The article contains the subject code MA3303, which deals with the Anna University B.E Electrical and Electronics Engineering Semester – III Probability and Complex Functions Syllabus. Unit wise detailed syllabus of this subject MA3303 is included in this article. You can get assistance for note preparation or can understand the chapters contain topics in one place.
Effective results need effective preparation and having the required knowledge of the topics included in the subject. If you want to perform well in academics proper guidance and the subject syllabus in mind are necessary, this article MA3303 – Probability and Complex Functions Syllabus will fulfill the details regarding your preparation.
If you want to know more about the syllabus of B.E Electrical and Electronics Engineering connected to an affiliated institution’s four-year undergraduate degree program. We provide you with a detailed Year-wise, semester-wise, and Subject-wise syllabus in the following link B.E Electrical and Electronics Engineering Syllabus Anna University, Regulation 2021.
Aim Of Objectives:
- This course aims to provide the required skills to apply statistical tools to engineering problems.
- To introduce the basic concepts of probability and random variables.
- To introduce the basic concepts of two-dimensional random variables.
- To develop an understanding of the standard techniques of complex variable theory in particular analytic function and its mapping property.
- To familiarize the students with complex integration techniques and contour integration techniques which can be used in real integrals.
- To acquaint the students with Differential Equations which are significantly used in engineering problems.
MA3303 – Probability and Complex Functions Syllabus
Unit I: Probability And Random Variables
Axioms of probability – Conditional probability – Baye’s theorem – Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions – Functions of a random variable.
Unit II: Two-Dimensional Random Variables
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).
Unit III: Analytic Functions
Analytic functions – Necessary and sufficient conditions for analyticity in Cartesian and polar coordinates – Properties – Harmonic conjugates
Construction of analytic function – Conformal mapping – Mapping by functions w = z + c, cz,—,1 z z“ – Bilinear transformation.
Unit IV: Complex Integration
Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s and Laurent’s series – Singularities – Residues – Residue theorem – Application of residue theorem for evaluation of real integrals – Applications of circular contour and semicircular contour (with poles NOT on real axis).
Unit V: Ordinary Differential Equations
Higher order linear differential equations with constant coefficients – Method of variation of parameters – Homogenous equation of Euler’s and Legendre’s type – System of simultaneous linear first-order differential equations with constant coefficients – Method of undetermined coefficients.
Text Books:
- Johnson. R.A., Miller. I and Freund. J., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 9th Edition, 2016.
- Milton. J. S. and Arnold. J.C., “Introduction to Probability and Statistics”, Tata McGraw Hill, 4th Edition, 2007.
- Grewal. B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 44th Edition, 2018.
References:
- Devore. J.L., “Probability and Statistics for Engineering and the Sciences”, Cengage Learning, New Delhi, 8th Edition, 2014.
- Papoulis. A. and Unnikrishnapillai. S., “Probability, Random Variables and Stochastic Processes”, McGraw Hill Education India, 4th Edition, New Delhi, 2010.
- Ross. S.M., “Introduction to Probability and Statistics for Engineers and Scientists”, 5th edition, Elsevier, 2014.
- Spiegel. M.R., Schiller. J. and Srinivasan. R.A., “Schaum’s Outline of Theory and Problems of Probability and Statistics”, Tata McGraw Hill Edition, 4th Edition, 2012.
- Walpole. R.E., Myers. R.H., Myers. S.L. and Ye. K., “Probability and Statistics for Engineers and Scientists”, Pearson Education, Asia, 9th Edition, 2010.
- Kreyszig. E, “Advanced Engineering Mathematics”, John Wiley and Sons, 10th Edition, New Delhi, 2016.
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