Introduction - Integral And Differential Calculus

Integral and Differential Calculus The study of either integral or differential calculus depends ultimately on a careful study of the real number system. Therefore, I will approach calculus as a deductive system of real number which undefined properties of real numbers are listed as axioms or postulates. To develop calculus as a complete, formal mathematical theory, it would be necessary to state, in addition to the axioms for the real number system, a list of various “methods of proof” which would be permitted for the purpose of deducing theorems from the axioms. Every statement in the theory would then have to be justified either as an “established law” (for example, an axiom, a definition, or a previously proved theorem) or as the result of applying one of the acceptable methods of proof to an established law. Table of context Date

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Set Theory

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Real Number System

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Mathematical Induction Continuous Function Integral Calculus

Basic notation and terminology which is necessary to all discussions in mathematics The field axioms, the order axioms and the completeness axioms for the real number system Mathematical induction is the standard practice of proof in mathematics. The concept of continuity of a function The area under a continuous region of a function Problems involving the technique of integrations The concept of tangent line to a function are developed, and basic calculation are presented Problems involving the technique of differentiation of a function The fundamental theorem of calculus, the remarkable connection between differential calculus and integral calculus Calculus of some of the common functions which describe many phenomena in the nature

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Application of Integral Calculus Differential Calculus

Application of Differential Calculus 9 The Relation between Integral and Differential Calculus 1 Calculus of Logarithm, 0 Exponential and Inverse Trigonometric functions 11 Polynomial Approximation to functions 1 Summary

Analytic mathematics involving techniques in calculus Exam (Advanced Placement, uni finals)

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