Numerical Methods I26667
- Centre
- Faculty of Science and Technology
- Degree
- Bachelor's Degree In Mathematics
- Academic course
- 2024/25
- Academic year
- 2
- No. of credits
- 6
- Languages
- Spanish
- Basque
- English
- Code
- 26667
TeachingToggle Navigation
Teaching guideToggle Navigation
Description and Contextualization of the SubjectToggle Navigation
This course, together with the third year course Numerical Methods II, aims to offer a systematic presentation of some of the most important and elementary numerical analysis techniques. In both courses, it is compulsory to do computer assignments using a programming language. Both courses are intended to equip the students with a basic and transversal formation in the field, that will enable them to understand and apply the acquired knowledge and abilities in multiple interrelated directions.
Since this course is offered in English, at least a B2 level is strongly recommended.
Skills/Learning outcomes of the subjectToggle Navigation
COMPETENCES
M05CM01 Knowing the basic techniques of numerical analysis and their translation into algorithms or constructive methods to solve problems.
M05CM02 Programming the studied numerical methods in a computer using a structured language and applying them effectively.
M05CM03 Using packages in which some of the studied methods are applied, and which can serve as a auxiliary tool to one's own codes.
M05CM04 Analyzing the convenience of one or more numerical methods for a given problem, based on the error analysis, the computational cost and other characteristics.
M05CM05 Evaluating the obtained results and drawing conclusions after a computational procedure, and being able to communicate everything both orally and in writing.
LEARNING RESULTS
Using numerical solution algorithms, programming numerical methods in a computer, by implementing these algorithms in a structured programming language, and applying them effectively.
Theoretical and practical contentToggle Navigation
THEORETICAL CONTENTS
1. INTRODUCTION TO NUMERICAL CALCULUS: Computer arithmetic and error propagation.
2. BASIC MATLAB NOTIONS
3. RESOLUTION OF LINEAR SYSTEMS OF EQUATIONS: Direct methods. Minimum square methods and overdetermined systems.
4. RESOLUTION OF NONLINEAR EQUATIONS AND SYSTEMS. Roots searching methods for nonlinear equations. Fix point methods and Newton's method.
PRACTICAL CONTENTS
The computer assignments are associated to the theoretical contents, reinforcing their learning by implementing the studied algorithms in an adequate way.
MethodologyToggle Navigation
The theoretical contents will be taught during the master (M) classes, following the lecture notes uploaded in the virtual class at platform eGela. These master lectures will be supplemented with problem sessions (classroom sessions, GA), where the students will solve questions where they will have to apply the acquired theoretical knowledge. In the seminar sessions (S), questions and examples relative to the contents of the course will be developed; these will be usually provided to the students so they can work previously on them, with the aim of facilitating the discussion in the seminar sessions.
In addition, the students will have to do computer assignments oriented to the goals of this course, using a programming language. In this course, we will use MATLAB.
Assessment systemsToggle Navigation
- Continuous Assessment System
- Final Assessment System
- Tools and qualification percentages:
- See GUIDELINES (ORIENTACIONES) below (%): 100
Ordinary Call: Orientations and DisclaimerToggle Navigation
In the ordinary exam call, the continuous assessment system will have the following percentages:
Final exam: 60%
Computer assignments: 10%
Seminars: 10%
Partial exams: 20%
In order to apply this method of evaluation, a minimum grade of 4 out of 10 is required in the final written exam; otherwise, the final grade will be the one obtained in that exam.
FINAL EXAM CRITERIA
The student that does not want to be assessed through the continuous assessment system has the right to do a final assessment exam; however, he or she must give written notice of withdrawal from the continuous assessment system during the first 15 weeks of the autumn term. In that case, the evaluation for that student will be a final assessment exam, plus a complimentary test to be done together with the final exam, that can be an oral exposition, an activity in front of a computer or doing some written assignment; it will measure the acquisition of the course competences will be assessed.
NOT TAKING THE FINAL EXAM
In spite of assessing the activities done during the course, a student who does not take the final exam will obtain the grade "No presentado".
Extraordinary Call: Orientations and DisclaimerToggle Navigation
In the extraordinary exam call, the same criterion applies as in the ordinary call.
All the activities done during the course (computer assignments, exercises, seminars) will be evaluated in both calls). Therefore, the student that has passed those activities during the course will have to do only the written exam.
The student who has not passed the assessable activities, or who has chosen the final exam assessment system, will have to pass a complimentary test, in order to assess those activities. That test can be an oral exposition, an activity in front of a computer or doing some written assignment. The value of the test in the final grade will be the same as in the ordinary exam call.
Compulsory materialsToggle Navigation
Notes and other teaching materials made available by the instructor in platform eGela.
BibliographyToggle Navigation
Basic bibliography
C.B. Moler: Numerical Computing with MATLAB, SIAM, 2004.
J.M. Sanz-Serna: Diez lecciones de Cálculo Numérico, Universidad de Valladolid, 2010.
J. Stoer and R. Bulirsch: Introduction to Numerical Analysis. Springer-Verlag, Inc., 1993.
K.E. Atkinson: An Introduction to Numerical Analysis, John Wiley & Sons, 1989.
