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# Engineering Mathematics-II

Higher Engineering Mathematics is a comprehensive book for undergraduate students of engineering. The book comprises of chapters on algebra, geometry and vectors, calculus, series, differential equations, complex analysis, transforms, and numerical techniques. Language: English

Pages: 390

Author: Prof. P. Panigrahi, Prof. J. Kumar, Prof. P.V.S.N. Murthy and Prof. S. Kumar

Price: Free ## Outlines of Engineering Mathematics-II

### Module 1: Matrices and Linear Algebra

Lesson 1: Linear Equations and Matrices

Lesson 2: Rank of a Matrix and Solution of a Linear System

Lesson 3: Inverse of Matrices by Determinants and Gauss-Jordan Method

Lesson 4: Vector Spaces, Linear Dependence and Independence

Lesson 5: Basis and Dimension of Vector Spaces

Lesson 6: Eigenvalues and Eigenvectors of Matrices

Lesson 7: The Cayley Hamilton Theorem and Applications

Lesson 8: Diagonalization of Matrices

Lesson 9: Linear and Orthogonal Transformations

### Module 2: Complex Variables

Lesson 11: Limit, Continuity, Derivative of Function of Complex Variable

Lesson 12: Analytic Function, C-R Equations, Harmonic Functions,

Lesson 13: Line Integrals in Complex Plane

Lesson 14: Cauchy’ Integral Theorem and Cauchy’s Integral Formula

Lesson 15: Infinite Series, Convergence Tests, Uniform Convergence

Lesson 16: Power Series

Lesson 17: Taylor and Laurent series

Lesson 18: Zeros and singularities

Lesson 19: Residue Theorem

### Module 3: Fourier Series and Fourier Transform

Lesson 20: Introduction

Lesson 21: Fourier Series of a Periodic Function

Lesson 22: Convergence Theorems

Lesson 23: Half Range Sine and Cosine Series

Lesson 24: Integration and Differentiation of Fourier Series

Lesson 25: Bessel’s Inequality and Parseval’s Identity

Lesson 26: Complex Form of Series

Lesson 27: Fourier Integral

Lesson 28: Fourier Integrals (Cont.)

Lesson 29: Fourier Sine and Cosine Transform

Lesson 30: Fourier Transform

Lesson 31: Fourier Transform (Cont.)

Lesson 32: Fourier Transform (Cont.)

Lesson 33: Finite Fourier Transform

### Module 4: Partial Differential Equations

Lesson 34: Partial Differential Equations

Lesson 35: Linear First Order Equation

Lesson 36: Geometric Interpretation of a First Order Equation

Lesson 37: Integral Surface through a Given Curve – The Cauchy Problem

Lesson 38: Non-Linear First Order p.d.e – Compatible System

Lesson 39: Non – linear p.d.e of 1st order complete integral – Charpit’s method

Lesson 40: Special Types of First Order Non-Linear p.d.e

Lesson 41: Classification of Semi-linear 2nd order Partial Differential Equations

Lesson 42: Solution of Homogeneous and Non-Homogeneous Linear Partial Differential Equations

Lesson 43: Non-Homogeneous Linear Equation

Lesson 44: Method of Separation of Variables

Lesson 45: One Dimensional Heat Equation

Lesson 46: One Dimensional Wave Equation

Lesson 47: Laplace Equation in 2-Dimension

Lesson 48: Application of Laplace and Fourier Transforms to Boundary Value Problems in p.d.es

Lesson 49: Laplace And Fourier Transform Techniques To Wave Equation and  Laplace Equation

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