Short Title:  Mathematics 7 

Full Title:  Mathematics 7 

Field of Study:  Electronics and automation 

Reviewed By:  JOHN ANDREW DONNELLAN 

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 71) and Stocastic Processes (Part 72). 

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 timevarying 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 
EndofSemester Final Examination 
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 
80.00 
EndofSemester 
TU Dublin – Tallaght Campus reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
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 Learner Workload 
9.00 
Total Weekly Contact Hours 
6.00 
Workload: Part Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
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 Learner Workload 
9.00 
Total Weekly Contact Hours 
6.00 
Module ResourcesRequired Book Resources 

 Recommended Book Resources 

 Glyn James... [et al.], Advanced modern engineering mathematics [ISBN: 0130454257]
 Dexter J. Booth,, Engineering Mathematics [ISBN: 9781403942463]
 Hwei P. Hsu 1997, Schaum's outline of theory and problems of probability, random variables, and random processes, McGrawHill New York [ISBN: 0070306443]
 S. Unnikrishna Pillai Athanasios Papoulis,, Probability, Random Variables and Stochastic Processes International Edition [ISBN: 9780071226615]
 Erwin Kreyszig,, Advanced Engineering Mathematics, Textbook and Student Solutions Manual [ISBN: 0470084847]
 Gilbert Strang 2006, Linear algebra and its applications, Thomson Brooks/Cole Belmont, Calif. [ISBN: 9780030105678]
 Croft and R. Davison 2003, Mathematics for Engineers – A Modern Interactive Approach, 2nd ed Ed., Prentice Hall [ISBN: 013120193X]
 Daniel Fleisch 2008, A Student's Guide to Maxwell's Equations, 1 Ed., Cambridge University Press [ISBN: 9780521701471]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
