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.
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
- Plane
- 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
- Chapter 1 Introduction
- 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
- Moment Generating Functions
- Chapter 5 Introduction
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.