1. General information
Course:
MATHEMATICAL INSTRUMENTS FOR ENGINEERING I
Code:
38300
Type:
BASIC
ECTS credits:
6
Degree:
345 - UNDERGRADUATE DEGREE PROGRAMME IN CIVIL ENGINEERING
Academic year:
2022-23
Center:
603 - E.T.S. CIVIL ENGINEERS OF CR
Group(s):
20
Year:
1
Duration:
First semester
Main language:
Spanish
Second language:
English
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
ROSA EVA PRUNEDA GONZALEZ
- Group(s):
20
Building/Office
Department
Phone number
Email
Office hours
Politecnico 2-D33
MATEMÁTICAS
3292
rosa.pruneda@uclm.es
It will be communicated at the beginning of the course.
Lecturer:
CRISTINA SOLARES MARTINEZ
- Group(s):
20
Building/Office
Department
Phone number
Email
Office hours
Edificio Politécnico/2-D32
MATEMÁTICAS
3255
cristina.solares@uclm.es
It will be communicated at the beginning of the course.
2. Pre-Requisites
To achieve the learning objectives of the subject, knowledge and skills that are supposed to be guaranteed in the pre-university education are required. In particular, knowledge of basic geometry and trigonometry, elementary mathematical operations (powers, logarithms, fractions), polynomials, matrices, derivation, integration and fundamentals of graphical representation of functions are necessary.
With regard to basic skills in the handling of instruments is the elementary management of computers: access, file and directories management, etc.
3. Justification in the curriculum, relation to other subjects and to the profession
In this subject, mathematical and computer concepts are studied, which constitute an essential part of the training of a future engineer.
Concepts related to vector spaces, matrix calculation, systems of linear equations, real functions of real variable (continuity, derivability, integration), sequences, expansion of a function into power series, which are basic for various subjects throughout the career, are studied. : Mathematical Instruments for Engineering II, Fundamentals of Physics, Mechanics of Rigid Solid, Differential Equations, Resistance of Materials, Hydraulic Engineering, Calculation of Structures, etc.
4. Degree competences achieved in this course
| Course competences | |
|---|---|
| Code | Description |
| CE01 | Students can apply their knowledge in the practical solution of civil engineering problems, with capacity for the analysis and definition of the problem, the proposal of alternatives and their critical evaluation, choosing the optimal solution with technical arguments and with capacity of defense against third parties. |
| CE02 | Students have the ability to broaden their knowledge and solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study. Self-study ability, to undertake further studies with a high degree of autonomy |
| CE04 | Students have the ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial derivative equations; numerical methods; numerical algorithms; statistics and optimization. |
| CE06 | Students have a basic knowledge of the use and programming of computers, operating systems, databases and software with engineering application. |
| CG01 | Students achieve general knowledge of Information and Communication Technologies (ICT). |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| Students know how functions and data are approximated by means of power and Fourier series expansions and their applications. | |
| Students can handle functions of one and several variables including their derivation, integration and graphic representation. They know the fundamentals and applications of Differential and Integral Calculus. | |
| Students are familiar with computer use: operative systems, databases, programming languages, and software applied to civil engineering. | |
| Students are able to express correctly both orally and in writing and, in particular, they can use the language of mathematics as a way of expressing accurately the quantities and operations in civil engineering. Students get used to teamwork and behave respectfully. | |
| Students use mathematical and computer tools to pose and solve civil engineering problems. | |
| Students can handle and perform elementary operations with real and complex numbers. | |
| Students know the fundamentals and applications of Linear Algebra: matrix theory, systems of equations and linear applications. | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
-
Unit 1: Linear Algebra
-
Unit 1.1: Vector spaces: Spaces and subespaces. Euclidean space. Linear combinations. Basis and dimension. Coordinates. Sum of subespaces. Change of basis.
-
Unit 1.2: Inner product spaces: Distance. Metric spaces. Normed spaces. Orthogonal sets.
-
Unit 1.3: Matrices: Operations. Inverse. Rank. Determinant. Decomposition. Intersection of subspaces.
-
Unit 1.4: Systems of Linear Equations: Compatibility. Transformations. Gaussian elimination method. Resolution. Equivalence of linear system equations. Resolution in a set of selected variables. Resolution of a modified system. Applications: Water supply networks, structures, transportation problem, planning and production problem, etc.
-
Unit 1.5: Linear Transformations: Matrix representation. Change of basis. Invariant subspaces. Operations. Diagonalization. Eigenvalues and eigenvectors.
-
Unit 1.6: Bilinear and Quadratic Forms: Bilinear Forms. Matrix representation of a bilinear form. Quadratic forms. Diagonalization of a quadratic form. Applications.
-
Unit 1.7: Cones: Convex sets. Types of linear combinations. The Gamma Algorithm. Solutions of a modified system.
-
Unit 1.8: Polytopes and Polyhedra: Polytope. Polyhedra. Intersections.
-
Unit 1.9: Systems of Linear Inequalities: Compatibility of a system of linear inequalities. Resolution. Applications.
-
-
Unit 2: Calculus
-
Unit 2.1: Real numbers. Introduction. The set of natural numbers N. Operations with natural numbers. The set of integer numbers Z. Operations with integer numbers. The set of rational numbers Q. Operations with rational numbers. The set of real numbers R. Operations with real numbers.
-
Unit 2.2: Complex numbers. Introduction. Complex numbers. Operations with complex numbers: addition and product of complex numbers, root of a complex number, natural logarithm and power of a complex number. Application of complex numbers to geometric transformations: translation, rotation, homotecy, product of homotecy by rotation, product of inversion by axial symmetry.
