Course code: 252301 | Subject title: MATHEMATICS III | ||||
Credits: 6 | Type of subject: Mandatory | Year: 2 | Period: 1º S | ||
Department: Estadística, Informática y Matemáticas | |||||
Lecturers: | |||||
PALACIAN SUBIELA, JESUS FCO. (Resp) [Mentoring ] |
Laplace transforms. Properties. Transforms calculation. Inverse Laplace transform. Properties of Laplace transforms. Application to the solution of ordinary differential equations and integro-differential equations. Applications in engineering.
Fourier series. Related integrals. Real and complex forms.
Fourier transforms. Properties. Transforms calculation. Inverse Fourier transform. Properties of Fourier transforms. Application to the solution of boundary differential equations. Applications in engineering.
Integral transforms. Differential equations. Applications to Engineering.
The students should be proficient in the contents of the subjects Mathematics I and II.
CFB1: Ability to solve mathematical problems arising in Engineering. Aptitude to apply knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, ordinary and partial differential equations, numerical methods, numerical algorithms, statistics and optimisation.
CFB3: Basic knowledge on use and computer programming, operating systems, data bases and software application in engineering.
At the end of the training period the student is able to:
Methodology - Activity | Attendance | Self-study |
A-1 Exposition/Participative Classes | 41 | |
A-2 Practical classes | 13 | 6 |
A-3 Individual practice and study time | 75 | |
A-4 Exams and evaluation activities | 6 | |
A-5 Tutorials | 9 | |
Total | 60 | 90 |
The system designed for evaluation has three different options to pass the course, namely, option 1: pass the two partial exams that will be held in the regular session of classes; option 2: pass the ordinary exam that will be held in January; option 3: pass the extraordinary exam that will be held in January. In the tables given below more details are given about percentages, the lessons and related questions.
Option 1
Learning outcome | Evaluation system | Weight (%) | Possibility of resit |
R1, R2, R3, R5 | Partial exam (lessons 1,2, 3): problems solving with the same level of difficulty of those given in the class | 50% | yes, passing the ordinary or extraordinary final exams |
R3, R4, R6, R7 | Partial exam (lessons 4, 5, 6 and 7): problems solving with the same level of difficulty of those given in the class | 50% | yes, passing the ordinary or extraordinary final exams |
Option 2
Learning outcome | Evaluation system | Weight (%) | Possibility of resit |
R1, R2, R3, R4, R5, R6, R7 | Final exam for the students that did not pass the subject through option 1 problems solving with the same level of difficulty of those given in class. |
100 | Yes |
Option 3
Learning outcome | Evaluation system | Weight (%) | Possibility of resit |
R1,R2,R3,R4,R5,R6,R7 | Final exam for those who has not passed the course using options 1 and 2: problems solving with the same level of difficulty of those given in the class | 100% | no |
1. Calculus Supplements
1.1 Numerical sequences and series. Series convergence tests
1.2 Power series. Convergence tests
1.3 Taylor series
1.4 Improper integrals. Convergence tests. Parametric integrals: derivation
1.5 Eulerian functions. Special functions
1.6 Lab practice
2. Introduction to Complex Numbers
2.1 The set C of complex numbers
2.2 Binomial and polar forms. Modulus and argument. Euler formula
2.3 Polynomial functions. Fundamental Theorem of Algebra
2.4 Rational functions. Zeroes and poles
2.5 Complex-valued functions of a real variable: derivation and integration. Complex functions of a complex
variable: elementary examples
2.6 Lab practice
3. Laplace transform
3.1 Definition and existence conditions
3.2 Inverse Laplace transforms
3.3 Fundamental properties
3.4 Convolution and impulse. Transfer functions
3.5 Application to ordinary differential equations, initial value problems and integro-differential equations
3.6 Lab practice
4. Fourier series
4.1 Trigonometric Fourier series
4.2 Convergence theorems. Parseval´s identity
4.3 Periodic extensions, odd and even periodic extensions
4.4 Hilbert spaces, orthonormal sequences and generalised Fourier series
4.5 Lab practice
5. Problems of Sturm-Liouville
5.1 Eigenvalues and eigenfunctions of linear differential operators
5.2 Regular and periodic problems. Properties of the solutions
5.3 Introduction to singular problems: practical examples, related special functions
5.4 Lab practice
6. Partial differential equations: separation of variables
6.1 Basics on partial differential equations
6.2 Second order linear partial equations: classification and examples
6.3 Heat equation, wave equation and Laplace equation
6.4 Boundary problems. Method of separation of variables
6.5 Lab practice
7. Fourier transform
7.1 Definition and examples. Fourier Integral Theorem. Riemann-Lebesgue Theorem
7.2 Basic properties
7.3 Convolution
7.4 Applications: solution of differential equations in unbounded domains, potential equation, heat transmission
and vibrations
7.5 Lab practice
Access the bibliography that your professor has requested from the Library.
BASIC BIBLIOGRAPHY:
SUPPLEMENTARY BIBLIOGRAPHY: