Academic Year:
2025/26
558 - Bachelor's Degree in Industrial Design and Product Development Engineering
25867 - Mathematics I
Teaching Plan Information
Academic year:
2025/26
Subject:
25867 - Mathematics I
Faculty / School:
110 - Escuela de Ingeniería y Arquitectura
Degree:
558 - Bachelor's Degree in Industrial Design and Product Development Engineering
ECTS:
6.0
Year:
1
Semester:
First semester o Second semester
Subject type:
Basic Education
Module:
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1. General information
The purpose of this subject is for students to acquire a solid foundation in the fundamentals of Differential and Integral Calculus of functions of one and several variables and in the numerical solution of problems in these disciplines; learns to solve a problem in a rigorous way, selecting the most efficient techniques and strategies; and is able to use a mathematical software for its solution.
These approaches and objectives are aligned with some of the Sustainable Development Goals (SDGs) of the Agenda 2030 (https://www.un.org/sustainabledevelopment/es/), in such a way that the acquisition of the learning results of the subject will contribute to some extent to their achievement.
The recommended profile to take the subject is to have the knowledge and skills acquired in the subjects of Mathematics I and II of the Baccalaureate, in particular:
- Analysis of functions of one variable: elementary functions, graphical representation, limits, continuity, derivation, integration.
- Affine geometry.
- Conic sections.
2. Learning results
- Has aptitude to apply the acquired knowledge of Differential and Integral Calculus and Numerical Methods.
- Solves mathematical problems that may arise in Engineering.
- Knows how to use numerical methods in the solution of some mathematical problems.
- Knows the reflexive use of symbolic and numerical calculation tools.
- Possesses scientific-mathematical thinking skills that allow them to ask and answer certain mathematical questions.
- Is skilled in handling mathematical language; in particular, symbolic and formal language.
3. Syllabus
1. Differential and Integral Calculus of functions of one variable.
- Real numbers.
- Real functions of real variable. Limits and continuity.
- Derivation. Applications of the derivative.
- Solving nonlinear equations.
- Polynomial approximation: Taylor's polynomial. Interpolation.
- Integration. Integration methods. Numerical integration. Applications of the definite integral.
2. Differential and Integral Calculus of functions of several variables.
- The geometry of the plane and space.
- Functions of various variables. Domains. Graphical representation. Limits and continuity.
- Partial derivatives and gradient vector. Differentiability and tangent plane.
- Higher order derivatives. Calculation of relative extremes.
- Multiple integral.
4. Academic activities
Theoretical-practical classes (40 hours)
Presentation and explanation of the theoretical contents, accompanied by illustrative examples and problem solving.
Problem Sessions (8 hours)
Problem solving in small subgroups guided by the teacher.
Computer practices (12 hours)
Analysis and programming of mathematical algorithms using symbolic and numerical programming software installed in EINA's computer laboratories.
Personal study
Assessment tests
5. Assessment system
The subject will be evaluated in the global assessment mode. However, tests will be scheduled throughout the semester in order to facilitate the gradual passing of the subject. In both evaluation modalities, each test will be evaluated from 0 to 10 points, being necessary to obtain a grade greater than or equal to 4.5 points to average. The final grade will be obtained by applying the corresponding percentages.
Continuous assessment
1. Two tests on the theoretical and practical contents of the subject (80%)
- Mid-term test on the contents of Differential and Integral Calculus of functions of one variable (40%).
- Test during the exam period of the first call on the contents of Differential and Integral Calculus of functions of several variables (40%).
The evaluation criteria are: mastery of mathematical concepts and ability to apply them in problem solving, use of efficient strategies and procedures, correct use of terminology and notation.
2. Completion of the practices of the subject (20%)
It will be evaluated through the delivery of problems before and after the completion of each practice session.
The evaluation criteria are: ability to select the most appropriate method, command mastery, correct interpretation of the results obtained.
Global evaluation (First and second call)
1. Written test on the theoretical and practical contents of the subject (80%).
2. Written test on computer practices (20%).
6. Sustainable Development Goals
4 - Quality Education
5 - Gender Equality