Elementary Analysis - 1st Edition - ISBN: 9780080117775, 9781483158983

Elementary Analysis

1st Edition

The Commonwealth and International Library: Mathematics Division, Volume 2

Authors: K. S. Snell J. B. Morgan
Editors: W. J. Langford E. A. Maxwell
eBook ISBN: 9781483158983
Imprint: Pergamon
Published Date: 1st January 1966
Page Count: 304
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Description

Elementary Analysis, Volume 2 introduces several of the ideas of modern mathematics in a casual manner and provides the practical experience in algebraic and analytic operations that lays a sound foundation of basic skills. This book focuses on the nature of number, algebraic and logical structure, groups, rings, fields, vector spaces, matrices, sequences, limits, functions and inverse functions, complex numbers, and probability. The logical structure of analysis given through the treatment of differentiation and integration, with applications to the trigonometric and logarithmic functions, is also briefly discussed. This volume begins with a description of the trigonometric functions of the general angle and an introduction to the binomial theorem and series. The rest of the chapters cover the numerical solution of equations, analytical geometry, Argand Diagram, numerical methods, and methods of approximation that form an important section of modern applied mathematics. This publication is valuable to teachers and students in training colleges.

Table of Contents


Preface

Introduction: A summary of Basic Ideas from Volume 1

15. Trigonometric Functions of the General Angle

Angles

Vectors

Trigonometrical Ratios

Special Angles

The General Angle

Periodic Functions

Graphs

General Formula, cos2θ+ in2θ=1

Inequalities

16. Functions of Compound Angles

Unit Vectors

Compound Angles

Multiple Angles

Sums and Products

Even and Odd Functions

Parameters

Inverse Functions

The Circle

17. Differentiation and Integration of the Trigonometric Functions

Gradient of the Sine Function

Radians and Degrees

Differentiation of a Vector

Motion in a Circle

Inequalities

Derivative of Tan x

Integration

Substitution

Polar Coordinates

Area of a Sector

18. Applications of the Trigonometric Functions

Dot Product of Vectors

Compound Angle Formula

Triangle Formula and Problems

Simple Harmonic Motion

Approximations

Three Dimensions

Projections

19. Polynomials

The Remainder Theorem

The Factor Theorem

The Identity Theorem

Synthetic Division

Evaluation of a Polynomial

Repeated Factors

20. Symmetric Functions of the Roots of a Polynomial Equation

Complex Roots

Symmetric Functions

Sums of Powers of Roots

Approximation for the Greatest Root

21. The Binomial Theorem

The Expansion of (a + x)n

The Binomial Theorem

Approximations

Proof by Induction

22. The Binomial Series

Limit Sum

The Binomial Series

Partial Fractions

Expansions

Approximations

23. Numerical Solution of Equations

Linear Interpolation

Newton's Method

Trigonometric Equations

Recurrence Relations and Iterative Methods

Expansions

24. Analytical Geometry

Vectors—A Recapitulation

Coordinates as Vectors

Transformations

Change of Axes

Polar Coordinates

The Parabola, Hyperbola, Circle and Ellipse

Orthogonal Projection

25. The Argand Diagram

Lengths in the Argand Diagram

Geometrical Illustrations

Inversion

Complex Equation of a Line and Circle

Similarity

Conformal Transformations

The Equation xn=1

26. Matrices and Determinants

Successive Transformations

Definition of a Matrix

Addition

Product

Applications

Unit Matrix

Solution of Linear Equations

Elementary Row Operations

The Inverse Matrix

Determinants

Cofactors

Singular Matrices

Quadratic Forms

27. The Exponential and Logarithmic Functions

Limit of a Function

Continuous Functions

Definite Integrals

The Mean Value Theorem for Integrals

The Fundamental Theorem

The Logarithmic Function

The Logarithmic Series

The Exponential Function and Series

Logarithmic Differentiation

Integration of Rational, Algebraic and Trigonometric Functions

Integration by Parts

28. Introduction to Probability Theory

The Concept of Probability

A Sample Space

Alternative or Disjoint Events

Combined Events

Permutations

Combinations

Set Theory and Probability

Independent Events

Tree Diagrams

Binomial Distribution

The Value of an Expectation

Answers

Index


Details

No. of pages:
304
Language:
English
Copyright:
© Pergamon 1966
Published:
Imprint:
Pergamon
eBook ISBN:
9781483158983

About the Author

K. S. Snell

J. B. Morgan

About the Editor

W. J. Langford

E. A. Maxwell