# Advanced Engineering Mathematics: Engineering Mathematics-I, (As per syllabus of JNTU)

ISBN: 9788126543878

388 pages

## Description

Engineering Mathematics-I 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 explanations of the theory and numerous step-by-step solved problems and examples. The questions have been hand-picked from the previous years’ question papers and are suitable to the current pattern of questions asked. Extreme care has been taken to provide careful and correct mathematics, outstanding exercises and helpful worked examples.

Chapter 1 Theory of Matrices

1.1 Introduction

1.2 Basic Concepts: Matrices

1.3 Determinants

1.4 Real Matrices: Symmetric, Skew-Symmetric and Orthogonal

1.5 Complex Matrices

1.6 Adjoint and Inverse of a Matrix

1.7 Inverse of a Matrix by Elementary Transformations (Gauss-Jordan Method)

1.8 Rank of a Matrix

1.9 System of Linear Equations

1.10 Vectors: Linear Dependence and Indpendence

1.11 System of Linear Equations: Triangular Systems

1.12 Characteristic Equation

1.13 Eigenvalues and Eigenvectors

1.14 Cayley-Hamilton Theorem

1.15 Diagonalization and Powers of a Matrix

1.16 Applications of Matrices to Engineering Problems

1.17 Linear Transformation

1.18 Orthogonal Transformation

1.19 Quadratic Forms

Chapter 2 Differential Calculus Methods

2.1 Introduction

2.2 Rolle’s Theorem

2.3 Lagrange’s Mean Value Theorem

2.4 Cauchy’s Mean Value Theorem

2.5 Functions of Several Variables

2.6 Partial Derivatives

2.7 Total Derivatives

2.8 Jacobians

2.9 Functionally Dependent Functions

2.10 Maxima and Minima

2.11 Constrained Maxima and Minima (Lagrange’s Method of Undetermined Multipliers)

Chapter 3 Improper Integrals and Multiple Integrals

3.1 Introduction

3.2 Improper Integrals of First Kind

3.3 Improper Integrals of Second Kind

3.4 Beta and Gamma Functions

3.5 Double Integrals

3.6 Triple Integrals

3.7 Change of Order of Integration in a Double Integral

3.8 Change of Variables

3.9 Rectification of Standard Curves