translation advanced mathematics 10.11

KNOWLEDGE GUIDE INFORMATION FOR THE STUDENT

COURSE 2010-2011

MODULE DESCRIPTION

MODULE: AMPLIACIÓN DE MATEMÁTICAS

ENGLISH NAME: ADVANCED MATHEMATICS

Code UPM: 565000222 SUBJECT: MATHEMATICS ECTS CREDITS: 6 LEVEL: BASIC DEGREE: BACHELOR IN ELECTRICAL ENGINEERING TYPE: MANDATORY COURSE: FIRST SEMESTER: SECOND

ACADEMIC COURSE 2010-2011 September- January February - June

TAUGHT TIME

Only Spanish Only English Both LANGUAGE

ADVANCED MATHEMATICS KNOWLEDGE GUIDE of 15


COURSE 2010-2011

DEPARTMENT

APPLIED MATHEMATICS (EUITI)

COORDINATOR

Isabel Álvaro Hernando

TEACHERS

NAME AND SURNAMES

Isabel Álvaro Hernando

Gabriel Asensio Madrid

Lucía Cerrada Canales

Pedro M. González Manchón

ROOM

A-229

C-103

B-349

C-104

E-mail

[email protected] [email protected]

[email protected]

[email protected]

Fco. Javier López de Elorriaga A-223 Franciscojavier.lopezdeelorriaga@ upm.es

José Manuel Poncela Pardo Jesús San Martín Moreno

Dolores Sotelo Herrera

Isaías Uña Juárez

Agustín de la Villa Cuenca

B-250 A-222 B-348 B-249 B-436

[email protected]

[email protected]

[email protected]

[email protected]

[email protected]

REQUIRED PREVIOUS KNOWLEDGE TO FOLLOW THE MODULE

Infinitesimus Calculus PASSED MODULES

OTHERS Basic science vocabulary



RESULTS OF THE PREVIOUS KNOWLEDGE

COURSE 2010-2011 Intuitive aspects of mathematics and how to use the resources of the previous modules studied. Computer resources achieved until now. Development of Basic geometric resources. Update combinatorics and inductive processes. Development of the representation of one-variable functions. Understanding the implicit and parametric writting of some frequent curves and surfaces (circles, propellers, cylinders cones, spherical, paraboloid) Using in easy way the derivation and integration of one variable.



COURSE 2010-2011

KNOWLEDGE OBJECTIVES

Code CE1

REQUIREMENTS AND LEVEL ASSIGNED TO THE MODULE

ABILITY

Capacity to identify and solve some engineering problems. LEVEL

Application

Code RA-01 RA-02 RA-03

KNOWLEDGE RESULTS OF THE MODULE Capacity to know, understand and use the integral calculus. Capacity to know, understand and use the ordinay differentials equations. Capacity to know, understand and use the Laplace Transformation.



COURSE 2010-2011

KNOWLEDGE CONTENTS AND ACTIVITIES

Chapter Chapter 1: Scalar and Vectorial Fields.

CONTENIDOS ESPECÍFICOS (TEMARIO)

Points 1.1. Scalar Fields. Curves and level surfaces. Gradient. 1.2. Vectorial Fields. Field lines. Divergency and rotacional. 2.1. Conservative fields and its potencial function. 2.2. Line integral concept. 2.3. Existency condition of the potencial function. Calculus of potencial function. 3.1. Building of double integral. 3.2 Calculus of double integrals. Variable changes. 3.3. Green Theorem. 3.4. Building of the triple integral. 3.5. Calculus of triple integrals. Change of variables. 4.1. Area element of a surface. 4.2. Surface integrals. 4.3. Stokes Theorem.

Code achievements

LO-01

Chapter 2: Line Integral.

Chapter 3: Double Integral. Triple Integral.

Chapter 4: Surface Integral.

