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2020/2021

Mathematics II

Code: 105038 ECTS Credits: 6
Degree Type Year Semester
2502444 Chemistry FB 1 2
The proposed teaching and assessment methodology that appear in the guide may be subject to changes as a result of the restrictions to face-to-face class attendance imposed by the health authorities.

Contact

Name:
David Marín Pérez
Email:
David.Marin@uab.cat

Use of Languages

Principal working language:
catalan (cat)
Some groups entirely in English:
No
Some groups entirely in Catalan:
Yes
Some groups entirely in Spanish:
No

Prerequisites

Matemàtiques I

Objectives and Contextualisation

The course  has three fundamental parts: the differential calculus, integral calculus and vector analysis.
										
											
										
											The objectives of the course are:
										
											
										
											(i) Understand the basics in each of these parts. These concepts include both the definitions of the mathematical objects that are introduced and their interrelation.
										
											
										
											(ii) Know how to apply the concepts studied coherently to the approach and resolution of problems.
										
											
										
											(iii) Acquire skills in mathematical writing and in calculus.

Competences

  • Adapt to new situations.
  • Communicate orally and in writing in one’s own language.
  • Learn autonomously.
  • Manage, analyse and synthesise information.
  • Obtain information, including by digital means.
  • Propose creative ideas and solutions.
  • Reason in a critical manner
  • Recognise and analyse chemical problems and propose suitable answers or studies to resolve them.
  • Resolve problems and make decisions.
  • Show an understanding of the basic concepts, principles, theories and facts of the different areas of chemistry.

Learning Outcomes

  1. Adapt to new situations.
  2. Apply the suitable mathematical tools to deal with and resolve chemistry problems.
  3. Communicate orally and in writing in one’s own language.
  4. Interpret mathematical language to deal with chemistry problems.
  5. Learn autonomously.
  6. Manage, analyse and synthesise information.
  7. Obtain information, including by digital means.
  8. Propose creative ideas and solutions.
  9. Reason in a critical manner
  10. Resolve problems and make decisions.

Content

(1) Functions of several variables
										
											
										
											- Geometry of the plane and space.
										
											- Graph of a function, curves and level surfaces.
										
											- Directional derivatives, gradient.
										
											- Differentiality. Chain rule. Derivatives of higher order. Absolute and relative extrems. 
										
											- Critical points, saddle points. Hessian criterion for the relative extrems. Lagrange multipliers for the calculation of absolute extremes.
										
											
										
											(2) Multiple integrals.
										
											
										
											- Iterated integrals. Fubini theorem. Principle of Cavalieri.
										
											- Variable change theorem. Polar, cylindrical and spherical coordinates. Calculation of masses and centers of masses.
										
											
										
											(3) Integral on curves and surfaces.
										
											
										
											- Parametric curves and surfaces.
										
											- implicitly given surfaces. Vector tangent to a curve at one point. Tangent plane and normal vector on a surface.
										
											- Length of a curve. Area of a surface. Line integrals.
										
											- Flow of a vector field.

Methodology

The methodology will be the standard for this type of subject with theory classes, problems and a practical session.

Activities

Title Hours ECTS Learning Outcomes
Type: Directed      
Problems 22 0.88 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Seminars 2 0.08 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Solving problems 39 1.56 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Theory 25 1 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Type: Supervised      
Tutories 12 0.48 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Type: Autonomous      
Study 39 1.56 1, 2, 5, 3, 6, 4, 7, 8, 9, 10

Assessment


The assessment consists of a work (compulsory), which will count 10% of the semester's score, of an intersemestral exam (compulsory) that will count 40% of the semester's mark, and a final semester exam (obligatory) that will count 50% of the note of the semester. In order to pass the subject, the average of the corresponding qualifications will be greater or equal to 5, and that each one of these qualifications will be greater or equal to 3. There will be a recovery exam at the end of the course and the student will approve the subject if he / she meets the above conditions by substituting the partial and final exam grades for those obtained in the recovery exam. To participate in the recovery students must have previously been evaluated in a set of activities whose weight equals to a minimum of two thirds of the total grade of the subject.

Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Final Exam 50% 3 0.12 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Midterm Exam 40% 3 0.12 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Recovery Exam 90% 3 0.12 1, 2, 5, 3, 6, 4, 7, 8, 9, 10
Work in group 10% 2 0.08 1, 2, 5, 3, 6, 4, 7, 8, 9, 10

Bibliography

J. E. Marsden y A.J. Tromba. Cálculo vectorial, cuarta edición. Addison-Wesley Longman, 1998.

S. L. Salas y E. Hille. Calculus, Vol. 1 y 2, tercera edición. Reverté, Barcelona, 1995 y 1994.

B. Demidovich. Problemas y ejercicios de Análisis Matemático. Ed. Paraninfo.