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Algebra and Calculus  
Published by Vijay Nicole Imprints Private Limited
Publication Date:  Available in all formats
ISBN: 9789394681309

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Description

Table of contents

Biographical note

Designed to cater to the requirements of first year engineering students, this book completely covers the prescribed syllabus of SSN College of Engineering, (An Autonomous Institution Affilliated to Anna University, Chennai), Kalavakkam, Chennai.

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Description

Designed to cater to the requirements of first year engineering students, this book completely covers the prescribed syllabus of SSN College of Engineering, (An Autonomous Institution Affilliated to Anna University, Chennai), Kalavakkam, Chennai.

Table of contents
  • Cover
  • About the Author
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • UNIT - I TRIGONOMETRIC SERIES
    • Introduction
    • De Moivre’s Theorem
      • Roots of a Complex Number
    • Expansion of sin nθ, cos nθ and tan nθ in powers of sin θ, cos θ and tan θ
      • Addition Formulae for Any Number of Angles
    • Complex Function
      • Circular Functions of a Complex Variable
    • Hyperbolic Functions
    • Inverse Hyperbolic Functions
    • Logarithmic Function
  • UNIT - II MATRICES
    • Introduction
    • Rank of a Matrix
      • Simultaneous Linear Equations
      • Rouche’s Theorem
      • Homogeneous System of Linear Equations
      • Linear Independence and Dependence of Vectors
    • Eigen Values and Eigen Vectors
      • Introduction
      • Properties of Eigen Values and Eigen Vectors
    • Cayley-Hamilton Theorem
    • Similar Matrices
      • Diagonalisation of a Matrix
    • Orthogonal Matrix
      • Properties
    • Quadratic Forms
      • Nature of the Quadratic Form
      • Simultaneous Reduction of Two Quadratic Forms
      • Canonical Forms of Conics
      • Canonical Forms of Quadratics
  • UNIT - III DIFFERENTIAL CALCULUS
    • Curvature
      • Definition of Curvature
      • Curvature of a Circle
    • Radius of Curvature
      • Definition
      • Cartesian Form of Radius of Curvature
      • Parametric Form of Radius of Curvature
    • Polar Form of Radius of Curvature
    • Centre and Circle of Curvature
      • Definition
      • The Centre of Curvature
      • Equation of Circle of Curvature
    • Involutes and Evolutes
      • Evolute
      • Involute
      • Procedure for the Equation to the Evolute of the Curve y = f (x)
    • Properties of Evolutes
      • Geometrical Method of Proof
    • Envelopes
      • Family of Curves
      • Envelope—Definition
      • Analytical Method of Finding the Equation of Envelope
    • Envelope of Two Parameter Family
    • Property of Envelope
      • Examples of Property of Envelope
      • Evolute as the Envelope of Normals
  • UNIT - IV FUNCTIONS OF SEVERAL VARIABLES
    • Partial Derivatives
      • Definition
      • Total Differentiation
      • Derivatives of Implicit Functions
    • Euler’s Theorem for Homogeneous Functions
    • Total Derivatives
    • Functions of Functions and Implicit Functions
    • Taylor’s Theorem
    • Jacobians
      • Properties
    • Maxima and Minima of Functions of Two variables
      • Definition—Maximum
      • Definition—Minimum
      • Working Rule for Finding the Extreme Values of f(x,y)
      • Constrained Maxima and Minima
      • Lagrange’s Method of UndeterminedMultipliers
    • Differentiation under the Integral Sign
  • UNIT - VINTEGRAL CALCULUS
    • Introduction
      • Double Integrals
      • Evaluation of Double Integrals
      • Beta and Gamma Function
      • Relation between Beta and Gamma Functions
      • Area as Double Integral
    • Changing the Order of Integration
      • Application of Beta Gamma Functions to Multiple Integrals
    • Transformation from Cartesian Coordinates to Polar Coordinates
    • Triple Integrals
      • Evaluation of Triple Integrals
      • Volume as Triple Integral
  • Two Marks Questions and Answers
  • Solved Question Bank
  • Index
Biographical note

B Praba is presently Associate Professor, Department of Mathematics, SSN College of Engineering, Chennai. She has 22 years of research and teaching experience and has written books on Discrete Mathematics, Statistics, Random Process and Queuing Theory and Statistics for Management. She has obtained her Ph.D., from Ramanujan Institute for Advanced Study in Mathematics, Chennai.

S Kalavathy is Professor, Department of Mathematics, RMD Engineering College, Chennai. She has over 23 years of experience in teaching Mathematics and has written several books including best sellers on Engineering Mathematics and Operational Research.

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