BM0549 Supplementary Mathematics (Aviation Transport)

Code BM0549
Name Supplementary Mathematics (Aviation Transport)
Status Compulsory/Courses of Limited Choice
Level and type Undergraduate Studies, Professional
Field of study Aviation Transport
Faculty Faculty of Civil and Mechanical Engineering
Academic staff Emma Šidlovska, Vitālijs Pavelko
Credit points 6.0
Parts 1
Annotation The study course provides knowledge of ordinary and partial differential equations of mathematical methods, Fourier analysis, vector analysis and field theory, probability theory and mathematical statistics as well as application of mathematical models of damage and failure accumulation in aircraft operation modeling and aircraft safety analysis and aerosol analysis for successful mastering of aerohydromechanics..
Contents
Content Full- and part-time intramural studies Part time extramural studies
Contact hours Independent work Contact hours Independent work
Research of periodic processes. Fourier protrusion in real and complex form. Fourier transform. Signal spectral projection. 8 6 0 0
Process research with first order differential equations. Reactive motion, Tsiolkovsky formula. Transition processes in electrical circuits. 4 4 0 0
Investigation of processes using second and higher order linear differential equations with constant coefficients. Special oscillations in mechanical and electrical systems. Forced oscillations. Reson 6 4 0 0
Scalar and vector fields in physics, aerodynamics and hydrodynamics. Gradients, divergence, rotor. Continuity equation. 4 4 0 0
Modeling of aerodynamic and hydrodynamic processes. Modeling of aviation engine thermal and thermodynamic processes. Corresponding equations and problems of mathematical physics. Variable Separation. 8 4 0 0
Probabilities of damage and refusal. Classical definition of probability. Basic concepts of probability theory. 4 4 0 0
Sum and multiplication of events. Sum of incompatible events. Multiplication of independent events. 4 4 0 0
Conditional probability. Multiplication of events and sum probabilities in the general case. Full probability formula. 4 4 0 0
Beiesa formula. Application of full probability and Beies formulas in damage and rejection analysis. Bernoulli rehearsal scheme. Binomial distribution. Poisson distribution. Poisson's flow of events. 4 4 0 0
Bernoulli rehearsal scheme. Binomial distribution. Poisson distribution. Poisson's flow of events. 4 4 0 0
Discrete and continuous random variables. Statistical definition of probability. Probability density. 4 4 0 0
Mathematical hope and variance. Average distance and average time to failure. 4 4 0 0
Distribution functions. Moda. Median. Central moments. Asymmetry factor. Excess. 4 4 0 0
Even distribution. Exponential distribution. Normal distribution. Weibull distribution. 4 4 0 0
Mathematical models of damage and failure accumulation. Durability distribution functions. Basics of reliability theory. 4 4 0 0
Numerical solution of first order differential equations and study of solution stability. Laboratory work. Mathcad (Matlab). 2 4 0 0
Investigation of the equation of oscillations in the modes of special oscillations and forced oscillations. Laboratory work. Mathcad (Matlab). 4 4 0 0
Working with discrete distributions. Laboratory work. MS Excel. 2 5 0 0
Verification of the compliance of the continuous random variable with the normal and exponential distributions. Laboratory work. MS Excel. 2 5 0 0
Total: 80 80 0 0
Goals and objectives
of the course in terms
of competences and skills 		The aim of the study course is to promote the in-depth acquisition of knowledge in solving the problems of aircraft aerodynamics, aerohydromechanics and safety analysis by applying mathematical knowledge. The tasks of the study course are to teach: - the application of calculations of differential equations for the study of mechanical and electrical systems; - scalar field gradient and vector field divergence and rotor calculation; - the Fourier method in solving partial differential equations; - mathematics and physics tasks in modelling aircraft operation; - mathematical models of damage accumulation; - probability theory, damage and refusal to calculate probability.
Learning outcomes
and assessment 		Is able to study the transition processes in mechanical and electrical systems, as well as to analyze the special oscillations and forced oscillations of the systems using 1st order differential equations and higher order linear differential equations with constant coefficients. - Laboratory works. Homework.
Able to solve simple mathematical physics problems with partial differential equations, which arise in modeling aircraft operation. - Homework. Tests. Testing.
Able to calculate the probabilities of events using the classical definition of probability, theorems on the sum and multiplication of events, full probability formula, Beies formula. - Homework. Tests. Testing.
Can work with discrete and continuous distributions and can calculate mode, median, mathematical expectation, variance, standard deviation, asymmetry factor and excess. - Laboratory works. Homework.
Able to apply mathematical methods in aircraft operation modeling and aircraft safety analysis. - Exam.
Evaluation criteria of study results
Laboratory works - 15%
Tests - 20%
Calculations (homework) - 30%
Testing - 5%
Exam - 30%
 
Course prerequisites Higher mathematics, physics, technical mechanics.
Course planning
Part CP Hours Tests
Lectures Practical Lab. Test Exam Work
1 6.0 30.0 40.0 10.0 *
[Extended course information PDF]