UIT-RGPV (Autonomous) Bhopal
Subject code IT Subject Mathematics-III
Semester: IV
For credits & marks refer your scheme
Course Objectives The objective of the course is to familiarize the engineering students with techniques of Fourier expansion, transform techniques, numerical computations and their applications in engineering sciences. It aims to equip the students to deal with advanced level of mathematics and applications that would be essential for their disciplines. COURSE CONTENTS
Unit I
Vector Calculus Differentiation of vectors, scalar and vector point function, Gradient, Geometrical meaning of gradient, Directional derivative, Divergence and curl, Physical interpretation of divergence and curl.Line integral, Surface integral and Volume integral, Stokes theorem (Greens, theorem as a special case) and Gauss divergence theorem.
Unit II Solution of Algebraic and Transcendental Equations Bisection method. Iteration methods based on first degree equation Secant method, Method of false position, Newton-Raphson method. System of Simultaneous linear equations Gauss elimination method, Gauss Jordan’s Method, Crout’s Method,
Jacobi’s method and Gauss-Seidal method.
Unit III Interpolation Difference Operators, Interpolation formulae for equally and unequally spaced intervals. Numerical Integration Trapezoidal, Simpsons 1/3, Simpsons 3/8 and Weddle’s formulae.
Unit IV Fourier Series Euler’s formula, Fourier series for discontinuous functions, Expansion of odd and even periodic functions, Half range series. Introduction to Fourier Transform CO 1 Develop the concept of vector calculus and its applications CO 2 Illustrate the numerical method of solving algebraic and transcendental equations as well as simultaneous linear equations. CO 3 Analyze the concept of Interpolation and Numerical Integration CO 4 Understand the concept of Fourier series and Fourier transform and its application in various engineering problems. CO 5 Develop the concept of Laplace Transform and Inverse Laplace Transform to solve boundary value problems.
Academic Session 2020 - 21 Unit Vb 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 derivative and integral. Inverse Laplace transform
& its properties, Convolution theorem, Applications of Laplace transforms to solve the ordinary differential equations
Books Recommended
1. BS. Grewal, Higher Engineering Mathematics, Khanna Publishers. MK. Jain, Iyengar, R.K.Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Publishers.
B.V. Rammana, Higher Engineering Mathematics, Tata McGraw Hill New Delhi. BS. Grewal , Numerical Methods in Engineering and Science, Khanna Publishers 5. E. Kreyzig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons
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