Public University of Navarre



Castellano | Euskara | Academic year: 2015/2016 | Previous academic years:  2014/2015  |  2013/2014 
Bachelor's degree in Industrial Engineering at the Universidad Pública de Navarra
Course code: 242206 Subject title: MATHEMATICS II
Credits: 6 Type of subject: Basic Year: 1 Period: 2º S
Department: Mathematics and Computer Engineering
Lecturers:
PORTERO EGEA, LAURA   [Mentoring ]

Partes de este texto:

 

Module/Subject matter

 
Basic training / Mathematics.

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Contents

 

  • Functions of several variables: limits, continuity, differentiation, Taylor series and graphics.
  • Multiple integration. Applications.
  • Vector calculus.
  • Ordinary differential equations.

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Descriptors

 
Elements of differential and integral calculus in several variables. Ordinary differential equations.

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General proficiencies

 
General proficiencies that a student should acquire in this course:

  • CG3: Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations.
  • CG4: Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in engineering.

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Specific proficiencies


Specific proficiencies that a student should acquire in this course:

  • CFB1: Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, geometry, differential geometry, calculus, differential equations, numerical methods, algorithms, statistics and optimization.

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Learning outcomes


At the end of the course, the student is able to:

  1. Apply the basic elements of differential calculus in several variables: gradient, divergence, curl, Stokes' theorem.
  2. Apply the basic elements of integral calculus in several variables.
  3. Determine the length of a curve, the area of a surface, the volume of a solid, etc., by means of integration techniques.
  4. Apply elements of differential and integral calculus to problems arising in Engineering.
  5. Recognize and solve some basic types of ordinary differential equations.

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Methodology


The course consists of 6 credits, distributed in 4.5 theoretical and 1.5 practical credits. The whole-class theoretical lessons include the description of basic concepts and methods.  The small-group practical sessions are devoted to the solution of problems and applications. Finally, teacher-assisted tutoring is available for students all along the semester in order to solve possible queries and questions arising in the study of the subject.

The following table shows the distribution of the activities in the course:
 

Methodology - Activity  On-site hours  Off-site hours
 A-1: Theoretical lessons  46  
 A-2: Practical lessons  14  
 A-3: Individual study    75
 A-4: Exams and assessment  5  
 A-5: Tutoring  10  
 TOTAL  75  75

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Evaluation

Aspect Assessment activity Weight (%)
CG3, CG4, CFB1 Written exam covering the contents of lessons 1 and 2 (this exam can be retaken) 35
Written exam covering the contents of lessons 3 and 4 (this exam can be retaken) 45
Written exam covering the contents of lesson 5 (this exam can be retaken) 20

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Agenda

 

  1. Functions, limits and continuity in Rn. Basic concepts in scalar and vector functions of several variables. Limits. Continuity: definition and local and global properties.
  2. Differential calculus in Rn. Directional and partial derivatives. Jacobian matrix and gradient vector. Differentiability. Chain rule. Higher-order derivatives. Hessian matrix. Taylor series. Relative extrema. Constrained optimization: the theorem of Lagrange multipliers. Absolute extrema on closed and bounded regions. Applications.
  3. Integral calculus in Rn. Riemann integral. Elementary regions. Fubini's theorem. Change of variable theorem. Polar, cylindrical and spherical coordinates. Applications.
  4. Vector calculus. Scalar and vector fields. Conservative fields. Potential function. Line and surface integrals of scalar and vector fields. Circulation and flux. Divergence and curl. Green's, divergence and Stokes' theorems. Applications.
  5. Ordinary differential equations. Basic notions on differential equations. First-order ordinary differential equations. Existence and uniqueness of solution. Some elementary integration methods. Higher-order linear differential equations. Applications.

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Bibliography

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



Basic bibliography:

  • R.A. Adams. Calculus: a complete course. Addison Wesley.
  • E. Kreyszig. Advanced engineering mathematics. John Wiley & Sons.
  • J.E. Marsden, A.J. Tromba. Vector calculus. W.H. Freeman.
  • R.K. Nagle, E.B. Saff, Ecuaciones diferenciales y problemas con valores en la frontera. Pearson Educación.

Additional bibliography:

  • M. Braun. Differential equations and their applications: an introduction to applied mathematics. Springer-Verlag.
  • R.E. Larson, R.P. Hostetler. Cálculo y geometría analítica. McGraw-Hill.
  • S.L. Salas, E. Hille, G.J. Etgen. Calculus: una y varias variables. Reverté.
  • D.G. Zill. Ecuaciones diferenciales con aplicaciones de modelado. Thomson.

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Languages


English.

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Location


Lecture room building at Arrosadia Campus.

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