Matrices and Calculus  
Published by Vijay Nicole Imprints Private Limited
Publication Date:  Available in all formats
ISBN: 9789394681705

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

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Designed to cater to the requirements of first year engineering students, this book completely covers the prescribed syllabus of Sri Sivasubramaniya Nadar 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 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 - II SEQUENCES AND SERIES
    • Sequences
      • Infinite Series
    • Convergence, Divergence and Oscillation of a Series
    • General Properties of Series
    • Series of Positive Terms
    • Comparison Tests
    • Integral Test
    • D’Alembert’s Ratio Test
    • Alternating Series
      • Definition
    • Leibnitz Theorem
    • Series of Positive or Negative Terms
      • Definition
  • 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
      • Geometrical 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 Undetermined Multipliers
    • Differentiation under the Integral Sign
  • UNIT - V INTEGRAL 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

Dr. B. Praba, Professor & Head, Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering has 33 years of research and teaching experience. She received her Ph.D. under UGC JRF from the Ramanujan Institute for Advanced Study in Mathematics, University of Madras. She is a prolific writer and contributed six books on various topics in mathematics which include Discrete Mathematics, Probability and Random processes. She is also a researcher working on Rough set theory, Algebraic graph theory, etc. She has more than 140 publications in various indexed international journals and conference proceedings. She also proved herself by publishing a book chapter in Wiley Book Series. She has received “Outstanding Educator & Scholar Award” in 2017 and best researcher award for the year 2009. She is a recognized supervisor of Anna University-Chennai, VIT University - Vellore and Sri Chandrasekharendra Saraswathi Viswa Mahavidyalaya University-Kanchipuram. Eight students have been awarded their Ph.D degree and more than three students are currently working for their degree under her guidance. She acted as a resource person for various faculty development programs, workshops and international conferences.

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