FREE CALCULUS

A Liberation From Concepts And Proofs

By: Qun Lin

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Hardcover | 26 May 2008

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Hardcover
110 Pages

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22.86 x 15.24 x 1.12

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Conventional calculus is too hard and too complex. Students are forced to learn too many theorems and proofs. In Free Calculus, the author suggests a direct approach to the two fundamental concepts of calculus - differentiation and integration - using two inequalities. Regular calculus is condensed into a single concise chapter. This makes the teaching of physics in step with the calculus teaching.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Booktopia Publisher Services World Scientific Publishing

Preface	p. vii
Calculus in Terms of Images:	p. 1
Hill Behavior and Slope	p. 1
Hill Height and Slope: Unconstructive Tangent Formula	p. 2
Review for FT	p. 5
Hillside Length and Slope: Pythagoras Theorem	p. 9
Area and Slope	p. 10
Explaining All of Calculus in a Single Figure	p. 11
Calculus and Novels	p. 12
Official Calculus:	p. 15
A Case: Height and Slopes	p. 15
Translating into Function Language	p. 17
Generalized First Inequality	p. 30
Generalized Second Inequality	p. 31
Rules of Differentiation	p. 33
Arithmetic of derivatives	p. 33
Derivatives of rational functions and trigonometric functions	p. 36
Derivatives of composite functions and inverse functions	p. 37
Tables of Derivatives and Integrals	p. 39
Rules of Integration	p. 40
A Calculus Net	p. 42
Taylor's Series	p. 44
Euler's Formula	p. 45
Possible Generalizations	p. 46
Differential Equations of First Order	p. 51
A Simplest Differential Equation	p. 51
Varieties of Simplest Differential Equation	p. 52
The test equation	p. 52
Linear differential equation	p. 54
Separable equation	p. 54
More General Equations	p. 55
Tests for Euler's Algorithm	p. 55
General Euler's Algorithm	p. 57
Differential Equations of Second Order	p. 59
Initial Value Problems	p. 59
Eigenvalue Problem	p. 63
Boundary Value Problem	p. 65
Weak Equation	p. 66
Finite Element Solution and Interpolation	p. 68
Generalization	p. 69
Summary	p. 72
Free Calculus	p. 73
Function Spaces, Norms, and Triangle Inequality	p. 73
Angle and Schwartz's Inequality	p. 77
Inner Product	p. 78
Orthogonality and Projection	p. 79
Different Inner Products and Norms	p. 81
Abstract Calculus	p. 82
Appendix	p. 83
Calculus of Functional Analysis Becomes Elementary Algebra	p. 85
Introduction	p. 85
Derivative Definition Becomes an Elementary Inequality	p. 85
Fundamental Theorem Becomes Another Elementary Inequality	p. 86
Acknowledgments	p. 87
References	p. 88
Bibliography	p. 89
Table of Contents provided by Ingram. All Rights Reserved.

FREE CALCULUS

A Liberation From Concepts And Proofs

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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