1. General information
Course:
MATHEMATICS
Code:
57301
Type:
BASIC
ECTS credits:
12
Degree:
409 - CHEMISTRY
Academic year:
2022-23
Center:
1 - FACULTY OF SCIENCE AND CHEMICAL TECHNOLOGY
Group(s):
20
23
Year:
1
Duration:
AN
Main language:
Spanish
Second language:
English
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
HENAR HERRERO SANZ
- Group(s):
20
23
Building/Office
Department
Phone number
Email
Office hours
Margarita Salas/341
MATEMÁTICAS
926295412
henar.herrero@uclm.es
Lecturer:
HELIA DA CONCEICAO PEREIRA SERRANO
- Group(s):
20
23
Building/Office
Department
Phone number
Email
Office hours
Margarita Salas/Despacho 327
MATEMÁTICAS
926052237
heliac.pereira@uclm.es
Require appointment by email.
2. Pre-Requisites
To achieve the learning objectives is necessary knowledge and skills that are supposed to be guaranteed in the training prior to entering the university. In particular, basic knowledge of geometry, algebra and trigonometry, elementary mathematical operations (powers, logarithms, exponentials, fractions, ...), basic knowledge of derivation and integration of real functions of a real variable, and fundamentals of graphical representation of functions.
3. Justification in the curriculum, relation to other subjects and to the profession
As in any scientific discipline, in Chemistry, Mathematics is an indispensable tool for the understanding and development of any of its branches. Mathematics is the foundation and origin of modern theories of atomic and molecular structure, they allow to deal with problems of thermochemistry and kinetics with simplicity and elegance, they are present in the approach and development of all experimental chemical, academic and professional activities. The mathematical concepts studied in the Mathematics course provide an essential tool and constitute a precise language that is used by most of the basic subjects. The subject of Mathematics helps to enhance the abstraction, rigor, analysis and synthesis capacities necessary for any other scientific discipline.
4. Degree competences achieved in this course
| Course competences | |
|---|---|
| Code | Description |
| CB01 | Prove that they have acquired and understood knowledge in a subject area that derives from general secondary education and is appropriate to a level based on advanced course books, and includes updated and cutting-edge aspects of their field of knowledge. |
| E17 | Develop the ability to relate to each other the different specialties of Chemistry, as well as this one with other disciplines (interdisciplinary character) |
| G01 | Know the principles and theories of Chemistry, as well as the methodologies and applications characteristic of analytical chemistry, physical chemistry, inorganic chemistry and organic chemistry, understanding the physical and mathematical bases that require |
| T02 | Domain of Information and Communication Technologies (ICT) |
| T03 | Proper oral and written communication |
| T05 | Organization and planning capacity |
| T07 | Ability to work as a team and, where appropriate, exercise leadership functions, fostering the entrepreneurial character |
| T08 | Skills in interpersonal relationships |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| Get used to teamwork, express yourself orally and in writing, and behave respectfully. | |
| Knowing how to derive, integrate and represent functions of one and several variables, as well as the meaning and applications of the derivative and the integral. | |
| Know how to model chemical processes through differential equations, solve them and interpret results. | |
| Know how to use the language of Mathematics. | |
| Know the matrix theory and know how to carry out the corresponding calculations. | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
-
Unit 1: Linear Algebra
-
Unit 1.1: Matrix and determinants
-
Unit 1.2: Linear equations systems
-
Unit 1.3: Solving linear equations systems with MatLab
-
-
Unit 2: Vector Spaces
-
Unit 2.1: Definition of vector space
-
Unit 2.2: Vector subspaces
-
Unit 2.3: Linear combination. Generator systems
-
Unit 2.4: Linear independence and dependence
-
Unit 2.5: Basis. Dimension
-
Unit 2.6: Subspaces equations
-
Unit 2.7: Change of basis
-
-
Unit 3: Euclidean vector spaces
-
Unit 3.1: Scalar product. Euclidean vector space
-
Unit 3.2: Norm and angle
-
Unit 3.3: Orthogonality. Gram-Schmidt method
-
-
Unit 4: Linear transformations
-
Unit 4.1: Linear transformation
-
Unit 4.2: Kernel and image
-
Unit 4.3: Matrix representation
-
Unit 4.4: Operations
-
Unit 4.5: Change of basis
-
-
Unit 5: Eigenvalues and eigenvectors
-
Unit 5.1: Eigenvalues and eigenvectors
-
Unit 5.2: Proper subspaces
-
Unit 5.3: Diagonalizing a matrix
-
Unit 5.4: Diagonalizing a matrix with Matlab
-
-
Unit 6: One variable Integral and differential calculus
-
Unit 6.1: Limits and continuity
-
Unit 6.2: Derivative
-
Unit 6.3: Maximum and minimum. Convexity
-
Unit 6.4: Taylor polinomial
-
Unit 6.5: Definite and indefinite integrals
-
Unit 6.6: Improper integrals
-
Unit 6.7: Graphics, derivation and integrals with Matlab
-
-
Unit 7: Multivariable differential calculus
-
Unit 7.1: Multivariable functions
-
Unit 7.2: Global and directional limits. Continuity
-
Unit 7.3: Partial derivatives. Gradient
-
Unit 7.4: Chain rule
-
Unit 7.5: Taylor polinomial
-
Unit 7.6: Critical points. Maximum and minimum.
