Higher Math for Beginners

Description

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. … 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. 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