Bradburn / Kneebone / Hoare Exploring University Mathematics

Lectures Given at Bedford College, London
1. Auflage 2014
ISBN: 978-1-4831-4816-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 130 Seiten, Web PDF

Exploring University Mathematics, Volume 3 provides information pertinent to pure and applied mathematics. This book discusses the close relationship between mathematics and physics. Organized into seven chapters, this volume begins with an overview of the concept of mapping in mathematics, which provides a correspondence between elements of one set with elements of another. This text then examines the theory of inflatable structures in the study of the hovercrafs in two dimensions. Other chapters consider the explicit investigation of logic by mathematicians whereby mathematics has been conceived as pre-eminently a deductive science. This book discusses as well how Taylor's formula is used in various aspects, including integration, approximating functions, finding roots of algebraic equations, and solving differential equations in forms suitable for computer calculations. This book is intended to be suitable for students on a degree course in mathematics. Mathematicians, teachers, and research workers will also find this book extremely useful.

Autoren/Hrsg.

Bradburn, Mary

Kneebone, G. T.

Hoare, M. R.

Hardiman, N. J.

Inhaltsverzeichnis

1;Front Cover;1
2;Exploring University Mathematics;4
3;Copyright Page ;5
4;Table of Contents;6
5;EDITORIAL;8
6;CHAPTER 1. SYMMETRY OF PYRAMIDS AND PRISMS;12
6.1;Mappings;12
6.2;Isometric mappings;13
6.3;The identity mapping;16
6.4;Rotations;16
6.5;Inversion in a point and reflections in a plane;19
6.6;Symmetry operations;20
6.7;Twofold axes and n-fold axes;20
6.8;Two perpendicular axes of symmetry;21
6.9;Inversions and improper rotations;21
6.10;Extensions;26
6.11;References for further reading;28
7;CHAPTER 2. MATHEMATICS AND THE PHYSICIST;29
7.1;Models and explanations;30
7.2;Functions and laws;35
7.3;The uses of an equation;38
7.4;How simple is Nature?;43
7.5;Difficulty and dimensions;48
7.6;Are solutions really necessary?;55
8;CHAPTER 3. CUSHION CRAFT;59
8.1;Introduction;59
8.2;Isometric transformations;64
8.3;Mechanical considerations;73
8.4;Two-dimensional hovercraft;75
9;CHAPTER 4. LOGIC;81
9.1;Introduction;81
9.2;Mathematical logic;84
9.3;The language of mathematical logic and its use;86
9.4;Logic and set theory;89
9.5;References for further reading;92
10;CHAPTER 5. SPACE AND SPACES;93
11;CHAPTER 6. SOME APPLICATIONS OF THE TAYLOR SERIES IN NUMERICAL ANALYSIS;105
11.1;Taylor's series;105
11.2;References for further reading;114
12;CHAPTER 7. SOME IRRATIONAL NUMBERS;115
12.1;References for further reading;132