LO-02

LO-02 LO-03 LO-04 LO-05

LO-06 LO-07 LO-08



COURSE 2010-2011

Chapter 5: Ordinary differential equations: separate, homogeneous and linear of first order.

4.4. Divergency Theorem of Gauss. 5.1. Concept of ordinary differential equation. 5.2. Separate variables differential equations. 5.3. Homogeneous equations. 5.4. Linear equations of first order. 6.1. Integral curves. 6.2. Exact and no exact differential equations. 6.3. Integrant Factor. 6.4. Ortoghonal path. 7.1. Vectorial space of the solutions of the homogeneous equation. 7.2. Structure of the general integral of the complete equation. 7.3. Constant changing Method. 8.1. Definitions: Property and linearity. 8.2. Transform of the derivate and the simpler functions.

LO-09 LO-11

Chapter 6: Integral curves and integral factors.

Chapter 7: Linear differential equations of higher order.

LO-10 LO-11

Chapter 8: Laplace Transform.

LO-11

Properties of the simpler functions. Applications. 8.3. Derivation of the transform respect to the parameter. 8.4. Product of Transforms.

LO-11 LO-12



COURSE 2010-2011

Chapter 9: Linear differential equation Systems.

8.5. Translation Theorems. 8.6. Transforms of periodic functions and some non continuous functions. 8.7. Application of the solution of the linear differential equations. 9.1. Solving of linear differential equations Systems through D operator. 9.2. Solving of linear differential equations Systems through Laplace Transform.

LO-11 LO-13



COURSE 2010-2011

SHORT DESCRIPTION OF THE ORGANIZATIVE RESOURCES AND TEACHING METHODS USED

Oral exposition of the teacher with participation of the student.

THEORY LECTURES

2 weekly hours.

EXERCISES LECTURES

Solving of the exercises by the part of the students and checking for the teacher. The teacher will solve the model exercises. Presentation of the problems for the students and possibly submission. 2 weekly hours.

LABORATORY WORK

INDIVIDUAL WORK

It is possible to order to the student any coursework in order to complete the knowledge.

GROUP WORK

QUESTIONS HOURS

Solving of the doubts of the students related to the contents of the module.



COURSE 2010-2011

REFERENCES

RECURSOS DIDÁCTICOS

Ampliación de Matemáticas. Teoría. F.J. López de Elorriaga (2004) Cálculus I y II. Apostol. Ed. Reverté. (1996)

Cálculo II. Carcía/López/Rodríguez/Romero/de la Villa. Ed. Clag S.A (1996) Calculus. Volumen II. Salas/Hille/Etgen. Ed. Reverté (2002) Cálculo de varias variables. Bradley /Smith. Ed. Prentice Hall. (1998) Cálculo. Vol.2. Larson/Hostetler/Edwards. Ed. McGraw-hill (1999) Cálculo Vectorial. Marsden/Tromba. Ed. Addison- Wesley. (1991) Ecuaciones diferenciales ordinarias. Teoría y problemas. Villa Cuenca, Agustín de la; García López, Alfonsa. Ed. Clag S.A (2002) Matemáticas avanzadas para ingeniería. Kreyszig, E. Ed. Linusa. (2004) Métodos Matemáticos. San Martín/Tomeo/Uña. Ed. Thomson (2005) Problemas resueltos de Ampliación de Matemáticas. F.J. López de Elorriaga (2005) Problemas resueltos de Cálculo en varias variables. Uña/San Martín/Tomeo. Ed. Thomson (2007) https://moodle.upm.es/ y seguir el enlace Titulaciones propias.

http://OCW.upm.es WEB RESOURCES

EQUIPMENT

Other Exercises notebook.



COURSE 2010-2011 CRONOGRAMA DE TRABAJO DE LA ASIGNATURA

MONTH FORTNIGHT ROOM ACTIVITIES

LAB SINGLE WORK GROUP WORK ASSIGMENT MODE OTHERS

Febr.

