3-D Analytical Geometry and Probability

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Publication Date Sun May 01 00:00:00 UTC 2005 Available in all formats

ISBN: 9789394681583

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ISBN: 9788182090897 Price: INR 180.00

Description

Table of contents

Biographical note

This book offers a graduate level exposition of selected topics in 3-D Analytical Geometry and Probability. It is designed to cover the requirements of the new syllabi for second year B.Sc. Mathematics students of all universities in Tamil Nadu. Even a beginner who likes to get an expertise in Solid Geometry and Probability Theory can find this book very useful and enriching.

Cover
Title Page
Copyright Page
Preface
Contents
Part I 3-D Analytical Geometry
- Chapter 1 Introduction
  - Introduction
  - Coordinate Axes and Coordinate Planes
    - Coordinates of a Point
    - Distance Between Two Points
    - Definition—Tetrahedron
  - Angle Between Two Lines
    - Direction Angles and Direction Cosines of a Line
    - Definition—Direction Cosines
    - Direction Cosines of Coordinate Axes
    - Relation Between Direction Cosines of a Straight Line
    - Direction Ratios
    - Direction Ratios of the Line Joining Two Points
    - Angle Between Two Lines
    - Condition for Parallelism and Perpendicularity of Two Lines
- Chapter 2 The Plane
  - Plane
    - Definition
    - General Form of the Equation of a Plane
    - Intercept Form
    - Normal Form
    - Angle Between Two Planes
    - Equation of a Plane Passing through the Line of Intersection of Two Given Planes
- Chapter 3 The Straight Lines
  - General Form of Equation of a Line
  - Symmetrical Form of the Equations of a Line
  - Transformation of General Form into Symmetrical Form
  - The Plane and the Straight Line
    - Angle Between a Line and a Plane
    - A Line of Greatest Slope in a Plane
  - Coplanar Lines
    - First Method
    - Second Method
  - Lines Intersecting Two Given Lines
  - Skew Lines
    - Definition—Skew Lines
  - Shortest Distance Between the Lines
    - Definition
- Chapter 4 The Sphere
  - Definition
  - Equation of a Sphere whose Centre and Radius are Given
  - General Form of Equation of a Sphere
  - Plane Section of a Sphere
  - Equation of a Circle
  - Equation of a Sphere Passing through a Given Circle
    - The Intersection of Two Spheres
  - Tangent and Tangent Plane
    - Equation of the Tangent Plane to a Sphere
    - Length of the Tangent from an External Point to a Sphere
  - Orthogonal Spheres
    - Condition for the Two Spheres to Cut Orthogonally
Part II Probability
- Chapter 5 Introduction
  - Historically
  - Basic Terms
  - Measurement of Probability
    - Classical Approach
    - Axiomatic Approach to Probability
  - Probability Function
    - Set Theoretic Notations
  - Addition Theorem of Probability
    - Boole’s Inequality
  - Conditional Probability
    - Some Results on Independent Events
  - Multiplication Theorem on Probability
    - Multiplication Theorem of Probability for Independent Events
    - Some Theorems on Conditional Probability
    - Baye’s Theorem
- Chapter 6 Random Variables
  - Introduction
  - Random Variable (R.V.)
    - Distribution Function
    - Discrete Random Variables
    - Continuous Random Variables
    - Two-dimensional Random Variables
    - Independent Random Variables
- Chapter 7 Mathematical Expectation
  - Definition
  - Properties of Expectation
    - Addition Theorem of Expectation
    - Multiplication Theorem of Expectation
  - Moment, Mean and Standard Deviation
- Chapter 8 Moment and Probability Generating Functions
  - Moment Generating Functions
    - Definition
    - Deficiencies of Moment Generating Functions
    - Properties of Moment Generating Function
    - Standard Variate
    - Chebychev’s Inequality
  - Probability Generating Function
    - Definition
    - Probability Generating Function for Two Variables X1 and X2
    - Simple Results on Probability Generating Function
    - Probability Generating Function for Different Distributions

Dr S Santha is currently Lecturer, Department of Mathematics, Sri Meenakshi Government College for Women, Madurai.Prior to this,she was the Head,Department of Mathematics , Noorul Islam College of Engineering , Kanyakumari . She has over 21 years of experience in teaching Mathematics.

