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.
Table of contents
- Cover
- Title Page
- Contents
- About the Author
- Dedication
- Preface
- 1. Eigenvalues and Eigenvectors
-
2. Quadratic Forms
- 2.1 Introduction
- 2.2 Quadratic Forms
- 2.3 Canonical Form (or) Sum of the Squares Form
- 2.4 Nature of Real Quadratic Forms
- 2.5 Reduction of a Quadratic Form to Canonical Form
- 2.6 Sylvestor’s Law of Inertia
- 2.7 Methods of Reduction of a Quadratic Form to a Canonical Form
- 2.8 Singular Value Decomposition of a Matrix
- 3. Solution of Algebraic and Transcendental Equations
-
4. Interpolation
- 4.1 Introduction
- 4.2 Interpolation with Equal Intervals
- 4.3 Symbolic Relations and Separation of Symbols
- 4.4 Interpolation
- 4.5 Interpolation Formulas for Equal Intervals
- 4.6 Interpolation with Unequal Intervals
- 4.7 Properties Satisfied by Δ ′
- 4.8 Divided Difference Interpolation Formula
- 4.9 Inverse Interpolation Using Lagrange’s Interpolation Formula
- 4.10 Central Difference Formulas
- 5. Curve Fitting
- 6. Numerical Differentiation and Integration
- 7. Numerical Solution of Ordinary Differential Equations
-
8. Fourier Series
- 8.1 Introduction
- 8.2 Periodic Functions, Properties
- 8.3 Classifiable Functions—Even and Odd Functions
- 8.4 Fourier Series, Fourier Coefficients and Euler’s Formulae in (a, a +2 π)
- 8.5 Dirichlet’s Conditions for Fourier Series Expansion of a Function
- 8.6 Fourier Series Expansions: Even/Odd Functions
- 8.7 Simply-Defined and Multiply-(Piecewise) Defined Functions
- 8.8 Change of Interval: Fourier Series in Interval (a, a + 2l) :
- 8.9 Fourier Series Expansions of Even and Odd Functions in (−l, l )
- 8.10 Half-Range Fourier Sine/Cosine Series: Odd and Even Periodic Continuations
- 8.11 Root Mean Square (RMS) Value of a Function
-
9. Fourier Integral Transforms
- 9.1 Introduction
- 9.2 Integral Transforms
- 9.3 Fourier Integral Theorem
- 9.4 Fourier Integral in Complex Form
- 9.5 Fourier Transform of f (x)
- 9.6 Finite Fourier Sine Transform and Finite Fourier Cosine Transform (FFCT)
- 9.7 Convolution Theorem for Fourier Transforms
- 9.8 Properties of Fourier Transform
- 9.9 Parseval’s Identity for Fourier Transforms
- 9.10 Parseval’s Identities for Fourier Sine and Cosine Transforms
-
10. Partial Differential Equations
- 10.1 Introduction
- 10.2 Order, Linearity and Homogeneity of a Partial Differential Equation
- 10.3 Origin of Partial Differential Equation
- 10.4 Formation of Partial Differential Equation by Elimination of Two Arbitrary Constants
- 10.5 Formation of Partial Differential Equations by Elimination of Arbitrary Functions
- 10.6 Classification of First-Order Partial Differential Equations
- 10.7 Classification of Solutions of First-Order Partial Differential Equation
- 10.8 Equations Solvable by Direct Integration
- 10.9 Quasi-Linear Equations of First Order 0.10 Solution of Linear, Semi-Linear and Quasi-Linear Equations
- 10.11 Nonlinear Equations of First Order
- 10.12 Euler’s Method of Separation of Variables
- 10.13 Classification of Second-Order Partial Differential Equations
- 10.14 Two-dimensional Wave Equation
-
11. Z-Transforms and Solution of Difference Equations
- 11.1 Introduction
- 11.2 Z-Transform: Definition
- 11.3 Z-Transforms of Some Standard Functions (Special Sequences)
- 11.4 Recurrence Formula for the Sequence of a Power of Natural Numbers
- 11.5 Properties of Z-Transforms
- 11.6 Inverse Z-Transform
- 11.7 Application of Z-Transforms: Solution of a Difference Equations by Z-Transform
- 11.8 Method for Solving a Linear Difference Equation with Constant Coefficients
-
12. Special Functions
- 12.1 Introduction
- 12.2 Gamma Function
- 12.3 Recurrence Relation or Reduction Formula
- 12.4 Various Integral Forms of Gamma Function
- 12.5 Beta Function
- 12.6 Various Integral Forms of Beta Function
- 12.7 Relation Between Beta and Gamma Functions
- 12.8 Multiplication Formula
- 12.9 Legendre’s Duplication Formula
- 12.10 Legendre Functions
- 12.11 Bessel Functions
- 13. Functions of a Complex Variable
- 14. Elementary Functions
- 15. Complex Integration
- 16. Complex Power Series
- 17. Calculus of Residues
- 18. Argument Principle and Rouche’s Theorem
- 19. Conformal Mapping
- Notes
- Question Bank
- Acknowldegements
- Copyright
Product information
- Title: Engineering Mathematics, Volume 2
- Author(s):
- Release date: March 2012
- Publisher(s): Pearson India
- ISBN: 9788131784952
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