RGPV B.E 3rd Semester (ME/AU/CM/FT/IP/MI) M-III Syllabus

This is to inform you that RGPV has declared Mathematics III syllabus for B.E 3rd Semester ME/AU/CM/FT/IP/MI branch students.

M-III (BE III ) ME/AU/CM/FT/IP/MI Branches )

Course Contents (Proposed)

Unit: I Fourier Series: 

Fourier Series for Continuous & Discontinuous Functions, Expansion of odd and even periodic

functions, Half range Fourier series, Complex form of Fourier Series, Parseval’s formula.

Unit: II 

Fourier Transform: Complex Fourier Transform, Fourier Sine and Cosine Transforms.

Unit: III 

Laplace Transform: Introduction of Laplace Transform, Laplace Transform of elementary Functions, Properties of Laplace Transform, Change of Scale Property, First and Second Shifting Properties, Laplace Transform of Derivatives and Integrals. Inverse Laplace Transform & its Properties, Convolution theorem, Applications of Laplace Transform in solving the Ordinary Differential Equations.

Unit: IV

Functions of Complex Variables : Analytic functions, Harmonic Conjugate, Cauchy-Riemann Equations, Line Integral, Cauchy’s Theorem, Cauchy’s Integral Formula, Singular Points, Poles & Residues, Residue Theorem , Application of Residues theorem for Evaluation of Real Integrals.

Unit: V

Vector Calculus: Differentiation of Vectors, Scalar and Vector Point functions, Gradient, Directional derivative, Divergence and Curl. Line Integral, Surface Integral and Volume Integral, Stoke’s Theorem and Gauss divergence theorem. 

References:

1. Erwin Kreyszig: Advanced Engineering Mathematics, Wiley India.

2. B.S. Grewal: Higher Engineering Mathematics , Khanna Publication.

3. Engineering Mathematics By Samnta Pal and Bhutia, Oxford Publication

4. Ramana: Advance Engg. Mathematics, TMH New Delhi

5. Numerical Methods for Engineers by Steven C. Chapra, McGraw Hill Education

6. Introductory Methods of Numerical Analysis by S. S. Sastry, PHI Learning Pvt. Ltd.

7. Numerical Methods By Shrimanta Pal, Oxford