Academic management

Mathematics as an abstract Topic (part of the Syllabus) is the framework for the Course on Numerical Methods in the Degree on Engineering on Mining & Energetic Resources. This course is shared by all the Engineering Degrees in this University. Due to its 'basic' nature, its contents are indispensable for the other modules of the Degree.

Knowledge of the basic elements of Algebra and Calculus is advisable.

BOE specific competence:

Develop the necessary capacities for the resolution of the mathematicalproblems arising in engineering. Ability to apply knowledge on: linear algebra; geometry: differential geometry; differential and integral calculus; differential equations and partial differential equations; numerical methods; numerical algorithms; statistics and optimization.

General and cross-cutting skills:

Acquire knowledgein basic and technological subjects that will equip them for learning new methods and theories, and will provide them with versatility to adapt to new situations.

Acquire capabilities to solve problems with initiative, decision making, creativity and critical reasoning.

Ability to communicate and transmit knowledge, abilities and skills in the field of Industrial Engineering, both in oral form as well as written, and all kinds of audiences.

Enhance honesty, responsibility, ethical commitment and spirit of solidarity as well as the ability to work as a team.

General competences for the Bachelor's Degree in Civil Engineering:

CG01: Scientific-technical skills for the exercise of the profession of Technical Engineer of Public Works and knowledge of the functions of advice, analysis, design, calculation, project, construction, maintenance, conservation and exploitation.

CG02: Understanding of the multiple technical and legal constraints that arise in the construction of a public work, and ability to use contrasted methods and accredited technologies, in order to achieve greater efficiency in construction with respect for the environment and the protection of the safety and health of workers and users of public works.

CG04: Capacity to project, inspect and direct works, in their field.

CG05: Capacity to maintain and conserve the hydraulic and energy resources, in their field.

CG07: Capacity to carry out studies and designs of surface or underground water abstraction, in their field.

Learning Results:

RA1: Identify the different type of errors that can be made within the use of the numerical methods and compare their efficiency with respect the type of problem to be solved, the required accuracy and the computational cost.

RA2:  Use of the most adequate methods to calculate the roots of a non linear equation.  

RA3:  Describe, analyze and use of the numerical methods for the resolution of linear and non                      linear systems

RA4: Numerical resolution of interpolation problems, one dimensional data fit and function approximation.

RA5: Use of formulas to approximate the derivative and definite integral of a function.

RA6: Describe, use and compare the basic numerical methods for the resolution of differential equations.

1 – Finite Arithmetic & Error Analysis

1.1: Error notions

1.2: Computer arithmetic

1.3: Error analysis

2 – Numerical solution  equations

2.1: Bisection

2.2: Fixed point

2.3: Newton

3 – Solution of systems of linear equations
3.1: Direct methods: Gauss, factorizations

3.2: Vector and matrix norms

3.3: Conditioning of a system

3.4: Iterative methods: Jacobi, Gauss-Seidel

4 – Interpolation

4.1: Polynomial interpolation: Lagrange's and Newton's formulas

4.2: Splines

5 – Least Squares

5.1: Overdetermined systems

5.2: Data fitting

6 – Numerical differentiation and integration

6.1: Simple quadrature formulas

6.2: Composite quadrature formulas

6.3: Numerical differentiation

7 – Numerical solution of differential equations

7.1: First order equations. One-step methods

7.2: First order systems of equations

Work plan:

Total work volume for the student:

i) The concepts laid out in the practical classes will be evaluated with a weight of 20% on the final mark of the course.

ii) A final “theoretical-practical” exam will be made, with a weight of 50% on the final mark of the course.

iii) The “laboratory” classes will be evaluated in a continuous way and they will weight 20% on the final mark. In order to be marked, an assitance ratio of 75% to these “laboratory” classes will be required.

iv) The active participation and fruitful attendance of the pupil will be taken into account, with a weight of 10% on the mark. This mark will be based on the answers of the pupil to the questions asked by the professor to the class as a whole.

v) Supplemental exams: a written exam will be made with a weight of 70% and a practical “laboratory” exam with a weight of 30%.

Remark: in the July exam, students will be able to select between taking the “practical” exam or using their qualifications according to points iii) and iv) above.

8.  Evaluation of the teaching process

Along the course, the activities performed will be revised in order to detect the strong and weak points and to introduce modifications to improve the process.

At the end of the course, an analysis of those activities will be performed and the results of the General Teaching Survey will be taken into account.

Recursos:

Classrooms for theoretical classes with computer and projector for the professor.

Classrooms with computers (one for each student) for the “laboratory” classes.

Virtual Classroom of the University of Oviedo.

Bibliografía:

Burden, R.; Faires,J.D. Numerical Analysis. Brookes Cole.

 Isaakson E. Keller, H.B., Analysis of Numberical Methods. Dover.

Mathews J.H., Fink, K. K.,Numerical Methods Using Matlab. Pearson.

Moler, C. Numerical Computing with Matlab.