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## Book Description

Designed for the core papers Engineering Mathematics II and III, which students take up across the second and third semesters, Engineering Mathematics Volume-II offers detailed theory with a wide variety of solved examples with reference to engineering applications, along with over 1,000 objective-type questions that include multiple choice questions, fill in the blanks, match the following and true or false statements.

1. Cover
2. Title Page
3. Contents
5. Dedication
6. Preface
7. 1. Eigenvalues and Eigenvectors
1. 1.1 Introduction
2. 1.2 Linear Transformation
3. 1.3 Characteristic Value Problem
4. 1.4 Properties of Eigenvalues and Eigenvectors
5. 1.5 Cayley-Hamilton Theorem
6. 1.6 Reduction of a Square Matrix to Diagonal Form
7. 1.7 Powers of a Square Matrix A— Finding of Modal Matrix P and Inverse Matrix A-1
9. 3. Solution of Algebraic and Transcendental Equations
10. 4. Interpolation
1. 4.1 Introduction
2. 4.2 Interpolation with Equal Intervals
3. 4.3 Symbolic Relations and Separation of Symbols
4. 4.4 Interpolation
5. 4.5 Interpolation Formulas for Equal Intervals
6. 4.6 Interpolation with Unequal Intervals
7. 4.7 Properties Satisfied by Δ ′
8. 4.8 Divided Difference Interpolation Formula
9. 4.9 Inverse Interpolation Using Lagrange’s Interpolation Formula
10. 4.10 Central Difference Formulas
11. 5. Curve Fitting
12. 6. Numerical Differentiation and Integration
1. 6.1 Introduction
2. 6.2 Errors in Numerical Differentiation
3. 6.3 Maximum and Minimum Values of a Tabulated Function
4. 6.4 Numerical Integration: Introduction
5. 6.5 Cubic Splines
6. 6.6 Gaussian Integration
13. 7. Numerical Solution of Ordinary Differential Equations
1. 7.1 Introduction
2. 7.2 Methods of Solution
3. 7.3 Predictor-Corrector Methods
14. 8. Fourier Series
1. 8.1 Introduction
2. 8.2 Periodic Functions, Properties
3. 8.3 Classifiable Functions—Even and Odd Functions
4. 8.4 Fourier Series, Fourier Coefficients and Euler’s Formulae in (a, a +2 π)
5. 8.5 Dirichlet’s Conditions for Fourier Series Expansion of a Function
6. 8.6 Fourier Series Expansions: Even/Odd Functions
7. 8.7 Simply-Defined and Multiply-(Piecewise) Defined Functions
8. 8.8 Change of Interval: Fourier Series in Interval (a, a + 2l) :
9. 8.9 Fourier Series Expansions of Even and Odd Functions in (−l, l )
10. 8.10 Half-Range Fourier Sine/Cosine Series: Odd and Even Periodic Continuations
11. 8.11 Root Mean Square (RMS) Value of a Function
15. 9. Fourier Integral Transforms
16. 10. Partial Differential Equations
1. 10.1 Introduction
2. 10.2 Order, Linearity and Homogeneity of a Partial Differential Equation
3. 10.3 Origin of Partial Differential Equation
4. 10.4 Formation of Partial Differential Equation by Elimination of Two Arbitrary Constants
5. 10.5 Formation of Partial Differential Equations by Elimination of Arbitrary Functions
6. 10.6 Classification of First-Order Partial Differential Equations
7. 10.7 Classification of Solutions of First-Order Partial Differential Equation
8. 10.8 Equations Solvable by Direct Integration
9. 10.9 Quasi-Linear Equations of First Order 0.10 Solution of Linear, Semi-Linear and Quasi-Linear Equations
10. 10.11 Nonlinear Equations of First Order
11. 10.12 Euler’s Method of Separation of Variables
12. 10.13 Classification of Second-Order Partial Differential Equations
13. 10.14 Two-dimensional Wave Equation
17. 11. Z-Transforms and Solution of Difference Equations
1. 11.1 Introduction
2. 11.2 Z-Transform: Definition
3. 11.3 Z-Transforms of Some Standard Functions (Special Sequences)
4. 11.4 Recurrence Formula for the Sequence of a Power of Natural Numbers
5. 11.5 Properties of Z-Transforms
6. 11.6 Inverse Z-Transform
7. 11.7 Application of Z-Transforms: Solution of a Difference Equations by Z-Transform
8. 11.8 Method for Solving a Linear Difference Equation with Constant Coefficients
18. 12. Special Functions
1. 12.1 Introduction
2. 12.2 Gamma Function
3. 12.3 Recurrence Relation or Reduction Formula
4. 12.4 Various Integral Forms of Gamma Function
5. 12.5 Beta Function
6. 12.6 Various Integral Forms of Beta Function
7. 12.7 Relation Between Beta and Gamma Functions
8. 12.8 Multiplication Formula
9. 12.9 Legendre’s Duplication Formula
10. 12.10 Legendre Functions
11. 12.11 Bessel Functions
19. 13. Functions of a Complex Variable
1. 13.1 Introduction
2. 13.2 Complex Numbers-Complex Plane
3. 13.3 Laplace’s Equation: Harmonic and Conjugate Harmonic Functions
20. 14. Elementary Functions
1. 14.1 Introduction
2. 14.2 Elementary Functions of a Complex Variable
21. 15. Complex Integration
22. 16. Complex Power Series
23. 17. Calculus of Residues
1. 17.1 Evaluation of Real Integrals
24. 18. Argument Principle and Rouche’s Theorem
25. 19. Conformal Mapping
26. Notes
27. Question Bank
28. Acknowldegements