-
Unit 2.3: Sequences and Series of real numbers. Introduction. Sequences of real numbers, definition. Limit of a sequence of real numbers. Theorems about sequence limits. Practical calculation of limits. Equivalent infinitesimals and infinites. Series of real numbers, definition. Convergence of a serie. Remainder of a serie. Properties of series. Geometrical series. Divergence criteria. Positive terms series: comparison tests, integral test, p-series, ratio and root test. Alternating series. Leibniz criterion. Series of any terms. Conditional and absolute convergence.
-
Unit 2.4: Real functions of real variable. Concept of function. Limit of functions. Function continuity. Differentiability of a function. Differentiation techniques. Differentials and approximation by the tangent. Local behaviour of differentiable functions. Increase and decrease. Concave and convex functions. Study of the variation of a function. Local and global maxima and minima. Applications.Graphic representation of functions.
-
Unit 2.5: Power series, Taylor and MacLaurin. Sequences and functional series.Concept of power series. Convergence of a power series. Expansion of a function into power series. Taylor and MacLaurin series.
-
Unit 2.6: Definite integrals and their properties. Concept of definite integral. Geometric representation. Definite integrals properties. Indefinite integrals, definition. The fundamental theorem of calculus. Special integration methods: by parts, rational functions, substitution, irrational, transcendent. Improper integrals, generalization of the integral concept. Parametric and Eulerian integrals. Applications to the calculation of plane areas, curve length, area and volume of a surface of revolution.
-
7. Activities, Units/Modules and Methodology
| Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
| Class Attendance (theory) [ON-SITE] | Lectures | CE01 CE02 CE04 CG01 | 1.12 | 28 | N | N | ||
| Class Attendance (practical) [ON-SITE] | Problem solving and exercises | CE01 CE02 CE04 CG01 | 0.78 | 19.5 | N | N | ||
| Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | CE01 CE04 CE06 CG01 | 0.08 | 2 | Y | N | ||
| Progress test [ON-SITE] | Assessment tests | CE01 CE02 CE04 CG01 | 0.16 | 4 | Y | N | ||
| Final test [ON-SITE] | Assessment tests | CE01 CE02 CE04 | 0.18 | 4.5 | Y | Y | ||
| Study and Exam Preparation [OFF-SITE] | Combination of methods | CE01 CE02 CE04 CE06 CG01 | 3.6 | 90 | N | N | ||
| Group tutoring sessions [ON-SITE] | Problem solving and exercises | CE01 CE02 CE04 CE06 | 0.04 | 1 | N | N | ||
| Individual tutoring sessions [ON-SITE] | Problem solving and exercises | CE01 CE02 CE04 CE06 | 0.04 | 1 | N | N | ||
| Total: | 6 | 150 | ||||||
| Total credits of in-class work: 2.4 | Total class time hours: 60 | |||||||
| Total credits of out of class work: 3.6 | Total hours of out of class work: 90 | |||||||
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
8. Evaluation criteria and Grading System
| Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
| Final test | 60.00% | 100.00% | The test includes the partial examinations and the ordinary / extraordinary examinations |
| Other methods of assessment | 40.00% | 0.00% | Includes resolution of problems or cases. Includes progress tests. |
| Total: | 100.00% | 100.00% |
According to art. 4 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 12.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).
Evaluation criteria for the final exam:
-
Continuous assessment:The evaluation is made up of 3 partials, each one evaluated by means of 60%- exam grade and 40% -problem solving and/or progress tests grade (average grades). The minimum mark required in the partial exams is 4 out of 10. The minimum mark to pass the ordinary call is 5 out of 10, mark which is obtained as the mean of the 3 partials. The partial exams with a minimum mark of 4 are kept for the ordinary and extraordinary sessions. The note in resolution of problems or cases is saved for the ordinary and extraordinary calls.
All the assessable activities that have been carried out during the course are recovered.
Grades are not saved from previous courses. -
Non-continuous evaluation:The student will have to do a global exam that will include all the course and competences content. To pass the course, the student must obtain at least a 5 out of 10, which will constitute 100% of his/her grade.
Unless stated otherwise, continuous evaluation criteria will be applied to all students.
Grades are not saved from previous courses.
Anyone choosing non-continuous assessment must notify it to the lecturer within the class period of the subject. The option is only available if the student¿s participation in evaluation activities (from the continuous assessment) has not reached 50% of the total evaluation for the subject.
For the retake exam, the assessment type used for the final exam will remain valid.
Specifications for the resit/retake exam:
Same that in final exam.
Specifications for the second resit / retake exam:
The student will have to do a global exam that will include all the course and competences content. To pass the course, the student must obtain at least a 5 out of 10, which will constitute 100% of his/her grade.
Grades are not saved from previous courses.
Grades are not saved from previous courses.
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Group tutoring sessions [PRESENCIAL][Problem solving and exercises] | 1 |
| Individual tutoring sessions [PRESENCIAL][Problem solving and exercises] | 1 |
| Unit 1 (de 2): Linear Algebra | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 12 |
| Progress test [PRESENCIAL][Assessment tests] | 4 |
| Final test [PRESENCIAL][Assessment tests] | 3 |
| Unit 2 (de 2): Calculus | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 13 |
| Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 7.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Final test [PRESENCIAL][Assessment tests] | 1.5 |
| Global activity | |
|---|---|
| Activities | hours |
10. Bibliography and Sources
