Rashtrasant Tukadoji Maharaj Nagpur University, Maharashtra, Civil Engineering Semester 3, Applied Mathematics – III Syllabus

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Unit - 1 LAPLACE TRANSFORM

Unit 1

Laplace Transform

1.1 Definition

1.2 Properties Statement only

1.3 Inverse Laplace transform using partial fraction method and properties of Laplace transform

1.4 Convolution theorem Statement only

1.5 Laplace transform of periodic functions Statement only

1.6 Unit step function and unit impulse function Statement only

Unit - 2 FOURIER SERIES & FOURIER TRANSFORM

Unit 2

Fourier Series Fourier Transform

2.1 Fourier Series Periodic functions and their Fourier expansions

2.2 Even and odd functions

2.3 Change of interval

2.4 Half range expansions

2.5 Fourier Transform Definition and Properties excluding FFT

2.6 Fourier integral theorem

Unit - 3 FUNCTIONS OF COMPLEX VARIABLES

Unit 3

Functions of Complex Variables

3.1 Analytic function

3.2 CauchyRiemann conditions

3.3 Harmonic function Excluding orthogonal system

3.4 MilneThomson method

3.5 Cauchy integral theorem integral formula Statementonly

3.6 Taylor’s Laurent’s series Statement only

3.7 Zeros and singularities of analyticfunction

3.8 Residue theorem Statement only

Unit - 4 PARTIAL DIFFERENTIAL EQUATIONS

Unit 4

Partial Differential Equations

4.1 Partial differential equations of first order first degree i.e. Lagrange’s form

4.2 Method of separations of variables

Unit - 5 MATRICES

Unit 5

Matrices

5.1 Linear dependence of vectors

5.2 Eigen values and Eigen vectors

5.3 Reduction to diagonal form

5.4 Singular value decomposition Sylvester’s theorem Statement only

5.5 Largest eigen value and corresponding eigen vector by iteration method

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