-
Unit 7.7: Lagrange multiplier method
-
Unit 7.8: Graphics, derivation and optimization with Matlab
-
-
Unit 8: Multiple integrals
-
Unit 8.1: Doble integrals
-
Unit 8.2: Triple integrals
-
Unit 8.3: Linear integral
-
Unit 8.4: Surface integral
-
Unit 8.5: Integration with Matlab
-
-
Unit 9: Ordinary differential equations
-
Unit 9.1: Introduction to differential equations
-
Unit 9.2: Solving first order differential equations
-
Unit 9.3: Solving second order differential equations
-
Unit 9.4: Qualitative properties of differential equationsof differential equations
-
Unit 9.5: Solving ordinary differential equations with Matlab
-
-
Unit 10: Systems of Ordinary differential equations
-
Unit 10.1: Solving systems of first order ordinary differential equation
-
Unit 10.2: Qualitative properties of systems of first order ordinary differential equations
-
Unit 10.3: Solving systems of ordinary differential equations with Matlab
-
ADDITIONAL COMMENTS, REMARKS
The contents are divided into 3 parts:
I. Linear Algebra (Unit 1 to Unit 5)
II. Integral and Differential Calculus (Unit 6 to Unit 8)
III. Ordinary Differential Equations (Unit 9 and Unit 10).
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 | CB01 E17 G01 | 2.24 | 56 | N | N | ||
| Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | CB01 E17 G01 | 1.72 | 43 | N | N | ||
| Computer room practice [ON-SITE] | Practical or hands-on activities | CB01 E17 G01 T02 | 0.4 | 10 | Y | Y | ||
| Progress test [ON-SITE] | Assessment tests | CB01 E17 G01 | 0.08 | 2 | Y | N | ||
| Progress test [ON-SITE] | Assessment tests | CB01 E17 G01 | 0.24 | 6 | Y | Y | ||
| Final test [ON-SITE] | Assessment tests | CB01 E17 G01 | 0.12 | 3 | Y | Y | ||
| Study and Exam Preparation [OFF-SITE] | Self-study | T03 T05 T07 T08 | 7.2 | 180 | N | N | ||
| Total: | 12 | 300 | ||||||
| Total credits of in-class work: 4.8 | Total class time hours: 120 | |||||||
| Total credits of out of class work: 7.2 | Total hours of out of class work: 180 | |||||||
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 |
| Progress Tests | 20.00% | 0.00% | Two progress test: one in the first semester and other one in the second semester. |
| Test | 70.00% | 90.00% | Three tests during the all course. |
| Assessment of activities done in the computer labs | 10.00% | 10.00% | Test using the software MATLAB. |
| 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:Evaluation criteria not defined
-
Non-continuous evaluation:Evaluation criteria not defined
Specifications for the resit/retake exam:
Evaluation criteria not defined
Specifications for the second resit / retake exam:
Evaluation criteria not defined
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Progress test [PRESENCIAL][Assessment tests] | 3 |
| Progress test [PRESENCIAL][Assessment tests] | 6 |
| Final test [PRESENCIAL][Assessment tests] | 3 |
| Unit 1 (de 10): Linear Algebra | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 2 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 10 |
| Unit 2 (de 10): Vector Spaces | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 11 |
| Unit 3 (de 10): Euclidean vector spaces | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 10 |
| Unit 4 (de 10): Linear transformations | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 11 |
| Unit 5 (de 10): Eigenvalues and eigenvectors | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 10 |
| Unit 6 (de 10): One variable Integral and differential calculus | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 9 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 6 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 2 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 26 |
| Unit 7 (de 10): Multivariable differential calculus | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 8 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 6 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 2 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 25 |
| Unit 8 (de 10): Multiple integrals | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 8 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 7 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 25 |
| Unit 9 (de 10): Ordinary differential equations | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 7 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 6 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 28 |
| Unit 10 (de 10): Systems of Ordinary differential equations | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 6 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 6 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 24 |
| Global activity | |
|---|---|
| Activities | hours |
10. Bibliography and Sources
