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Elementary Calculus by H. Jerome Keisler

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List of Chapters available

Appendix

Preface

Epilogue

Contents

Chapters name :

Real and Hyperreal Numbers

Differentiation

Continuous Function

Integration

Limits,Analytic Geometry and Approximations

Application of the Integral

Trigonometric Functions

Exponential and Logarithmic Functions

Infinite Series

Vectors

Partical Differentiation

Multiple Integrals

Vector Calculus

Differential Equations

Book Details

We want you to reason with mathematics. We are not trying to get everyone to give formalized proofs in the sense of contemporary mathematics; `proof' in this course means convincing argument.' We expect you to use correct reasoning and to give careful explanations. The projects bring out these issues in the way we nd best for most students, but the pure mathematical questions also interest some students. This book of mathematical background" shows how to ll in the mathematical details of the main topics from the course. These proofs are completely rigorous in the sense of modern mathematics technically bulletproof. We wrote this book of foundations in part to provide a convenient reference for a student who might like to see the \theorem - proof" approach to calculus.



 


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