERTTS L-OWWUSU-GYAW wrote 11 years ago.
Hi I have enjoyed the lectures very much. What a great
lecturer. I was wondering, where can I get calculus 2
lectures - if there is?

Wonder wrote 11 years ago.
solve problems

chandan kumar wrote 12 years ago.
This is a very good video and one can learn a lot from by
watching and observing this .BUT THIS IS VERY UNFORUTNET
IS PROVIDED BY THIS SITE IS VERY BAD AND DOES NOT PROVIDES
ANY GOOD PLATEFORM ATALL.

menna wrote 12 years ago.
what do i do when it says>>the video is not available
right now???

blank frank wrote 12 years ago.
This is great! Thank you! The lectures that are unavailable
can be found at the end of the previous lecture. ie, lecture
5 is included with lecture 4. This has been a wonderful
supplement to my Calculus class. However, Professor Delaware
wastes A LOT of paper! Get this guy a smart board, please.

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