Universitat Politècnica de Catalunya · BarcelonaTech

Fundamentals of Mathematics (2500201) – Course 2024/25 PDF

Syllabus

Learning Objectives

Mathematical concepts are discussed to understand relationships between different environmental variables. Emphasis is placed on a block of basic mathematical tools: matrix operations, solving linear systems of equations, derivation and integration of one-variable functions, plane and space geometry. 1. Manage trigonometric functions including their derivation and integration. Ability to analyze sequences and series in the context of engineering. 2. Solve maximum and minimum problems using differential calculus related to simple engineering problems. 3. Solve integrals of one variable, looking for a relationship with simple engineering problems. Mathematical Foundations. Knowledge of real numbers. Knowledge of successions and calculation of limits. Knowledge of numerical series and convergence. Knowledge of function theory including continuity and limit analysis. Differential calculus knowledge of variable functions real including maximum and minimum problems in simple engineering problems and optimization. Knowledge of integral calculation of functions of a real variable. Trigonometry knowledge. At the end of the course, the student will have had to: a) achieve knowledge and computational fluency on matrices and systems of linear equations, basic linear transformations in plane and space, differential and integral calculus of real functions of real variable; b) to acquire basic knowledge about the use of Matlab, having had to practice with problems posed in some of the subjects that configure the syllabus of the subject; c) get started in the numerical resolution of some problems.

Competencies

Especific

Recognize the biological bases and foundations of the plant and animal field in engineering: notions of genetics, biochemistry and metabolism, physiology, organisms and environment, population dynamics, flows of matter and energy and changes in ecosystems, biodiversity, principles of the kinetics of microbial growth and reactor theory.

Solve mathematical problems that may arise in engineering by applying knowledge about: linear algebra, geometry, differential geometry, differential and integral calculus, optimization, ordinary differential equations.

Obtain basic knowledge about the use and programming of computers, operating systems, databases and basic numerical calculation and applied to engineering.

Manage the basic concepts about the general laws of mechanics and thermodynamics, concept of field and heat transfer, and apply them to solve engineering problems.

Apply the basic principles of general chemistry, organic and inorganic chemistry and their applications in engineering.

Describe the global functioning of the planet: atmosphere, hydrosphere, lithosphere, biosphere, anthroposphere, biogeochemical cycles (C, N, P, S), soil morphology and apply it to problems related to geology, geotechnics, edaphology and climatology.

Generic

Identify, formulate and solve problems related to environmental engineering.

Apply the functions of consulting, analysis, design, calculation, project, construction, maintenance, conservation and exploitation of any action in the territory in the field of environmental engineering.

Total hours of student work

Hours Percentage
Supervised Learning Large group 30h 50.00 %
Medium group 30h 50.00 %
Self Study 90h

Teaching Methodology

Theoretical, problem-solving and practical classes will be given. The subject is face-to-face and the class work will be evaluated, in addition to the exams proposed for the course. Class participation will be valued very positively. Class attendance will not be enough to pass the course, which means that the student must spend an average of 4 hours a week studying outside the classroom.

Grading Rules

The evaluation calendar and grading rules will be approved before the start of the course.

Two exams are held throughout the semester: * EP1 = Partial Exam 1, weight = 50% of the grade for the subject. * EP2 = Partial Exam 2, weight = 50% of the grade for the subject. If the grade obtained (EP1 + EP2) / 2 exceeds the approved one, that is, it is greater than or equal to 5 points out of 10, then the subject is approved per course. Otherwise, you have to go to the reevaluation exam. The re-evaluation (R) will consist of a single exam covering the entire course content. The maximum grade for the re-evaluation will be five (5.0) and the final grade for the course will be the maximum grade between the ordinary evaluation and the re-evaluation exam. -Mark EP1=0.25*Theory+0.25*Practical Exercises+0.5*Problems. -Mark EP1=0.25*Theory+0.25*Practical Exercises+0.5*Problems. -Mark R=0.25*Theory+0.25*Practical Exercises+0.5*Problems.

Test Rules

Each assessment activity not performed in the scheduled period will be assigned a score of zero. Unless expressly authorized by the responsible teacher, a calculator, mobile phone, notes, book, or any other device (electronic or otherwise) that allows storage, reception may not be carried out for the face-to-face assessment tests. , send or consult information about the subject and / or manipulate mathematical expressions.

Office Hours

Face-to-face: to be agreed with the student. You must make an appointment in advance. Non-contact: by e-mail whenever the student wants to use it.

Bibliography

Basic

Complementary