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Calculus Revisited: Single Variable Calculus

Calculus Revisited: Single Variable Calculus (Res.18-006, MIT OCW). Taught by Professor Herbert Gross, this course gives an overview of single variable calculus covering various topics: sets, functions, differential calculus, integral calculus, trigonometric functions, logarithms, and infinite series. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time. (from ocw.mit.edu)

Part IV, Lecture 04 - One-Dimensional Area

The main difference between arc-length and either area or volume; the limit definition of arc-length; approximating errors and their magnitude when we use infinite sums.


Go to the Course Home or watch other lectures:

Part I - Sets, Functions and Limits (6)
P1Lec 01 - Analytic Geometry
P1Lec 02 - Functions
P1Lec 03 - Inverse Functions
P1Lec 04 - Derivatives and Limits
P1Lec 05 - A More Rigorous Approach to Limits
P1Lec 06 - Mathematical Induction
Part II - Differentiation (11)
P2Lec 01 - Derivatives of Some Simple Functions
P2Lec 02 - Approximations and Infinitesimals
P2Lec 03 - Composite Functions and the Chain Rule
P2Lec 04 - Differentiation of Inverse Functions
P2Lec 05 - Implicit Differentiation
P2Lec 06 - Continuity
P2Lec 07 - Curve Plotting
P2Lec 08 - Maxima and Minima
P2Lec 09 - Rolle's Theorem and its Consequences
P2Lec 10 - Inverse Differentiation
P2Lec 11 - The "Definite" Indefinite Integral
Part III - The Circular Functions (2)
P3Lec 01 - Circular Functions
P3Lec 02 - Inverse Circular Functions
Part IV - The Definite Integral (4)
P4Lec 01 - The Definite Integral
P4Lec 02 - Marriage of Differential and Integral Calculus
P4Lec 03 - Three-Dimensional Area
P4Lec 04 - One-Dimensional Area
Part V - Transcendental Functions (4)
P5Lec 01 - Logarithms without Exponents
P5Lec 02 - Inverse Logarithms
P5Lec 03 - What a Difference a Sign Makes
P5Lec 04 - Inverse Hyperbolic Functions
Part VI - More Integration Techniques (4)
P6Lec 01 - Some Basic Recipes
P6Lec 02 - Partial Fractions
P6Lec 03 - Integration by Parts
P6Lec 04 - Improper Integrals
Part VII - Infinite Series (6)
P7Lec 01 - Many Versus Infinite
P7Lec 02 - Positive Series
P7Lec 03 - Absolute Convergence
P7Lec 04 - Polynomial Approximations
P7Lec 05 - Uniform Convergence
P7Lec 06 - Uniform Convergence of Power Series