Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| Course code: 503108 | Subject title: MATHEMATICS II | ||||
| Credits: 6 | Type of subject: Mandatory | Year: 1 | Period: 2º S | ||
| Department: | |||||
| Lecturers: | |||||
| ROLDAN MARRODAN, ANGEL TEODORO (Resp) [Mentoring ] | |||||
Contents
Funciones, límites y continuidad. Conceptos básicos sobre funciones escalares o vectoriales de una o varias variables reales. Funciones elementales. Conjuntos de nivel. Límites. Continuidad de una función en un punto. Propiedades de funciones continuas.
Espacios vectoriales sobre R: Subespacios. Base y dimensión
Cálculo vectorial: campos vectoriales en R2 y R3. Divergencia y rotacional, integrales de línea, campos conservativos, función potencial, teorema de Green, integrales de flujo, teorema de Stokes, teorema de divergencia. Circulación y flujo.
General proficiencies
- CB1: Students are able to demonstrate they have acquired knowledge and understanding in a field of study based on the basic foundations gained within their general secondary education together with the support of advanced textbooks and aspects of the latest advances in the field.
- CG2: Adequate knowledge of the physical problems, technologies, equipment, and water and energy supply systems, the limits imposed by budgetary factors and building regulations, the relationships between installations and/or buildings with farms, agro-food industries and spaces related to gardening and landscaping with their social and environmental surroundings, as well as the need to relate those surroundings from that environment with human needs and environmental protection.
Specific proficiencies
- CE1: Ability to solve mathematical problems that may arise in engineering. Aptitude for applying knowledge towards: linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and partial derivatives, numerical methods and numerical algorithmic methods, statistics, and optimization
Learning outcomes
R1 - Operate with elementary functions; know the fundamental properties of these functions and become familiar with the ideas of limit, continuity and differentiability.
R2 - Know geometric concepts related to functions of one and several variables: function graphs, curves and level surfaces, parameteric curves and surfaces.
R3- Identify and solve different integrals: single, double, triple, surface, line.
R4- Know and apply fundamental theorems of calculus: Green, Stokes and Divergence.
R5- Identify and solve simple ordinary differential equations.
R6- Handle a symbolic processor at user level.
RESULTADOS DE APRENDIZAJE ENAEE
ENAEE-1: Knowledge and understanding of the scientific and mathematical principles of this branch of engineering.
Methodology
| Methodology - Activity | On-site hours | Off-site hours |
| A-1: Theoretical lessons | 45 | |
| A-2: Practical lessons | 15 | |
| A-3: Coursework | 5 | 5 |
| A-4: Individual study | 70 | |
| A-5: Exams and assessment | 5 | |
| A-6: Individual tutoring | 5 | |
| TOTAL | 75 | 75 |
Evaluation
| Learning outcomes | Assessment activity | Weight (%) | Resit assessment |
| R1, R2, R3, R4, R5, R6, R7 | Long-answer exam questions | 85% | Yes |
| R1, R2, R3, R4, R5, R6, R7 | Coursework | 15% | Yes |
For assessment purposes, the course is divided into three parts:
- Part A: related to lessons 1, 2 and 3 (45%).
- Part B: related to lessons 4 and 5 (40%).
- Part C: Coursework (15%).
In order to pass the subject in the regular evaluation, the average mark of all three parts must be greater or equal than 5.
In the resit assessment period the mark on a final exam covering the whole course must be greater or equal than 5. Only students who did not pass the course in the regular assessment can sit this exam.
Agenda
- Functions, limits and continuity in Rn. Basic concepts in scalar and vector functions of several variables. Limits. Continuity: definition and local and global properties.
- Differential calculus in Rn. Directional and partial derivatives. Jacobian matrix and gradient vector. Differentiability. Chain rule. Higher-order derivatives. Hessian matrix. Taylor series. Relative extrema. Constrained optimization: the theorem of Lagrange multipliers. Absolute extrema on closed bounded regions.
- Ordinary differential equations. Basic concepts of differential equations. First-order ordinary differential equations. Some elementary integration methods. Higher-order linear differential equations. Applications.
- Integral calculus in Rn. Riemann integral. Elementary regions. Fubini's theorem. Change of variable theorem. Polar, cylindrical and spherical coordinates. Line and surface integrals.
- Vector calculus. Vector fields. Divergence and curl. Line integrals. Conservative fields. Potential function. Flux integrals. Fundamental theorems of vector calculus.
Bibliography
Access the bibliography that your professor has requested from the Library.
- R.A. Adams. Calculus: a complete course. Addison Wesley.
- M. Braun. Differential equations and their applications: an introduction to applied mathematics. Springer-Verlag.
- E. Kreyszig. Advanced engineering mathematics. John Wiley & Sons.
- J.E. Marsden, A.J. Tromba. Vector calculus. W.H. Freeman.
Spanish textbooks:
- R.E. Larson, R.P. Hostetler. Cálculo y geometría analítica. McGraw-Hill.
- R.K. Nagle, E.B. Saff, Ecuaciones diferenciales y problemas con valores en la frontera. Pearson Educación.
- S.L. Salas, E. Hille, G.J. Etgen. Calculus: una y varias variables. Reverté.
- D.G. Zill. Ecuaciones diferenciales con aplicaciones de modelado. Thomson.