## Kreyszig's Applied Mathematics - 1

Rs569

Publisher

### Wiley India Pvt Ltd

Publication Year 2014
ISBN-13

### ISBN 9788126550753

ISBN-10 8126550759
Binding

#### Paperback

Number of Pages 552 Pages
Language (English)
Subject

#### Educational: Mathematics & numeracy

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.

Chapter 1 Linear Algebra

Introduction to Matrices
Definition and Notation: Matrices
Inverse of a Matrix by Elementary Transformations (or Gauss-Jordan Method)
Rank of a Matrix
System of Linear Equations
Consistency of Homogeneous Linear System of Equations
Linear Transformations (in General)
Eigenvalues and Eigenvectors
Cayley-Hamilton Theorem
Diagonalization and Powers of a Matrix
Vector Spaces
Chapter 2 Differential Calculus I

Introduction
Successive Differentiation: nth Derivative of Standard Functions
Leibniz's Theorem
Taylor's and Maclaurin's Theorems
Expansion of Functions
Asymptotes
Tracing the Curve in Cartesian Form
Tracing the Curves in Polar Form
Tracing of Curves in Parametric Form
Chapter 3 Differential Calculus 2

Introduction
Limits and Continuity
Partial Derivatives
Variables Treated as Constant
Euler's Theorem on Homogeneous Function
Total Differential
Jacobians
Taylor's and Maclaurin's Theorems and Expansion of Functions
Maxima and Minima of Function of Two Variables
Constrained Maxima and Minima (Lagrange's Method of Undetermined Multipliers)
Leibniz Rule for Differentiation under Integral Sign
Chapter 4 Integral Calculus

Definite Integral as a Limit of Riemann Sums
Area of Surfaces of Revolution
Volume of Solid of Revolution
Volume of Solid of Revolution (about x-Axis)
Double Integrals
Change of Order of Integration (Reverse Order of Integration)
Area using Double Integrals
Volume using Double Integral
Triple Integral for Cartesian Co-ordinates
Change of Variables in Multiple Integrals
Beta and Gamma Functions
Dirichlet's Integrals and Applications
Chapter 5 Infinite Series

Introduction
Sequences
Series
Geometric Series
Series of Positive Terms
Harmonic Series of Order p (p-Series)
Comparison Tests
D'Alembert's Ratio Test
More Tests for Convergence (Optional)
Integral Test
Cauchy's nth Root Test
Leibniz Test on Alternating Series
Series of Positive and Negative Terms
Power Series
Convergence of Exponential, Logarithmic and Binomial Series
Uniform Convergence of Series of Functions