Engineering Mathematics. Volume-I

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Cover Preface to the Second Edition Preface to the First Edition Acknowledgements Contents Syllabus Module1: Differential Calculus-I 1.1 Introduction 1.2 nth Derivatives of Some Standard Functions 1.3 Leibnitz’s Theorem 1.4 Polar Curves 1.5 Radius of Curvature 1.6 Derivatives of Arc Lengths Module 2: Differential Calculus-II 2.1 Introduction 2.2 Taylor’s Theorem and Maclaurin’s Series 2.3 Indeterminate Forms 2.4 L’Hospital’s Rule 2.5 Partial Differentiation 2.6 Function of Two Variables 2.7 Partial Differential Coefficients 2.8 Homogeneous Functions 2.9 Total Derivative 2.10 Differentiation of Composite Functions (or) Chain Rule 2.11 Jacobian 2.12 Properties of Jacobians 2.13 Taylor’s Expansion of a Function of Two Variables 2.14 Maxima and Minima of Functions of Two Variables 2.15 Errors and Approximation Module 3: Vector Calculus 3.1 Introduction 3.2 Scalar and Vector Point Functions 3.3 Derivative of a Vector Valued Functions 3.4 Gradient, Divergence and Curl 3.5 Solenoidal Vector Function 3.6 Curl of a Vector Function 3.7 Vector Identities 3.8 Orthogonal Curvilinear Coordinates 3.9 Unit Vectors or Base Vectors and Scalar Vectors 3.10 Introduction 3.11 Differentiation under the Integral Sign 3.12 Tracing of Curves 3.13 Procedure for Tracing Curves in Cartesian Form 3.14 Polar Form 3.15 Parametric Form 3.16 Applications Module 4: Integral Calulus 4.1 Reduction Formulae 4.2 Differential Equation 4.3 Solution of First Order, First Degree Equations 4.4 Equations Reducible to Variables Separable Type 4.5 Homogeneous Equations 4.6 Linear Equations 4.7 Equations Reducible to Linear Form 4.8 Exact Equations 4.9 Equations Reducible to Exact Form with Standard Integrating Factors 4.10 Applications of Differential Equations Module 5: Linear Algebra 5.1 Introduction 5.2 Elementary Transformations 5.3 Uses of Elementary Transformations 5.4 Rank of a Matrix 5.5 Solution of a System of Linear Homogeneous Equations 5.6 Solution of a System of Linear Non Homogeneous Equations 5.7 Linear Transformations 5.8 Gauss-Seidel Method 5.9 Eigenvalues and Eigenvectors 5.10 Orthogonal Transformation 5.11 Power Method or Rayleigh’s Power Method 5.12 LU-Decomposition/Factorization 5.13 Reduction to Diagonal Form 5.14 Quadratic Forms 5.15 Reduction of Quadratic Form to Canonical Form 5.16 Nature of Quadratic Form Model Question Paper-I Model Question Paper-II