Titular Professors
Precalculus Algebra.
3. Competences that this subject intend to develop:
General competences:
CG5 Understanding of the problems of structural design, construction and engineering related to building projects.
CB1 Students have to demonstrate to possess and understand knowledge of an area of study that starts from the base of the general secondary education, and is usually found at a level that, although it is supported by advanced textbooks, also includes some aspects that imply previous knowledge of the vanguard of its field of study.
Instrumental competences (IS):
IS9 Problem solving
Systemic competences (CS):
CS3 Capacity to apply knowledge into practice
Specific competences:
B20. MATHEMATICAL CALCULUS. Comprehension and knowledge of numerical calculus, mathematical analysis, analytic and differential geometry and algebraic methods, as the base to understand the physical phenomenon that makes reference to systems, equipments and services of building and urbanism.
Introductory unit: applied knowledge of numerical calculus, analytic and differential geometry, and algebraic methods.
4. Learning objectives:
8. Comprehension of the problems related to the structural conception, construction and engineering linked with the building´s projects.
5. Units in which the subject is organized:
The themes that are studied in this Mathematics subject correspond to linear algebra and are explained below:
1st SEMESTER: LINEAR ALGEBRA
1. SPACE REPRESENTATION
1.1 Systems of linear equations
1.2 Linear combination and linear independence of vectors
1.3 Vector spaces and subspaces
1.4 System of generators and bases
1.5 Operations of vector sub spaces
1.6 Inner vector spaces
2. LINEAR TRANSFORMATIONS
2.1 Types of transformations
2.2 Characterization
2.3 Change of basis
2.5 Eigenvectors and eigenvalues of an endomorphism
3. RESOLUTION OF CONICS AND QUADRICS
3.1 Quadratic forms in geometry
3.2 Classification of conics and quadrics
2ND SEMESTER: CALCULUS
1. MATHEMATICAL MODELS
1.1 Real function of real variable: domain and image, growth and decrease, symmetry, periodicity, dimensions.
1.2 Reverse function and composition of functions.
1.3 Elementary functions
2. ANALYSE AND SKETCH FUNCTIONS
2.1 Domain
2.2 Intercepts
2.3 Symmetry
2.4 End-behaviour
2.5 Intervals of increasing/ decreasing
2.6 Intervals of concavity
2.7 Areas
3. INTERPRET AND SKETCH MATHEMATICAL RESULTS
3.1 Structures application
3.2 Optimization problems
3.3 Areas
3.4 Surfaces of revolution
6. Methodological approach to achieve the objectives:
The methodology used for this subject includes two kinds of classes: theoretical classes and practical classes to exercise the knowledge acquired during the theoretical classes.
Total on-campus hours: 54% 4,5 cr. ETCS, divided in:
Lectures: (IS/CS/B) 65% (2,5 ECTS)
Practical classes: (CS/B) 35% (2 ECTS)
Total work-hours of the student: 46% 4 cr. ECTS divided in:
Supervised work: (CS/B) 37,5% (1,5 ECTS)
Non supervised work: (CS/B) 62,5% (2,5 ETCS)
YEARLY TIMING
Dedication to the subjects: 8,5 credits 26 hours/credit = 221 hours
Yearly dedication: 34 weeks (30 class + 4 exams)
Weekly dedication: 221 hours /36 weeks = 6,5 hours/week
Concept Total hours
Lectures 65
Practical classes 52
Individual study 65
Tutorship 39
Training activities:
A1 Lectures of concepts explanation. 30%
A2 Practical classes of problems, exercises solved by students with teacher assistance. 23%
A9 Work / self-study student. 29%
A11 Individual corrections. 18%
TOTAL YEARLY DEDICATION 221
Lectures
The professor teaches the theoretical concepts through lectures. In these classes the professor also solves problems that apply directly the explained concepts.
Classes dedicated to solve exercises.
In some classes the professor propose exercises to be solved by the students in that moment to help students to understand completely the topich during the class. The problems are more difficult than the ones solved during the lectures and have the objective to help students to relate the concepts of the same subject and with concepts of other subjects of the career. These exercises may be solved individually or in groups.
Exercises to solve at home
Beside the exercises to be solved in class, the student must solve other problems at home. The idea of these exercises is that students affirm the theoretical ideas so that they may apply them in practical contexts.
7. Evaluation the level of achievement of the objectives:
With the purpose of evaluating if the student has acquired an adequate level of the objectives proposed for this subject, several instruments are used to obtain the student´s information:
Exams (Competences: IS/CS) 60%
The students will be evaluated of all the themes studied during the subject along the course.
Exercises (Competences: IS/CS) 40%
The exercises solved in class in order to evaluate the knowledge acquired.
8. Bibliography
Calculus:
Ayres F., Schaum's outline of calculus. McGraw-Hill, 1999
Larson R., Hostetler R., Edwards B., Cálculus, Houghton Mifflin Co., 2002.
Algebra:
Anton H., Elementary linear algebra, John Wiley & Sons, 2000.