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# Kreyszig's Advanced Engineering Mathematics - Volume I (English)

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ISBN: 9788126543120 Publisher: Wiley
Year of publishing: 2013 Format: Paperback
No of Pages: 468 Language: English

First year Engineering Students of GBTU. Preface Chapter 1: Differential Calculus I Learning Objectives Introduction Successive Differentiation: nth Derivative of Standard Functions Leibnitz's Theorem...Read more

First year Engineering Students of GBTU. Preface Chapter 1: Differential Calculus I Learning Objectives Introduction Successive Differentiation: nth Derivative of Standard Functions Leibnitz's Theorem Partial Derivatives Homogeneous Function Total Derivatives Variables Treated as Constant Asymptotes Tracing the Curve in Cartesian Form Tracing of Curves in Parametric Form Tracing the Curves in Polar Form Important Points and Formulas True and False Questions Exercises Answers Chapter 2: Differential Calculus II Learning Objectives Introduction Taylor's and Maclaurin's Theorems and Expansion of Functions Expansion of Functions Jacobians Functionally Dependent Functions Errors and Approximations Maxima and Minima of Function of Two Variables Constrained Maxima and Minima (Lagrange's Method of Undetermined Multipliers) Important Points and Formulas True and False Questions Match the Following Exercises Answers Chapter 3: Linear Algebra Learning Objectives Introduction Basic Concepts: Matrices Determinants Real Matrices: Symmetric, Skew-Symmetric and Orthogonal Complex Matrices Adjoint and Inverse of a Matrix Inverse of a Matrix by Elementary Transformations (or Gauss-Jordan Method) Rank of a Matrix System of Linear Equations Vectors: Linear Dependence and Independence System of Linear Equations: Triangular Systems Characteristic Equation Eigenvalues and Eigenvectors Cayley-Hamilton Theorem Diagonalization and Powers of a Matrix Applications of Matrices to Engineering Problems Vector Spaces: Subspaces, Rank and Nullity Linear Transformations Kernel of a Linear Transformation Important Points and Formulas Multiple-Choice Questions True and False Questions Exercises Answers Chapter 4: Multiple Integrals Learning Objectives Introduction Double Integrals Triple Integrals Change of Order of Integration in a Double Integral Change of Variables Rectification of Standard Curves Area as a Double Integral (Area Enclosed by Plane Curves) Volume as a Triple Integral Volume of Solids Area of a Curved Surface Beta and Gamma Functions Dirichlet's Integrals and Applications Important Points and Formulas Multiple-Choice Questions Match the Following Exercises Answers Chapter 5: Vector Calculus Learning Objectives Introduction Vector Algebra Differentiation of a Vector Gradient of a Scalar Point Function Directional Derivative Angle of Intersection of Two Surfaces Divergence and Curl Solenoidal and Irrotational Vectors Vector Integration Surface and Volume Integrals Green's Theorem in the Plane Gauss Divergence Theorem Stokes' Theorem Important Points and Formulas Fill in the Blanks Exercises Answers Appendix

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