Elementary Analysis
The Commonwealth and International Library: Mathematics Division, Volume 1
- 1st Edition - January 1, 1956
- Imprint: Pergamon
- Authors: K. S. Snell, J. B. Morgan
- Editors: W. J. Langford, E. A. Maxwell
- Language: English
- Paperback ISBN:9 7 8 - 0 - 0 8 - 0 1 0 7 8 2 - 0
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 3 7 0 8 - 7
Elementary Analysis, Volume 1 introduces the reader to elementary analysis in an informal manner and provides the practical experience in algebraic and analytic operations to lay a… Read more
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Request a sales quoteElementary Analysis, Volume 1 introduces the reader to elementary analysis in an informal manner and provides the practical experience in algebraic and analytic operations to lay a sound foundation of basic skills. The preliminary ideas are illustrated by applications to the simpler algebraic functions. Emphasis is on fundamental principles, rather than manipulative techniques. This volume is comprised of 14 chapters and begins with a discussion on number systems, covering concepts ranging from number scales to rational and real numbers, binary operations, and deductive methods. The following chapters deal with sets, vectors and congruences, and functions. Exponential and logarithmic functions, the straight line, and linear function are also considered. The remaining chapters focus on the quadratic function; the principle of mathematical induction and its applications; differentiation and the inverse process; and integration and its applications. Differential equations are presented, along with the definite integral. This book will be of particular value to teachers and students in training colleges.
Preface
1. Number Systems
Number Scales
Denary Scales
Binary Scales
Rational Numbers
Geometrical Representation
Nested Intervals
Recurring Decimals
Irrational Numbers
Square Roots
Real Numbers
Geometrical Representation
Binary Operations
Axioms
Deductive Methods
Order
Inequalities
2. Sets
Definition of a Set
Equal Sets
Subsets
Empty Set
Inclusion
Operations on Sets
Algebra of Sets
Union and Intersection Tables
De Morgan's Rule
Counting Sets
Applications
3. Vectors and Congruences
Directed Lengths
Ordered Pairs
Coordinates
Vectors—Addition and Subtraction
Multiplication by a Scalar
Mid-points
The Section Formula
Homothetic Figures
Three Dimensions
Congruences
4. Functions
Relations
Graphical Representation
Mapping
Functions
Inverse Functions
Locus and Graph
Equation and Graph
5. Exponential and Logarithmic Function
Notation
The Exponential Function
Index Laws
The Logarithmic Function
An Inverse Function
The Laws of Logarithms
Logarithms to Base 10
Logarithms to Any Base
Napierian Logarithms
The Slide Rule
Graphical Solution of Equations
6. The Straight Line
Projections
The Distance Formula
Gradient
Positive and Negative Gradients
Equation of the Straight Line
Perpendicular Lines
Distance of a Point from a Line
Intersection of Two Lines
7. The Linear Function
Polynomials
The Linear Polynomial ax + b
Identity
Ordered Triples in 3-Space
Parametric Equations of a Line in 3-Space
Linear Polynomial in Two Variables
The Sign of ax + by + c
Linear Programming
8. The Quadratic Function
Graph of Quadratic Function
The Sign of(x - a)(x - b)
Graphical Solution of Inequalities
The Function y = ax2 + bx + c
The Quadratic Equation
Roots and Coefficients of a Quadratic Equation
Complex Numbers
The Algebra of Complex Numbers
9. Sequences, Series, Limits
Sequences
The Arithmetic Sequence
The Arithmetic Mean
The Geometric Sequence
The Geometric Mean
The Geometric Series
Limit of a Sequence
Limit of a Function
Formal Definition of a Limit
10. Mathematical Induction and Applications
The Principle of Mathematical Induction
Proof of the Principle
A Warning
Summation of Series
The Method of Differences
The Sigma Notation
The Limit Sum of a Series
11. Differentiation
Gradient of a Chord
Gradient of a Tangent
Gradient at a Point on a Curve
Gradient Formula
Derived Function
Differentiation of Powers of x
The Derivative of xn
The Chain Rule for Differentiation
Implicit Differentiation
12. Applications of Differentiation and the Inverse Process
Rate of Change
Stationary Values of a Function
Small Changes
Differential Equations
Velocity and Acceleration
13. Further Differentiation and the Applications
Differentiation of a Product
Differentiation of a Quotient
Implicit Differentiation
The Second Derivative
Acceleration
The Leibniz Notation
14. Integration and Applications
An Important Limit
The Definite Integral
An Example of an Integral
Area by Integration
Area Beneath a Curve
A Function Defined as a Definite Integral
The Fundamental Theorem
Square Bracket Notation
Applications of Integration
Volume of a Solid of Revolution
Mean Values
Centre of Mass
Numerical Integration
The Trapezium Rule
Simpson's Rule
Answers
Index
- Edition: 1
- Published: January 1, 1956
- Imprint: Pergamon
- No. of pages: 248
- Language: English
- Paperback ISBN: 9780080107820
- eBook ISBN: 9781483137087
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