Public University of Navarre



Academic year: 2023/2024 | Previous academic years:  2022/2023  |  2021/2022  |  2020/2021  |  2019/2020 
Bachelor's degree in Industrial Engineering at the Universidad Pública de Navarra
Course code: 252206 Subject title: MATHEMATICS II
Credits: 6 Type of subject: Basic Year: 1 Period: 2º S
Department: Estadística, Informática y Matemáticas
Lecturers:
ROLDAN MARRODAN, ANGEL TEODORO (Resp)   [Mentoring ]

Partes de este texto:

 

Module/Subject matter

Basic training / M11 Mathematics.

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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:

O1. Apply the basic elements of differential calculus on several variables: gradient, divergence, curl, Stokes theorems.
O2. Apply the basic elements of integral calculus in several variables, e.g., to determine the length of a curve, the area of a surface, the volume of a solid,... using integrals, and use numerical differentiation and integration techniques.
O3. Apply Calculus to Engineering.
O4. Understand the concept of differential equation, and solve basic ordinary differential equations.
O5. Apply partial differential equations: wave equation and heat equation.

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Methodology


 

Methodology - Activity  On-site hours  Off-site hours
 A-1: Theoretical lessons  45  
 A-2: Practical lessons  15  
 A-3: Individual study   75
 A-4: Tutoring and exams 15  
 TOTAL 75 75

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Relationship between formative activities and proficiencies/learning outcomes

Proficiency Activities
CG3: Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations. A-1: Theoretical lessons A-2: Practical lessons A-3: Individual study A-4: Tutoring and exams
CG4: Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in engineering. A-1: Theoretical lessons A-2: Practical lessons A-3: Individual study A-4: Tutoring and exams
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. A-1: Theoretical lessons A-2: Practical lessons A-3: Individual study A-4: Tutoring and exams

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Languages

English.

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Evaluation

 

Learning
outcome
Assessment
activity
Weight (%) It allows
test resit
Minimum
required grade
All Long-answer exam questions 60 Yes (in the final exam) 5
All Individual work 30 Yes (in the final exam) 5
All Practical exam questions 10 Yes (in the final exam) 5
         

 

For assessment purposes, the course is divided into two parts:

  • Part A (related to lessons 1, 2 and 3) is worth 55%.
  • Part B (related to lessons 4 and 5) is worth 45%.

In order to pass the subject the average mark of all two parts must be greater or equal than 5. The mark on a final exam covering the whole course (to be scheduled during the resit assessment period) is not less than 5. Only students who did not pass the course by continuous assessment can sit this exam.

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Contents

Vector functions of several variables.
Integral Calculus of functions of several variables. Applications.
Ordinary and partial differential equations.

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Agenda

  1. Functions, limits and continuity in Rn. Basic concepts in scalar and vector functions of several variables. Limits. Continuity.
  2. Differential calculus in Rn. Partial and directional derivatives. Gradient vector and Jacobian matrix. Differentiability. Chain rule. Higher-order derivatives. Hessian matrix. Taylor polynomials. Relative extrema. Constrained optimization: the theorem of Lagrange multipliers. Absolute extrema on closed and bounded regions. Applications.
  3. Differential equations. Basic notions on differential equations. First-order ordinary differential equations. Some elementary integration methods. Second-order linear differential equations. Introduction to partial differential equations. Applications.
  4. Integral calculus in Rn. The Riemann integral. Elementary regions. Fubini's theorem. Change of variables. Polar, cylindrical and spherical coordinates. Applications.
  5. Line and surface integrals. 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.

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Experimental practice program

Use of Mathematica and Wolfram Alpha computational intelligence for solving integral and differential problems.

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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, Ninth edition. 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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Location


Lecture room building at Arrosadia Campus.

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