Short Title: Mathematics 7 Mathematics 7
Module Code: MATH H4064

 Credits: 5
Field of Study: Electronics and automation
Module Delivered in 3 programme(s)
Reviewed By: JOHN ANDREW DONNELLAN
Module Author: CORA STACK
Module Description: 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).
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Derive and apply fundamental laws and techniques of basic probability theory.
LO2 Apply knowledge of key properties of probability distribution functions one dimensions random variables.
LO3 Derive mean and variance of standard distributions, such as Binomial, Poisson, Geometric, Normal and Exponential distributions and to apply knowledge of these distributions to problem solving in engineering.
LO4 Apply knowledge of key properties of probability distributions of joint random variables, to calculate parameters of joint PDF’s and CDF’s, to calculate marginal PDF’s, and to determine when random variables are independent. Be capable of determining properties of joint PDF’s and CDF’s under the assumption of independence.
LO5 Obtain probability distribution of functions (including linear transformations) of one, two and three dimensional random variables. Be able to calculate covariance, correlation etc for jointly distributed discrete and continuous random variables.
LO6 Apply knowledge of Chebychev’s inequality and the central limit theorem.
LO7 Explain basic concepts in stochastic processes as well as to calculate , statistical and time averages, autocorrelation, autocovariance for simple stochastic processes
LO8 Derive and apply results in the theory of Markov chains
LO9 Apply basic results in Poisson Processes.
LO10 Use standard properties and L’Hopital’s Rule to calculate limits and test series, including power series, for convergence.
LO11 Derive and use recursion formulas for functions defined via integrals.
LO12 Calculate partial derivatives for functions of several real variables and use the chain rule to relate sets of partial derivatives with respect to different variables.
LO13 Calculate double and triple integrals directly and using the change of variable formula.
LO14 Calculate gradients of scalar fields and divergence and curl of vector fields.
LO15 Calculate line and surface integrals directly and using the Gauss and Stokes theorems
LO16 Use vector calculus and Maxwell’s equations to calculate properties of static and time-varying electromagnetic fields.

## Module Content & Assessment

Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Continuous Assessment Refer to Programme Manual for Year 4 3,4,5,10,11,12 20.00 Week 10
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 80.00 End-of-Semester

TU Dublin – Tallaght Campus reserves the right to alter the nature and timings of assessment

Lecture Presentation of course material 6.00 Every Week 6.00
Independent Learning Time Student study and problem solving 3.00 Every Week 3.00
Total Weekly Contact Hours 6.00
Lecture Presentation of course material 6.00 Every Week 6.00
Independent Learning Time Student study and problem solving 3.00 Every Week 3.00
Total Weekly Contact Hours 6.00

## Module Resources

Required Book Resources
• Course notes, n/a
Recommended Book Resources
• Glyn James... [et al.], Advanced modern engineering mathematics [ISBN: 0-130454257]
• Dexter J. Booth,, Engineering Mathematics [ISBN: 978-1-403942463]
• Hwei P. Hsu 1997, Schaum's outline of theory and problems of probability, random variables, and random processes, McGraw-Hill New York [ISBN: 0-07030644-3]
• S. Unnikrishna Pillai Athanasios Papoulis,, Probability, Random Variables and Stochastic Processes International Edition [ISBN: 978-0071226615]
• Erwin Kreyszig,, Advanced Engineering Mathematics, Textbook and Student Solutions Manual [ISBN: 0-470084847]
• Gilbert Strang 2006, Linear algebra and its applications, Thomson Brooks/Cole Belmont, Calif. [ISBN: 978-0030105678]
• Croft and R. Davison 2003, Mathematics for Engineers – A Modern Interactive Approach, 2nd ed Ed., Prentice Hall [ISBN: 0-13120193X]
• Daniel Fleisch 2008, A Student's Guide to Maxwell's Equations, 1 Ed., Cambridge University Press [ISBN: 978-0-521-70147-1]
This module does not have any article/paper resources
This module does not have any other resources

## Module Delivered in

Programme Code Programme Semester Delivery
TA_EAELE_B Bachelor Degree in Engineering (Honours) in Electronic Engineering 7 Mandatory
TA_EELEC_B Bachelor of Engineering (Honours) in Electronic Engineering -- Add On Year 1 Mandatory
TA_EAENS_B Bachelor of Engineering (Hons) in Engineering Software 7 Mandatory