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Math 210 - Calculus I

This is a collection of video lectures for Math 210: Calculus I from UMKC (University of Missouri-Kansas city). Consisting of 31 lectures taught by Professor Richard Delaware, this course introduces the concepts and techniques of differential calculus and integral calculus. The topics covered here include a review of precalculus, limits of functions, the derivative of a function, applications of differential calculus, the integral of a function, and applications of integral calculus.

Lecture 25 - Area Defined as a Limit

Time Lecture Chapters
[00:00:00] 1. The Sigma Shorthand for Sums
[00:13:20] 2. Summation Properties & Handy Formulas
[00:22:25] 3. Definition of Area "Under a Curve"
[00:37:30] 4. Net "Area"
[00:41:15] 5. Approximating Area Numerically
[00:43:55] 6. Some Exercises

Go to the Course Home or watch other lectures:

Lecture 01 - Beginning, Graphing Technology
Lecture 02 - New Functions from Old, Families of Functions
Lecture 03 - Trigonometry for Calculus, Inverse Functions, Exponential & Logarithmic Functions
Lecture 04 - Intuitive Beginning
Lecture 05 - The Algebra of Limits as x -> a
Lecture 06 - The Algebra of Limits as x -> +/- ∞ : End Behavior
Lecture 07 - Continuous Functions
Lecture 08 - Trigonometric Functions
Lecture 09 - Measuring Rates of Change
Lecture 10 - What is a Derivative?
Lecture 11 - Finding Derivatives I & II
Lecture 12 - Finding Derivatives III & IV
Lecture 13 - When Rates of Change are Related
Lecture 14 - Implicit Differentiation, Derivatives Involving Logarithms
Lecture 15 - Derivatives Involving Inverses, Finding Limits Using Differentiation
Lecture 16 - Analyzing the Graphs of Functions I
Lecture 17 - Analyzing the Graphs of Functions II
Lecture 18 - Analyzing the Graphs of Functions III
Lecture 19 - Analyzing the Graphs of Functions IV
Lecture 20 - Optimization Problems
Lecture 21 - Newton's Method for Approximating Roots of Equations, The Mean Value Theorem for Derivative
Lecture 22 - One-Dimensional Motion & the Derivative
Lecture 22-5 - The Question of Area
Lecture 23 - The Indefinite Integral
Lecture 24 - The Indefinite Integration by Substitution
Lecture 25 - Area Defined as a Limit
Lecture 26 - The Definite Integral
Lecture 27 - The Fundamental Theorem of Calculus
Lecture 28 - One Dimensional Motion & the Integral
Lecture 29a - Plane Area
Lecture 29b - Volumes I
Lecture 30 - Volumes II
Lecture 30-03 - Length of a Plane Curve: Finding Arc Lengths
Lecture 30-04 - Length of a Plane Curve: Finding Arc Lengths of Parametric Curves
Lecture 31 - Average Value of a Function, Work
Lecture 31-06 - Work: An Exercise