1988Unpublished venueRequires access

The Fundamental Ideas of the Integral and Differential Calculus

Richard Courant, E. J. McShane

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Abstract

This chapter contains sections titled: The Definite Integral Examples The Derivative The Indefinite Integral, the Primitive Function, and the Fundamental Theorems of the Differential and Integral Calculus Simple Methods of Graphical Integration Further Remarks on the Connexion between the Integral and the Derivative The Estimation of Integrals and the Mean Value Theorem of the Integral Calculus The Existence of the Definite Integral of a Continuous Function The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus

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This chapter contains sections titled: The Definite Integral Examples The Derivative The Indefinite Integral, the Primitive Function, and the Fundamental Theorems of the Differential and Integral Calculus Simple Methods of Graphical Integration Further Remarks on the Connexion between the Integral and the Derivative The Estimation of Integrals and the Mean Value Theorem of the Integral Calculus The Existence of the Definite Integral of a Continuous Function The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus

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Available abstract

This chapter contains sections titled: The Definite Integral Examples The Derivative The Indefinite Integral, the Primitive Function, and the Fundamental Theorems of the Differential and Integral Calculus Simple Methods of Graphical Integration Further Remarks on the Connexion between the Integral and the Derivative The Estimation of Integrals and the Mean Value Theorem of the Integral Calculus The Existence of the Definite Integral of a Continuous Function The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus

Key concepts: Fundamental theorem of calculus, Mathematics, Differential calculus, Calculus (dental), Time-scale calculus, Daniell integral, Line integral, Mean value theorem (divided differences)

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