# Kreyszig's Applied Mathematics - I, (As per syllabus of KU)

ISBN: 9788126550753

552 pages

## Description

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

1.1 Introduction to Matrices

1.2 Definition and Notation: Matrices

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

1.4 Rank of a Matrix

1.5 System of Linear Equations

1.6 Consistency of Homogeneous Linear System of Equations

1.7 Linear Transformations (in General)

1.8 Eigenvalues and Eigenvectors

1.9 Cayley-Hamilton Theorem

1.10 Diagonalization and Powers of a Matrix

1.11 Quadratic Forms

1.12 Vector Spaces

Chapter 2 Differential Calculus I

2.1 Introduction

2.2 Successive Differentiation: nth Derivative of Standard Functions

2.3 Leibniz’s Theorem

2.4 Taylor’s and Maclaurin’s Theorems

2.5 Expansion of Functions

2.6 Asymptotes

2.7 Tracing the Curve in Cartesian Form

2.8 Tracing the Curves in Polar Form

2.9 Tracing of Curves in Parametric Form

Chapter 3 Differential Calculus 2

3.1 Introduction

3.2 Limits and Continuity

3.3 Partial Derivatives

3.4 Variables Treated as Constant

3.5 Euler’s Theorem on Homogeneous Function

3.6 Total Differential

3.7 Jacobians

3.8 Taylor’s and Maclaurin’s Theorems and Expansion of Functions

3.9 Maxima and Minima of Function of Two Variables

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

3.11 Leibniz Rule for Differentiation under Integral Sign

Chapter 4 Integral Calculus

4.1 Definite Integral as a Limit of Riemann Sums

4.2 Area of Surfaces of Revolution

4.3 Volume of Solid of Revolution

4.3.1 Volume of Solid of Revolution (about x-Axis)

4.4 Double Integrals

4.5 Change of Order of Integration (Reverse Order of Integration)

4.6 Area using Double Integrals

4.7 Volume using Double Integral

4.8 Triple Integral for Cartesian Co-ordinates

4.9 Change of Variables in Multiple Integrals

4.10 Beta and Gamma Functions

4.11 Dirichlet’s Integrals and Applications

Chapter 5 Infinite Series

5.1 Introduction

5.2 Sequences

5.3 Series

5.4 Geometric Series

5.5 Series of Positive Terms

5.6 Harmonic Series of Order p (p-Series)

5.7 Comparison Tests

5.8 D’Alembert’s Ratio Test

5.9 More Tests for Convergence (Optional)

5.10 Integral Test

5.11 Cauchy’s nth Root Test

5.12 Leibniz Test on Alternating Series

5.13 Series of Positive and Negative Terms

5.14 Power Series

5.15 Convergence of Exponential, Logarithmic and Binomial Series

5.16 Uniform Convergence of Series of Functions

Exercises

Answers