Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa

Contents

• Functions of several variables: limits, continuity, differentiation, Taylor series and graphics.
• Multiple integration.
• 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:

• G8 Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations
• G9 Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in computer engineering
• T1 Analysis and synthesis ability
• T3 Oral and written communication
• T4 Problem solving
• T8 Self-learning

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Specific proficiencies

Specific proficiencies that a student should acquire in this course:

• FB1 Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization
• FB3 Ability to understand and master the basic concepts of discrete matemathics, logic, algorithmics and computational complexity, and their applications to problem solving in engineering.

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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:
 

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Languages

English

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Evaluation

The contents of the course are assessed by means of two written exams. There is a mid-term exam covering the first third of the course syllabus, which involves the 35% of the final mark. The rest of the contents of the subject will be assessed in a final exam, and will involve the 65% of the final mark.

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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.

• R.A. Adams. Calculus: a complete course. Addison Wesley.
• M. Braun. Differential equations and their applications: an introduction to applied mathematics. Springer-Verlag.
• E. Kreyszig. Advanced engineering mathematics. John Wiley & Sons.
• J.E. Marsden, A.J. Tromba. Vector calculus. W.H. Freeman.

Spanish textbooks:

• R.E. Larson, R.P. Hostetler. Cálculo y geometría analítica. McGraw-Hill.
• R.K. Nagle, E.B. Saff, Ecuaciones diferenciales y problemas con valores en la frontera. Pearson Educación.
• 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

Arrosadia Campus

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