This version of Advanced Engineering Mathematics by Prof. Erwin Kreyszig, globally the most popular textbook on the subject, is restructured to present the content in a concise and easy-to-understand manner. It fulfills the need for a book that not only effectively explains the concepts but also aids in visualizing the underlying geometric interpretation. Every chapter has easy to follow explanation of the theory and numerous step-by-step solved problems and examples. The questions have been hand-picked to suit the current pattern of questions asked. Extreme care has been taken to provide careful and correct mathematics, outstanding exercises.


Table of Contents:
Preface Chapter 1 Differential Calculus I 1.1 Introduction 1.2 Successive Differentiation: nth Derivative of Standard Functions 1.3 Leibnitz’s Theorem 1.4 Partial Derivatives 1.5 Homogeneous Function 1.6 Total Derivatives 1.7 Variables Treated as Constant 1.8 Asymptotes 1.9 Tracing the Curve in Cartesian Form 1.10 Tracing of Curves in Parametric Form 1.11 Tracing the Curves in Polar Form Chapter 2 Differential Calculus II 2.1 Introduction 2.2 Taylor’s and Maclaurin’s Theorems and Expansion of Functions 2.3 Expansion of Functions 2.4 Jacobians 2.5 Functionally Dependent Functions 2.6 Errors and Approximations 2.7 Maxima and Minima of Function of Two Variables 2.8 Constrained Maxima and Minima (Lagrange’s Method of Undetermined Multipliers) Chapter 3 Linear Algebra 3.1 Introduction 3.2 Basic Concepts: Matrices 3.3 Determinants 3.4 Real Matrices: Symmetric, Skew-Symmetric and Orthogonal 3.5 Complex Matrices 3.6 Adjoint and Inverse of a Matrix 3.7 Inverse of a Matrix by Elementary Transformations (or Gauss-Jordan Method) 3.8 Rank of a Matrix 3.9 System of Linear Equations 3.10 Vectors: Linear Dependence and Independence 3.11 System of Linear Equations: Triangular Systems 3.12 Characteristic Equation 3.13 Eigenvalues and Eigenvectors 3.14 Cayley-Hamilton Theorem 3.15 Diagonalization and Powers of a Matrix 3.16 Applications of Matrices to Engineering Problems 3.17 Vector Spaces: Subspaces, Rank and Nullity 3.18 Linear Transformations Chapter 4 Multiple Integrals 4.1 Introduction 4.2 Double Integrals 4.3 Triple Integrals 4.4 Change of Order of Integration in a Double Integral 4.5 Change of Variables 4.6 Rectification of Standard Curves 4.7 Area as a Double Integral (Area Enclosed by Plane Curves) 4.8 Volume as a Triple Integral 4.9 Volume of Solids 4.10 Area of a Curved Surface 4.11 Beta and Gamma Functions 4.12 Dirichlet’s Integrals and Applications Chapter 5 Vector Calculus 5.1 Introduction 5.2 Vector Algebra 5.3 Differentiation of a Vector 5.4 Gradient of a Scalar Point Function 5.5 Directional Derivative 5.6 Angle of Intersection of Two Surfaces 5.7 Divergence and Curl 5.8 Solenoidal and Irrotational Vectors 5.9 Vector Integration 5.10 Surface and Volume Integrals 5.11 Green’s Theorem in the Plane 5.12 Gauss Divergence Theorem 5.13 Stokes’ Theorem Important Points and Formulas Fill in the Blanks Exercises Answers Appendix