## Course Detail

 Course Name Probability and Complex Variables Course Code 19MAT210 Program B. Tech. in Mechanical Engineering Semester Three Year Taught 2019

### Syllabus

Probability – Probability models and axioms, conditioning and Bayes’ rule Discrete random variables; probability mass functions; expectations, examples, multiple discrete random variables: joint PMFs, expectations, conditioning, independence Continuous random variables, probability density functions, expectations, examples, multiple continuous random variables, continuous Bayes rule, covariance and correlation. Statistics – Bayesian statistical inference, point estimators, parameter estimators, test of hypotheses, tests of significance.

Complex numbers, complex plane, polar form of complex numbers. Powers and roots, derivative. Analytic functions, Cauchy Riemann equations, Laplace equation, conformal mapping. Exponential function, trigonometric functions, hyperbolic functions, logarithms, general power and linear fractional transformation.

Complex line integral, Cauchy integral theorem, Cauchy integral formula, derivatives of analytical functions. Power series, Taylor series and McLaurin series. Laurent series, zeroes and singularities, residues, Cauchy residue theorem, evaluation of real integrals using residue theorem.

### Objectives and Outcomes

Course Objectives

The course is expected to enable the students

• To understand discrete and continuous random variables and to compute important measures.
• To carry out various statistical tests and to draw practical inferences.
• To perform calculus for complex variables.
• To apply complex analysis to integrals and series.

Course Outcomes

• CO1: To learn probabilistic models, random variables of one dimension and two dimension.
• CO2: To understand the theory of estimation
• CO3: To learn differentiation for complex functions
• CO4: To learn integration of complex functions.

CO – PO Mapping

 PO/PSO/ CO PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 PSO3 CO1 1 1 1 2 CO2 2 3 2 1 CO3 1 2 2 1 CO4 2 2 1 1

### Textbook / References

Reference(s)

• Introduction to Probability, D. Bertsekas and J. Tsitsiklis, 2nd Edition, Athena Scientific, 2008.
• Advanced Engineering Mathematics, Erwin Kreyszig, 10th Edition, Wiley, 2011.

Evaluation Pattern

 Assessment Weightage Test 1 (after 15th lecture hr) 25 *Continuous Assessment (CA) 25 Test 2 (after 30th Lecture hr) 30 *CA – Can be Quizzes, Assignment, Projects, and Reports.

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