U.M. Ascher and C. Greif: A First Course in Numerical Analysis, SIAM, 2011.
M.H. Holmes: Introduction to Scientific Computing and Data Analysis, Springer 2016.
In-depth bibliography
L.N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM, 1997.
N.J. Higham: Accuracy and Stability of Numerical Algoritms, SIAM, 1996.
A. Quarteroni, R.Sacco, F.Saleri: Numerical Mathematics, Springer, 2000.
Journals
Web addresses
GroupsToggle Navigation
16 Teórico (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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1-1 | 16:00-17:00 (1) | ||||
1-5 | 14:00-15:00 (2) | ||||
1-6 | 16:00-17:00 (3) | ||||
1-14 | 15:00-16:00 (4) | ||||
7-7 | 16:00-17:00 (5) | ||||
8-10 | 14:00-15:00 (6) | ||||
9-12 | 16:00-17:00 (7) | ||||
13-13 | 14:00-15:00 (8) | ||||
14-14 | 16:00-17:00 (9) |
Teaching staff
16 Seminar-1 (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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6-6 | 14:00-15:00 (1) | ||||
7-11 | 14:00-15:00 (2) | ||||
12-14 | 14:00-15:00 (3) |
16 Applied classroom-based groups-1 (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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1-1 | 17:00-18:00 (1) | ||||
1-6 | 17:00-18:00 (2) | ||||
7-7 | 17:00-18:00 (3) | ||||
9-12 | 17:00-18:00 (4) | ||||
15-15 | 15:00-16:00 (5) | 14:00-15:00 (6) |
Teaching staff
16 Applied computer-based groups-1 (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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2-6 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
9-11 | 10:30-11:30 (3) 12:00-13:00 (4) | ||||
12-14 | 10:30-11:30 (5) 12:00-13:00 (6) | ||||
15-15 | 12:00-13:00 (7) |
46 Teórico (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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1-1 | 16:00-17:00 (1) | ||||
1-5 | 14:00-15:00 (2) | ||||
1-6 | 16:00-17:00 (3) | ||||
1-14 | 15:00-16:00 (4) | ||||
7-7 | 16:00-17:00 (5) | ||||
8-10 | 14:00-15:00 (6) | ||||
9-12 | 16:00-17:00 (7) | ||||
13-13 | 14:00-15:00 (8) | ||||
14-14 | 16:00-17:00 (9) |
Teaching staff
46 Seminar-2 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-7 | 15:00-16:00 (1) | ||||
9-11 | 15:00-16:00 (2) | ||||
12-14 | 15:00-16:00 (3) |
46 Seminar-1 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-7 | 14:00-15:00 (1) | ||||
9-11 | 14:00-15:00 (2) | ||||
12-14 | 14:00-15:00 (3) |
46 Applied classroom-based groups-1 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
1-1 | 17:00-18:00 (1) | ||||
1-6 | 17:00-18:00 (2) | ||||
7-7 | 17:00-18:00 (3) | ||||
9-12 | 17:00-18:00 (4) | ||||
15-15 | 15:00-16:00 (5) | 14:00-15:00 (6) |
Teaching staff
46 Applied computer-based groups-2 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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2-6 | 09:30-11:30 (1) | ||||
9-11 | 09:30-11:30 (2) | ||||
12-14 | 09:30-11:30 (3) | ||||
15-15 | 10:30-11:30 (4) |
46 Applied computer-based groups-1 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
2-6 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
9-11 | 10:30-11:30 (3) 12:00-13:00 (4) | ||||
12-14 | 10:30-11:30 (5) 12:00-13:00 (6) | ||||
15-15 | 12:00-13:00 (7) |
66 Teórico (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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1-1 | 16:00-17:00 (1) | ||||
1-5 | 14:00-15:00 (2) | ||||
1-6 | 16:00-17:00 (3) | ||||
1-14 | 15:00-16:00 (4) | ||||
7-9 | 16:00-17:00 (5) | ||||
8-10 | 14:00-15:00 (6) | ||||
12-12 | 16:00-17:00 (7) | ||||
13-13 | 14:00-15:00 (8) | ||||
14-14 | 16:00-17:00 (9) |
66 Seminar-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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6-12 | 14:00-15:00 (1) | ||||
7-11 | 14:00-15:00 (2) | ||||
14-14 | 14:00-15:00 (3) |
66 Seminar-2 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-12 | 15:00-16:00 (1) | ||||
7-11 | 15:00-16:00 (2) | ||||
14-14 | 15:00-16:00 (3) |
66 Applied classroom-based groups-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
1-1 | 17:00-18:00 (1) | ||||
1-6 | 17:00-18:00 (2) | ||||
7-7 | 17:00-18:00 (3) | ||||
9-12 | 17:00-18:00 (4) | ||||
15-15 | 15:00-16:00 (5) | 14:00-15:00 (6) |
66 Applied computer-based groups-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
2-6 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
9-11 | 10:30-11:30 (3) 12:00-13:00 (4) | ||||
12-14 | 10:30-11:30 (5) 12:00-13:00 (6) | ||||
15-15 | 12:00-13:00 (7) |