This subject aims to provide students on the electronics degree programme with knowledge of key theoretical concepts and methods of Calculus of several variables (Part 7-1) and Stocastic Processes (Part 7-2).
Introduction to Probability Theory:
Random phenomena and experiments,definitions of probability, conditional probability, Bayes theorem,independence, Random variables (continuous and discrete): distributionfunctions, probability density functions (PDFs), joint random variables, marginaldistributions, conditional PDFs, independence.
Statistical Averages:
Function of a random variable, moments and centralmoments, the Chebyshev inequality, the Cauchy-Schwartz inequality, thecharacteristic function, joint moments, Correlation and covariance.Transformation of random variables
Special Distributions:
The binomial distribution, the Poisson distribution, thePoisson approximation to the binomial distribution, the Gaussian distribution.Distributions used in engineering. The exponential distribution. The CentralLimit Theorem
Introduction to Stochastic Processes:
Random Walks Markov chains. Statistics of random processes, statisticalaverages, autocorrelation, autocovariance, stationarity, crosscorrelation andcross-covariance, SSS and WSS, time averages and ergodicity.
Queueing Theory:
Introduction to Poisson processes.
Functions of One Variable:
Limit of a Sequence. Properties of limits. Convergence of bounded sequences. Limits for continuity and differentiability. L’Hopital’s Rule. Limit of a series. Convergence and tests for convergence. Absolute convergence. Review of Taylor and Maclaurin Series. Convergence of Power series. Functions defined via an Integral. Recursion formulas. The Gamma Function.
Calculus of a Several Variables:
Functions of several variables. Partial differentiation. Chain rule for partial derivatives. Cylindrical and spherical polar coordinates. Area and Volume elements. Double and Triple integrals. Change of variables formulas for Multiple Integrals.
Vector calculus:
Scalar and vector fields. Examples in electromagnetism. Field lines. The Nabla Operator. Gradient, directional derivative, divergence and curl. Properties of Nabla. Contours and Surfaces. Line element. Line Integrals. Scalar and vector surface elements. Surface Integrals. Gauss’ and Stokes’ Theorems. Maxwell’s Equations in Integral and point form. Applications of Vector Calculus and Maxwell’s Equations to static and time-varying electromagnetic fields.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 20 |
| Formal Examination | 80 |