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Mathematics

Code: 103242
Credits: 6
2026/2027
Degree programme Type Course
Food Science and Technology OB 1

Contact lecturer

Name :
Joachim Kock
Email :
joachim.kock@uab.cat

Teaching staff

Pau Reig Llunell
Julià Cufi Sobregrau

Group languages

You can consult this information at the end of the document.

Prerequisites

The subject has no established prerequisites. In spite of this, it is convenient for the student to have a good knowledge of the simplest algebraic calculations (operations with fractions and roots, powers of a binomial, simplification of algebraic expressions, rules of logical inference). It will also be convenient for the student to review polynomials (operations, roots, and factorial decomposition). It is also advisable that the student has had contact with the basic notions of differential calculus such as function, graphic and derivative.

Objectives

The objective of this subject is that the student acquires the knowledge and the basic mathematical tools to be able to understand, use and develop the mathematical models associated with the chemical, physical or biological phenomena. The ability of the student to express himself in mathematical language must help him to approach scientific texts, work with computer software and raise and solve problems. A first transversal objective to be achieved is the development of scientific rigor, logical thinking and the critical spirit.

Learning outcomes

  1. Analyse, summarise, resolve problems and make professional decisions.
  2. Apply the scientific method to resolving problems.
  3. Search for, manage and interpret information from different sources.
  4. Use IT resources for communication, the search for information within the field of study, data processing and calculations.
  5. Use symbolic calculus by implementing processes to solve specific problems in algebra, calculus or numbers.
  6. Master the language and the basic tools of linear algebra.
  7. Master the language and the basic tools of calculus (one or several variables).
  8. Use numerical methods to solve problems in algebra and calculus.
  9. Recognise the usefulness of mathematical methods in calculus, algebra and numbers, for modelling simple, real situations.
  10. Compare analytical methods with numerical methods: the advantages and disadvantages of each.
  11. Recognise the advantages and disadvantages of symbolic calculus tools.

Contents


1. Algebra

1.1 Sets of numbers. Sum and product operations, signs rule. Inequalities and absolute value. Real roots and power operations.

1.2 Polynomials. Roots and decomposition of polynomials.

2. Differential calculus of one variable

2.1 Concept of function. Examples of functions of real variable (polynomial, rational)

2.2 Limits of functions. Continuous functions

2.3 The derivative. Geometric interpretation and dynamic interpretation. Rule of the chain.

2.4 Inverse function. Exponential and logarithmic functions.

2.5 Growth and decrease of a function. Relative extremes. Graphical representation of functions

2.6 Optimization.

3. Integral calculus

3.1 Definite integral. The fundamental theorem of integral.

3.2 Calculation of some primitives.

4. Differential equations

4.1 Differential equations. Initial value problem.

4.2 Separable equations and linear equations. Applications to the balance of matter and the growth of populations


 

Learning activities and methodology

Title Hours ECTS Learning outcomes
Tutorials 6 0.24 1, 3, 6
Problems resolution 43 1.72 1, 2, 6, 7, 9
Practices in the computer room 8 0.32 5, 8, 9, 10, 11
Study 41 1.64 6, 7
Problems classes 19 0.76 1, 2, 6, 7, 9
Theory 23 0.92 6, 7

The teaching is distributed in:


Theory:

These are classes in which the teacher introduces the basic concepts corresponding to subject matter, showing examples of their application, taking into account the attendees and adapting to their level. The student will complement the teacher's explanations with the autonomous personal study.


Problems:

The classes of problems are done in small groups and in them both the understanding of the concepts introduced and the techniques of problem solving are worked on.


Practices with a computer:

The student learns to use a symbolic and numerical mathematical software. The practical classes are carried out in small groups.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Recovery exam 90 4 0.16 5, 6, 7, 8, 9
Second partial exam 45 2 0.08 5, 6, 7, 8, 9
First partial exam 35 2 0.08 5, 6, 7, 8, 9
Evaluation of practices 10 2 0.08 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Exercises test 10 0 0 5, 7, 8, 9

The subject will be evaluated according to the following criteria:

Practice exercises in the computer lab: 10%

An exercise class test: 10%

First partial exam: 35%

Second partial exam: 45%

Recovery test, only if necessary: 90%. The computer lab exercises grade will not be recoverable.

One or more assessment tests may be proposed during class time and with a maximum assessment of 10% additional to the previous one, always bearing in mind that the maximum overall mark cannot exceed 10 points.

This subject/module does not allow the single assessment system.

It will be considered that a student is not assessable if he has only participated in assessment activities that represent less than 15% of the final grade.

Bibliography

Primary:

Aguadé, J., Matemàtiques i modelització per a les ciències ambientals, UAB, 2018. http://ddd.uab.cat/record/158385

Secondary:

Salas, S. I Hille, E. Calculus: una y varias variables, Volum 1. Editorial Reverté, 2011 (llibre amb accés electrònic)

Batschelet, E., Matemáticas básicas para biocientíficos, Dossat, Madrid

Neuhauser, C., Matemáticas para ciencias, Prentice Hall, 2004

 

Software

The software used in the computer lab classes is Python with the module SymPy.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan first semester morning-mixed
(PAUL) Classroom practices 1 Catalan first semester morning-mixed
(SEM) Seminars 1 Catalan first semester morning-mixed
(PAUL) Classroom practices 2 Catalan first semester morning-mixed
(SEM) Seminars 2 Catalan first semester morning-mixed
(SEM) Seminars 3 Catalan first semester morning-mixed
(SEM) Seminars 4 Catalan first semester morning-mixed