Guías Docentes Electrónicas
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
3868
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 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. 6 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. 13.2) 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
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
Larson, R. Elementary Linear Algebra Wadsworth Publishing Co 978-1133110873  
Larson, R., Edwards, B. H. Calculus Cengage Learning, 978-1337275347 2017  
Larson, R.; Edwards, B. Cálculo 2 de varias variables McGraw Hill 9789701071342 2009  
Larson, R.; Edwards, B.; Falvo, D. Álgebra Lineal Grupo Anaya Comercial 9788436820607  
Larson, Ron (1941-) Cálculo 1 : de una variable / McGraw-Hill, 978-607-15-0273-5 2010 Ficha de la biblioteca
Lay Linear Algebra and its applications Pearson International 978-1292092232 2015  
Quarteroni, A., Saleri, F., Gervasio, P. Scientific Computing with Matlab and Octave Springer 978-3-642-45366-3 2014  
Quarteroni, Alfio Cálculo científico con MATLAB y Octave / Springer-Verlag Italia, 88-470-0503-5 2006 Ficha de la biblioteca
Stewart, J. Cálculo de una variable Thomson Learning 9789706860699 2001  
Stewart, J. Cálculo multivariable Thomson Learning 9789706861238 2002  
Stewart, James (1941-) Multivariable calculus / Cengage Learning, 978-1-305-26673-5 2016 Ficha de la biblioteca
Thomas, G. Cálculo de una variable Pearson 9702606438 2005  
Thomas, G. Cálculo de varias variables Pearson 9789702606444 2006  
Zill, D. Ecuaciones diferenciales con aplicaciones de modelado Thomson 9687529210 2007  
Zill, D. G. Ecuaciones diferenciales con problemas de valor en la frontera Cengage Learning, 2018  
Zill, D. G. First course in Differential equations with modeling applications Cengage Learning, 2018  
Zill, D. G. Differential Equations with Boundary-Value Problems Cengage Learning, 2018  
Zill, D. G.; Wright, W. S. Matemáticas V. Ecuaciones Diferenciales Cengage Learning, 2018  



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