1ª 2ª Chapter 1 (4 hours)

Chapter 2 (4 hours) Exam

1ª

Mar. 2ª

1ª

Chapter 2 (2 hours) Chapter 3 (6 hours) Chapter 3 (6 hours) Chapter 4 (2 hours) Chapter 4 (8 hours)

Monthly test

Exam

Monthly test

Apr. 2ª

1ª May.

Chapter 5 (4 hours) Chapter 6 (4 hours) Chapter 6 (2 hours) Chapter 7 (6 hours)

Exam

Monthly test



MONTH FORTNIGHT

2ª

ROOM ACTIVITES

Chapter 8 (8 hours)

LAB

COURSE 2010-2011 SINGLE WORK GROUP WORK ASSIGMENT MODE OTHERS

1ª Chapter 8 (2 hours) Chapter 9 (2 hours) Monthly test

Jun. 2ª

The schedule showed is designed for presence teaching lessons during 15 weeks in the semester. If the circumstances of the academic does not allow to satisfy, the proposed schedule will be adjusted by the Branch Academic Planning Center, redistributing the present programme maintaining the learning objectives presented in this Learning Guide.

ADVANCED MATHEMATICS

KNOWLEDGE GUIDE of 15


COURSE 2010-2011

ASSIGMENT MODE OF THE MODULE

EVALUACIÓN

Ref

LO-01

OBJECTIVE ACHIEVED The student is able to use the scalar and vector fields. Moreover, he/she can calculate the curves and level surfaces and field lines. The student understands the line integral concept. The student is able to recognise the conservative fields, the existence conditions of the potential function and how to obtain it.

Relacionado con RA:

01

LO-02

LO-03 The student is able to solve the double and triple integrals.

LO-04 The student is able to apply the parameters change in order to calculate double or triple integrals. LO-05 The student is able to relate the line Integrals with the double

integrals using the Green Theorem. The student is able to solve surface integrals.

01

01

01

LO-06 01

LO-07 The student is able to relate the surface integral with the line integral through the Stokes Theorem.

LO-08 The student is able to relate the surface integral with the triple

integral through the Gauss Theorem. LO-09 The student is able to recognize and to solve some first order differential equations. The student is able to apply the resolution of differential equations to the calculus of orthogonal paths. LO-10

01

01

02

02

LO-11 The student is able to recognise the ordinary differential equations when they appear in engineering applications.

ADVANCED MATHEMATICS

KNOWLEDGE GUIDE of 15

02


LO-12

LO-13

COURSE 2010-2011 The student is able to apply the Laplace Transform in order to solve linear differential equations with initial conditions. The student is able to solve linear differential equations Systems using the D operator and the Laplace transform.

03

03



COURSE 2010-2011

SUMMATIVE ASSIGMENT

SHORT DESCRIPTION OF THE ACTIVITES Homework

WEIGHT WHEN WHERE Anytime Room

Final 1ª F. Febr. Final 1ª F. Mar. Final 1ª F. Abr.

Room Room Room

5%

Exam 1 (half an hour) Exam 2 Exam 3 Monthly test 1 (1 hour ) Monthly test 2 Monthly test 3 Monthly test 4

Fin Febr. Room Fin Mar. Fin Abr. Fin May.

Room Room Room

5% 5%

5%

20% 20% 20% 20%



COURSE 2010-2011

ASSIGMENT CRITERION

The constant evaluation is composed by: - Homework (5%) -Three exams of half an hour with date and content showed in the Schedule. (15%) -Four monthly test with the contents showed in the Schedule. (80%) To pass the module the mark should be equal or more than 5 (above 10).

The student who obtains less of 5 in the constant evaluation will be attend the exam of the whole module, this exam will take place in the date given by the Department. In this case, the grade will be the maximum of the exam mark (NEF) and (2NEF+3NEC)/4 being

NEF= mark of the final exam NEC= mark of the constant evaluation

In the extraordinary exam (in September) the final grade will be the same than the exam mark.


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