T Pathinathan is Senior Scale Lecturer, Department of Mathematics, Loyola College, Chennai. He has 16 years of experience in teaching mathematics at various levels.

Description

Table of contents

Cover
Title Page
Copyright Page
Preface
Contents
Part I 3-D Analytical Geometry
- Chapter 1 Introduction
  - Introduction
  - Coordinate Axes and Coordinate Planes
    - Coordinates of a Point
    - Distance Between Two Points
    - Definition—Tetrahedron
  - Angle Between Two Lines
    - Direction Angles and Direction Cosines of a Line
    - Definition—Direction Cosines
    - Direction Cosines of Coordinate Axes
    - Relation Between Direction Cosines of a Straight Line
    - Direction Ratios
    - Direction Ratios of the Line Joining Two Points
    - Angle Between Two Lines
    - Condition for Parallelism and Perpendicularity of Two Lines
- Chapter 2 The Plane
  - Plane
    - Definition
    - General Form of the Equation of a Plane
    - Intercept Form
    - Normal Form
    - Angle Between Two Planes
    - Equation of a Plane Passing through the Line of Intersection of Two Given Planes
- Chapter 3 The Straight Lines
  - General Form of Equation of a Line
  - Symmetrical Form of the Equations of a Line
  - Transformation of General Form into Symmetrical Form
  - The Plane and the Straight Line
    - Angle Between a Line and a Plane
    - A Line of Greatest Slope in a Plane
  - Coplanar Lines
    - First Method
    - Second Method
  - Lines Intersecting Two Given Lines
  - Skew Lines
    - Definition—Skew Lines
  - Shortest Distance Between the Lines
    - Definition
- Chapter 4 The Sphere
  - Definition
  - Equation of a Sphere whose Centre and Radius are Given
  - General Form of Equation of a Sphere
  - Plane Section of a Sphere
  - Equation of a Circle
  - Equation of a Sphere Passing through a Given Circle
    - The Intersection of Two Spheres
  - Tangent and Tangent Plane
    - Equation of the Tangent Plane to a Sphere
    - Length of the Tangent from an External Point to a Sphere
  - Orthogonal Spheres
    - Condition for the Two Spheres to Cut Orthogonally
Part II Probability
- Chapter 5 Introduction
  - Historically
  - Basic Terms
  - Measurement of Probability
    - Classical Approach
    - Axiomatic Approach to Probability
  - Probability Function
    - Set Theoretic Notations
  - Addition Theorem of Probability
    - Boole’s Inequality
  - Conditional Probability
    - Some Results on Independent Events
  - Multiplication Theorem on Probability
    - Multiplication Theorem of Probability for Independent Events
    - Some Theorems on Conditional Probability
    - Baye’s Theorem
- Chapter 6 Random Variables
  - Introduction
  - Random Variable (R.V.)
    - Distribution Function
    - Discrete Random Variables
    - Continuous Random Variables
    - Two-dimensional Random Variables
    - Independent Random Variables
- Chapter 7 Mathematical Expectation
  - Definition
  - Properties of Expectation
    - Addition Theorem of Expectation
    - Multiplication Theorem of Expectation
  - Moment, Mean and Standard Deviation
- Chapter 8 Moment and Probability Generating Functions
  - Moment Generating Functions
    - Definition
    - Deficiencies of Moment Generating Functions
    - Properties of Moment Generating Function
    - Standard Variate
    - Chebychev’s Inequality
  - Probability Generating Function
    - Definition
    - Probability Generating Function for Two Variables X1 and X2
    - Simple Results on Probability Generating Function
    - Probability Generating Function for Different Distributions

Biographical note

T Pathinathan is Senior Scale Lecturer, Department of Mathematics, Loyola College, Chennai. He has 16 years of experience in teaching mathematics at various levels.

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