An Analytical Calculus Volume 2 For School and University [Paperback]

The books are written for students of science and engineering as well as for specialist mathematicians.The books are written for students of science and engineering as well as for specialist mathematicians. This treatment of algebraic and trigonometric functions is here developed to cover logarithmic, exponential and hyperbolic functions and the expansion of all these functions as power series. This volume, like the others, is well endowed with examples.The books are written for students of science and engineering as well as for specialist mathematicians. This treatment of algebraic and trigonometric functions is here developed to cover logarithmic, exponential and hyperbolic functions and the expansion of all these functions as power series. This volume, like the others, is well endowed with examples.This is the second of a series of four volumes covering all stages of development of the Calculus, from the last years at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies. with their emphasis on rigour. This treatment of algebraic and trigonometric functions is here developed to cover logarithmic, exponential and hyperbolic functions and the expansion of all these functions as power series. There is a chapter on curves and the idea of complex numbers is introduced for the first time. In the two final chapters, the author begins a systematic treatment of methods of integrating functions, introducing principles into what often seems rather a haphazard process. This volume, like the others, is well endowed with examples.Preface; 7. The logarithmic and exponential functions; 8. Taylor's series and allied results; 9. The hyperbolic functions; 10. Curves; 11. Complex numbers; 12. Systematic integration; 13. Integrals involving 'infinity'; Appendix; Answers to examples; Index.