Higher Maths for Beginners | Ya. B. Zeldovich, I. M. Yaglom

This book is a joint attempt of a physicist and a mathematician to write an entirely new type of book for future scientists and engineers.

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The purpose of this book is to enable the future physicist (chemist, engineer etc.) to use higher mathematics in his or her work by mastering its methods without going into full logical substantiation of them, allowing the student to view mathematics as a section of natural sciences and to solve as many concrete  problems as possible.

This book is intended for beginners, that is, for high-school students in the upper grades, students of trade schools and vocational schools, and students in the first years of college. We also have in mind anyone who by himself wishes to become better acquainted with higher mathematics, say, people who finished school some years ago

The book was translated from the Russian by Eugene Yankovsky and was first published by Mir in 1987.

Contents

Part 1. Elements of Higher Mathematics

Chapter 1. Functions and Graphs

Chapter 2. What is a derivative?

Chapter 3. What is an integral?

Chapter 4. Calculation of derivatives

Chapter 5. Integration Techniques

Chapter 6. Series, Simple Differential Equations

Chapter 7. Investigation of Functions, Some Problems of Geometry

Part 2. Higher Math Applied to Problems of Engineering and Physics

Chapter 8. Radioactive Decay and Nuclear Fission

Chapter 9. Mechanics

Chapter 10. Oscillations

Chapter 11. The Thermal Motion of Molecules. The Distribution of Air Density in Atmosphere

Chapter 12. Absorption and Emission of Light. Lasers

Chapter 13. Electric Circuits and Oscillatory Phenomena In Them

Part 3. Some Additional Topics

Chapter 14. Complex Numbers

Chapter 15. Functions The Physicist Needs

Chapter 16. Dirac’s Remarkable Delta Functions

Chapter 17. Applying Functions of a Complex Variable and The Delta Functions

Conclusion: What Next

Selected Readings

Appendices

Hints, Answers and Solutions

Name Index

Subject Index