Free calculus : a liberation from concepts and proofs / Qun Lin.

Format:

Book

Author/Creator:

Lin, Qun.

Language:

English

Subjects (All):

Calculus.

Mathematical analysis.

Physical Description:

1 online resource (108 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, NJ : World Scientific, c2008.

Language Note:

English

Summary:

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.

Contents:

Contents; Preface; 0. Calculus in Terms of Images:; 0.1. Hill Behavior and Slope; 0.2. Hill Height and Slope: Unconstructive Tangent Formula; 0.3. Review for FT.; 0.4. Hillside Length and Slope: Pythagoras Theorem; 0.5. Area and Slope; 0.6. Explaining All of Calculus in a Single Figure; 0.7. Calculus and Novels; 1. Official Calculus:; 1.0. A Case:Height and Slopes; 1.1. Translating into Function Language; 1.2. Generalized First Inequality; 1.3. Generalized Second Inequality; 1.4. Rules of Differentiation; 1.4.1. Arithmetic of derivatives

1.4.2. Derivatives of rational functions and trigonometric functions1.4.3. Derivatives of composite functions and inverse functions; 1.5. Tables of Derivatives and Integrals; 1.6. Rules of Integration; 1.7. A Calculus Net; 1.8. Taylor's Series; 1.9. Euler's Formula; 1.10. Possible Generalizations; 2. Differential Equations of First Order; 2.1. A Simplest Differential Equation; 2.2. Varieties of Simplest Differential Equation.; 2.2.1. Thetest equation; 2.2.2. Linear differential equation; 2.2.3. Separable equation; 2.3. More General Equations; 2.4. Tests for Euler's Algorithm

2.5. General Euler's Algorithm3. Differential Equations of Second Order; 3.1. Initial Value Problems; 3.2. Eigenvalue Problem; 3.3. Boundary Value Problem; 3.4. Weak Equation; 3.5. Finite Element Solution and Interpolation; 3.6. Generalization; 3.7. Summary; 4. Free Calculus; 4.1. Function Spaces, Norms, and Triangle Inequality; 4.2. Angle and Schwartz's Inequality; 4.3. Inner Product; 4.4. Orthogonality and Projection; 4.5. Different Inner Products and Norms; 4.6. Abstract Calculus; Appendix; Calculus of Functional Analysis Becomes Elementary Algebra; 1. Introduction

2. Derivative Definition Becomes an Elementary Inequality3. Fundamental Theorem Becomes Another Elementary Inequality; Acknowledgments; References; Bibliography

Notes:

Description based upon print version of record.

Includes bibliographic references (p. 89-90).

ISBN:

9786611938468

9781281938466

1281938467

9789812790842

9812790845

OCLC:

316004377