Cover -- Preface to theSecond Revised Edition -- Unit-1. Differential Calculus-I -- 1.1 Introduction -- 1.1 nth Derivative of Some Elementary Functions -- Exercise 1.1 -- 1.2 Leibnitz's Theorem -- Exercise 1.2 -- Exercise 1.3 -- Partial Differentiation -- 1.3 Function of Two Variables -- 1.4 Partial Differential Coefficients -- Exercise 1.4 -- 1.5 Homogeneous Function -- 1.6 Euler's Theorem on Homogeneous Functions -- Exercise 1.5 -- 1.7 Total Differential Coefficient -- Exercise 1.6 -- Curve Tracing -- 1.8 Procedure for Tracing Curves in Cartesian Form -- Exercise 1.7 -- 1.9 Polar Curves -- Exercise 1.8 -- 1.10 Parametric Curves -- Exercise 1.9 -- 1.11 Taylor's Theorem for Functions of Two Variables -- Exercise 1.10 -- Objective Type Questions -- Answers to Objective Type Questions -- Unit-ll. Differential Calculus-II -- 2.1 Jacobian -- Exercise 2.1 -- 2.2 Approximation of Errors -- Exercise 2.2 -- 2.3 Extrema of Function of Several Variables -- Exercise 2.3 -- 2.4 Lagrange's Method of Undetermined Multipliers -- Exercise 2.4 -- Objective Type Questions -- Answers to Objective Type Questions -- Unit-lll Matrices -- 3.0 Introduction -- 3.1 Definition of Matrix -- 3.2 Types of Matrices -- 3.3 Operations on Matrices -- 3.4 Track of Matrix -- 3.5 Properties of Transpose -- 3.6 Properties of Conjugate Matrices -- 3.7 Singular and Non-Singular Matrices -- 3.8 Adjoint of a Square Matrix -- 3.9 Inverse of a Matrix (Reciprocal) -- Exercise 3.1 -- 3.10 Elementary Row and Column Transformations -- 3.11 Method of Finding Inverse of a Non-Singular Matrix by Elementary Transformations -- Exercise 3.2 -- 3.12 Rank of a Matrix -- Exercise 3.3 -- 3.13 System of Linear Equations (Non-Homogeneous) -- 3.14 System of Homogeneous Equations -- 3.15 Gaussian Elimination Method -- Exercise 3.4 -- 3.16 Linear Dependence of Vectors -- Exercise 3.5.

3.17 Eigen Values and Eigen Vectors -- Exercise 3.6 -- 3.18 Cayley-Hamilton Theorem -- Exercise 3.7 -- 3.19 Diagonalization of a Matrix -- 3.20 Application of Matrices to Engineering Problems -- Exercise 3.8 -- Objective Type Questions -- Answers to Objective Type Questions -- Unit-lV. Multiple Integrals -- 4.1 Multiple Integrals -- 4.2 Double Integrals -- 4.3 Working Rule -- 4.4 Double Integration for Polar Curves -- Exercise 4.1 -- 4.5 Change of the Order of Integration -- 4.6 Change of Variables in a Multiple Integral -- Exercise 4.2 -- 4.7 Beta and Gamma Functions -- 4.8 Transformations of Gamma Function -- 4.9 Transformations of Beta Function -- 4.10 Relation between Beta and Gamma Functions -- 4.11 Some Important Deductions -- 4.12 Duplication Formula -- 4.13 Evaluate the Integrals -- Exercise 4.3 -- 4.14 Application to area (Double Integrals) -- Exercise 4.4 -- 4.15 Triple Integrals -- Exercise 4.5 -- 4.16 Application to Volume (Triple Integrals) -- Exercise 4.6 -- 4.17 Drichlet's* Theorem -- Exercise 4.7 -- Objective Type Questions -- Answers to Objective Type Questions -- Unit V. Vector Calculus -- 5.1 Vector Function -- 5.2 Vector Differentiation -- 5.3 Some Results on Differentiation -- Exercise 5.1 -- 5.4 Scalar Point Function -- 5.5 Vector Point Function -- 5.6 Gradient or Slope of Scalar Point Function -- 5.7 Geometrical Meaning of Gradient, Normal -- 5.8 Directional Derivative -- 5.9 Properties of Gradient -- Exercise 5.2 -- 5.10 Divergence of a Vector Point Function -- 5.11 Physical Interpretation of Divergence -- 5.12 Curl of a Vector -- 5.13 Physical Meaning of a Curl -- 5.14 Vector Identities -- Exercise 5.3 -- 5.15 Vector Integration -- 5.16 Line Integral -- 5.17 Surface Integral -- 5.18 Volume Integral -- Exercise 5.4 -- 5.19 Green's Theorem -- Exercise 5.5 -- 5.20 Stoke's Theorem.

5.21 Cartesian Representation of Stoke's Theorem -- Exercise 5.6 -- 5.22 Gauss's Divergence Theorem -- 5.23 Cartesian Representation of Gauss's Theorem -- Exercise 5.7 -- Objective Type Questions -- Answers to Objective Type Questions -- Unsolved Question Papers (2004-2009) -- Index.