Public University of Navarre



Castellano | Euskara | Academic year: 2015/2016 | Previous academic years:  2014/2015 
Bachelor's degree in Agricultural, Food and Rural Environment Engineering at the Universidad Pública de Navarra
Course code: 501101 Subject title: MATHEMATICS I
Credits: 6 Type of subject: Basic Year: 1 Period: 1º S
Department: Mathematics and Computer Engineering
Lecturers:
LOPEZ GARCIA, JOSE LUIS (Resp)   [Mentoring ]

Partes de este texto:

 

Module/Subject matter

Mathematics/ Mathematics I.

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Contents

Real-valued functions of one real variable.

Integration of real-valued functions of one real variable.

Vectors and matrices.

Inner product.

Diagonalization of matrices.

Applications of diagonalization of matrices.

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Descriptors

Differential and integral calculus, linear algebra.

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General proficiencies

  • CT6: Self-learning ability.
  • CT7: Problem solving proficiency with creativity, personal initiative, methodology and critical reasoning.

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Specific proficiencies

  • CE1: Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial differential equations; numerical methods, numerical algorithms, statistics and optimization.

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Learning outcomes

  • Work with elementary functions (polynomials, rational, trigonometric, logarithms, exponentials,...), to know their elementary properties and to have an idea about the concepts of limit, continuity and differentiablility.
  • Work with analytic expressions and to simplify and/or find apropriate bounds for them.
  • To kwnow the geometrical aspects related to funtions of one variable.
  • Solve approximation problems: Taylor, least squares, interpolation,...
  • Identify and compute the elementary forms of integrals of one variable, their physical and engineering applications.
  • To know the theoretical foundaments and the direct algorithms used in the resolution of algebraic linear systems.
  • The use of matrix calculus to solve practical problems.

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Methodology

Methodology - Activity Attendance Self-study
A-1 Lectures 44  
A-2 Practical classes 16  
A-6 Self-study   75
A-7 Exams, evaluation tests 5  
A-8 Office hours 10  
Total 75 75

 

 

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Languages

English.

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Evaluation

Continuous assessment

 

       
Learning outcomes Instrument Weight % Make up
       
      Self-learning ability.Problem solving proficiency with creativity, personal initiative, methodology.
  • Critical reasoning.
  • To communicate knowledge and skills in the engineering field.
  • Knowledge of the concepts of the subject.
  • Analysis and synthesis hability.

They are assessed using the following criteria:

  • Practical implementation of the theoretical concepts.
  • Correct interpretation of the problems statements.
  • Analysis and synthesis hability.
  • Identification of the key concepts and theoretical understanding of the subject.
  • Correct usage of the mathematical tools.

Assessments of the proficiencies: CT6, CT7 y CE1.

There is an exam corresponding to the first two chapters.

 

There is an exam corresponding to the next two chapters.

 

There is an exam corresponding to the last two chapters.

 


The active participation in the classroom will be positively evaluated.

 

30%

 

 

30%

 

 

40% 

 

 

 

Yes

 

 

Yes 

 

 

Yes 

 

 

 

 

Those students who do not overcome the subject in the continuous assessment, can use the recovery evaluation. The recovery evaluation will supose 100 % of the final mark.

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Agenda

1. Real-valued functions of a real variable

Real numbers. Limits and continuity. Differentiation. Taylor polynomial. Optimization. Calculus of zeros of a function.

 

2. Integrals of real-valued functions of a real variable

Definition and properties. The fundamental theorem of calculus. Improper and parametric integrals. Numerical integration. Applications.

 

3. Vectors and matrices

Linear combination of vectors, linear independence, bases, dimension and coordinates. Matrices: rank, determinant and inverse matrix. Linear systems. Applications.

 

4. Inner product

Vector length and orthogonality. Orthogonal projection. Least squares method. Construction of orthogonal bases. Applications.

 

5. Matrix diagonalization

Eigenvalues and eigenvectors. Characteristic polynomial. Eigenspaces. Algebraic and geometric multiplicity. Diagonalizable matrices.

 

6. Applications of matrix diagonalization

Polynomial functions of matrices. Difference equations systems. Quadratic forms. Diagonalization and classification of quadratic forms.

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Bibliography

Access the bibliography that your professor has requested from the Library.


 Basic bibliography:

  • The notes of the teacher.

Complementary bibliography:

  • R. A. Adams: Calculus. A complete course. Addison Wesley.
  • G. L. Bradley, K. J. Smith: Calculus. Prentice Hall.
  • R. E. Larson, R. P. Hostetler: Calculus. McGraw-Hill.
  • S. L. Salas, E. Hille, G. J. Etgen: Calculus. Reverté.
  • M. D. Weir: Thomas' Calculus. Pearson-Addison Wesley.
  • D. H. Griffel: Linear Algebra and its applications, Ellis Horwood Ltd.
  • S. Lang: Introduction to linear Algebra, Addison-Wesley.
  • D. C. Lay: Linear Algebra and its applications, Pearson Education.
  • D. J. S. Robinson: A course in Linear Algebra with applications, World Scientific.
  • G. Strang: Linear algebra and its applications, Thompson.

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Location

Lecture rooms building.

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