Engineering Mathematics-IV detail syllabus for Petroleum Engineering (Petro), 2017 scheme is taken from VTU official website and presented for VTU students. The course code (17MAT41), and for exam duration, Teaching Hr/week, Practical Hr/week, Total Marks, internal marks, theory marks, duration and credits do visit complete sem subjects post given below.
For all other petro 4th sem syllabus for be 2017 scheme vtu you can visit Petro 4th Sem syllabus for BE 2017 Scheme VTU Subjects. The detail syllabus for engineering mathematics-iv is as follows.
Course Objectives:
The objective is to provide students with mathematics fundamental, necessary to formulate, solve and analyze engineering problems by making them to learn the following topics
- Numerical methods to solve ordinary differential equations
- Finite difference method to solve partial differential equations
- Complex analysis
- Sampling theory
- Joint probability distribution and stochastic process
Module 1
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Module 2
Numerical Methods: Numerical solution of second order ordinary differential equations, Picard’s method, Runge-Kutta method and Milne’s method
Special Functions: Bessel’s functions- basic properties, recurrence relations, orthogonality and generating functions. Legendre’s functions – Legendre’s polynomial, Rodrigue’s formula, problems.
Module 3
Complex Variables: Function of a complex variable, limits, continuity, differentiability, Analytic Functions-Cauchy-Riemann equations in Cartesian and polar forms. Properties and construction of analytic functions. Complex line Integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue, poles, Cauchy’s Residue theorem with proof and problems.
Transformations: Conformal transformations, discussion of transformations and bilinear transformations.
Module 4
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Module 5
Sampling Theory: Sampling, Sampling distributions, standard error, test of hypothesis for means and proportions, confidence limits for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit.
Stochastic process
Stochastic process, probability vector, stochastic matrices, fixed points, regular stochastic matrices, Markov chains, higher transition probability.
Course Outcomes:
At the end of the course student will be able to:
- Use appropriate numerical methods to solve first and second order ordinary differential equations.
- Use Bessel’s and Legendre’s function which often arises when a problem possesses axial and spherical symmetry, such as in quantum mechanics, electromagnetic theory, hydrodynamics and heat conduction.
- State and prove Cauchy’s theorem and its consequences including Cauchy’s integral formula, compute residues and apply the residue theorem to evaluate integrals.
- Analyze, interpret, and evaluate scientific hypotheses and theories using rigorous statistical methods.
Text Books:
- B.V. Ramana “Higher Engineering Mathematics” Tata Mc Graw-Hill, 2006
- B.S. Grewal – Higher Engineering Mathematics, Khanna Publishers, 42nd Edition, 2013.
Reference Books:
- N P. Bali and Manish Goyal, “A text book of Engineering mathematics, Laxmi publications, latest edition.
- Kreyszig, Advanced Engineering Mathematics – 9th edition, Wiley, 2013.
- H. K Dass and Rajnish Verma,”Higher Engineering Mathematics”, S. Chand publishing, 1st edition, 2011.
For detail syllabus of all other subjects of BE Petro, 2017 scheme do visit Petro 4th Sem syllabus for 2017 scheme.
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