Public University of Navarre



CastellanoEuskara | Academic year: 2018/2019 | Previous academic years:  2017/2018 
Double degree in Agrifood Engineering and Rural Environment and Innovation of Food Processes and Products from Navarre Public University at the Universidad Pública de Navarra
Course code: 503101 Subject title: MATHEMATICS I
Credits: 6 Type of subject: Mandatory Year: 1 Period: 1º S
Department:
Lecturers:
YANGUAS SAYAS, PATRICIA (Resp)   [Mentoring ]

Partes de este texto:

 

Module/Subject matter

Mathematics/ Mathematics I.

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Descriptors

Differential and integral calculus of a single variable, linear algebra.

Area: Applied mathematics.

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General proficiencies

  • CB1: Students are able to demonstrate they have acquired knowledge and understanding in a field of study based on the basic foundations gained within their general secondary education together with the support of advanced textbooks and aspects of the latest advances in the field.
  • CB5: Students can develop the necessary learning skills to undertake further studies with a high degree of autonomy.

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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.
  • CG2: Adequate knowledge of the physical problems, technologies, equipment, and water and energy supply systems, the limits imposed by budgetary factors and building regulations, the relationships between installations and/or buildings with farms, agro-food industries and spaces related to gardening and landscaping with their social and environmental surroundings, as well as the need to relate those surroundings from that environment with human needs and environmental protection.

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Learning outcomes

  • (R1) Work with elementary functions (polynomials, rational, trigonometric, logarithms, exponentials,...), know their elementary properties and have an idea of the concepts of limit, continuity and differentiablility.
  • (R2) Work with analytic expressions and simplify and/or find apropriate bounds for them.
  • (R3) Solve approximation problems: Taylor, least squares, interpolation,...
  • (R4) Identify and compute the elementary forms of integrals in one variable; work with their physical and engineering applications and calculate volumes and areas.
  • (R5) Know the theoretical foundations and the direct algorithms for the resolution of algebraic linear systems.
  • (R6) Dominate the diagonalization of matrices: eigenvalues and eigenvectors.

     

    LEARNING OUTCOMES ENAEE

     

    ENAEE-1: Knowledge and understanding of the scientific and mathematical principles underlying the engineering branch.

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Methodology

 

Methodology - Activity Attendance Self-study
A-1 Lectures 45  
A-2 Practical lessons 15  
A-3 Assignments 5  5
A-4 Self-study   70
A-5 Exams, evaluation tests 5  
A-6 Office hours 5  
Total 75 75

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Relationship between formative activities and proficiencies/learning outcomes

 

Proficiency Formative activity
CE1 A-1, A-2, A-3, A-4, A-5, A-6
CB1- CB5 A-1, A-2, A-3, A-4, A-5, A-6
CG2 A-1, A-2, A-3, A-4, A-5, A-6

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Languages

English, Spanish and Basque.

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Evaluation

 

 Learning outcome   Evaluation system  Weight (%)   Possibility of resit 
 R1, R2, R3, R4, R5, R6, ENAEE-1.   Written exam   85  YES
 R1, R2, R3, R4, R5, R6, ENAEE-1.  Individual assignment   15  YES*

 

Continuous evaluation:

  • Part A: Chapters 1 and 2 are evaluated (50%).
  • Part B: Chapters 3 and 4 are evaluated (50%).

To pass the subject in the continuous evaluation it is necessary to get at least 3 points in part A, 3 points in part B and 5 points in the average of the grades of the two parts (here part means written exam + individual assignment).

 

Resit evaluation:

*It is a written exam that corresponds to the whole subject. It represents the 100 % of the final grade. The students that have not passed the subject in the continuous evaluation are allowed to take this exam. The exam may include questions related to the individual assigments.

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Contents

Number sets. Basic operations with real and complex numbers.

 

Functions, limits, continuity, differentiability, integrability. Basic concepts on real-valued functions of a single real variable. Elementary functions. Limits. Continuity of a function at a point. Properties of continuous functions. Differentiation, aplications of derivatives.

Definite and indefinite integrals, applications of integrals.

 

Vector spaces on R: subspaces. Basis and dimension.

 

Euclidean space: dot product and Euclidean norm, orthonormal bases, Gram-Schmidt orthogonalization.

 

Matrix diagonalization: eigenvalues and eigenvectors. Fundamental subspaces. Least-squares approximation.

 

Matrices: inverse matrix, linear systems, Rouché-Frobenius Theorem.

 

Determinants.

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Agenda

1. Real-valued functions of a real variable

Natural numbers, integers, rational numbers, real numbers and complex numbers. Real-valued functions of a real variable. Limits, continuity of a function at a point, properties of continuous functions. Derivative of a function at a point, chain rule, higher-order derivatives, properties of differentiable functions, the Newton-Raphson method, applications.

 

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

The Riemann integral, fundamental theorems of integral calculus, elementary integration methods, applications.

 

3. Vectors and matrices. The dot product

Matrices and determinants. Fundamental concepts, operations, linear systems, direct resolution methods, applications. Real vector spaces. Dot product and Euclidean norm, orthogonal projection, orthonormal bases, least squares approximation. Linear maps.

 

4. Matrix diagonalization

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

Polynomial functions of matrices. 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:

Calculus: A Complete Course (8th edition), R. A. Adams and C. Essex, Pearson Education, Canada, 2013.

Calculus (6th Edition), K.J. Smith, M.J. Strauss, M.D. Toda, Kendall/Hunt Publishing Co, Iowa, United States, 2014.

 

Introduction to Linear Algebra (2nd edition), S. Lang, Undergraduate Texts in Mathematics, Springer, New York, 1986.

Linear Algebra and Its Applications (4th edition), G. Strang, Cengage Learning, United Kingdom, 2006.

 

SUPPLEMENTARY BIBLIOGRAPHY:

Calculus With Analytic Geometry (8th edition), R. Larson, R.P. Hostetler, Houghton Mifflin Company, 2005.

Calculus (3rd edition), J. Rogawski and C. Adams, W. H. Freeman Publishers, 2015.

Calculus: One and several variables (10th edition), S. Salas, E. Hille, G. Etgen, John Wiley & Sons Inc., United States of America, 2007.

Calculus With Analytic Geometry (2nd edition), G.F. Simmons, The McGraw-Hill  Companies, Inc., New York, 1996.

Thomas' Calculus: Early Transcendentals (14th edition), G.B. Thomas, Jr., J. Hass, C. Heil, M. Weir, Pearson, Boston, 2018.

 

Linear Algebra and Its Applications: A first course, D.H. Griffel, Ellis Horwood Ltd., New York 1989.

Linear Algebra and Its Applications (5th edition), D.C. Lay, S.R. Lay and J.J. McDonald, Pearson Education Limited, Harlow (England) 2016.

Linear Algebra with Applications (7th edition), W.K. Nicholson, McGraw-Hill Ryerson Ltd., Toronto, 2013.

A course in Linear Algebra with Applications (2nd edition), D.J.S. Robinson, World Scientific Pub Co Inc., Singapore, 2006.

 

Mathematics for Life Sciences, C. Neuhauser, Prentice Hall PTR, 2001.

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Location

Lecture rooms building.

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