Summation of Infinitely Small Quantities 1st Edition by Natanson ISBN 0486843378‎ 978-0486843377

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ISBN 10: 0486843378
ISBN 13:‎ 978-0486843377
Author: Natanson

Translated and adapted from a popular Russian educational series, this concise book requires only some background in high school algebra and elementary trigonometry. It explores the fundamental concept of the integral calculus: the limit of the sum of an infinitely increasing number of infinitely decreasing quantities. Mastery of this concept enables the solution of geometry and physics problems, and is an excellent introduction to the systematic study of higher mathematics.
Starting with some algebraic formulas, the treatment proceeds to the determination of the pressure of a liquid on a vertical wall and the calculation of the work done in pumping liquid from a container. Subsequent chapters explore finding the volumes of a cone, pyramid, sphere, and other geometric forms and the measurement of the parabola, ellipse, and sinusoid. The text concludes with a selection of practice problems.
For advanced high school students and college undergraduates.

Summation of Infinitely Small Quantities 1st Table of contents:

Chapter 1. Some Algebraic Formulas

1. Introduction

2. The sum of the first n natural numbers

3. The sum of the squares

4. The sum of the cubes

5. The relationship between S1 and S3

6. The Σ notation

7. Some properties of the Σ notation

Chapter 2. Determination of the Pressure of a Liquid on a Vertical Wall

8. Introduction

9. A law of hydrostatics

10. The pressure on the wall of a rectangular tank

11. The pressure on a triangular plate, apex down

12. The pressure on a triangular plate, apex up

13. The pressure on a semicircular plate

Chapter 3. Calculation of the Work Done in Pumping Liquid from a Container

14. Pumping water out of a cylindrical boiler

15. Pumping water out of a conical tank

16. Pumping water out of a hemispherical tank

17. Pumping water out of a semicylindrical trough

Chapter 4. Finding Volumes

18. The volume of a cone

19. The volume of a pyramid

20. The volume of a sphere

21. The volume of the common portion of two cylinders

22. The volume of a cylindrical segment

23. Another method of solution; solutions of problems of sections 13 and 17

24. General remarks

25. The principle of Cavalieri

Chapter 5. The Parabola and the Ellipse

26. The area under a parabola

27. The volume of a paraboloid of revolution

28. The ellipse and its area

Chapter 6. The Sinusoid

29. A trigonometric sum

30. A subsidiary inequality

31. The sine of an infinitely small angle

32. The quadrature of the sinusoid

33. The volume enclosed by a rotating sinusoid

34. Mean values

35. Effective current

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Tags: Natanson, Small Quantities