Course: 2021/2022

Calculus II

(14462)

Requirements (Subjects that are assumed to be known)

Calculus I
Linear Algebra

In this second course of Calculus the students should acquire the mathematical background needed to understand and apply the concepts and techniques appearing in Statistics which involve several real variables. In particular they should become acquainted with functions of several variables, their properties of continuity, partial differentiability, differentiability and the calculus of double and triple integrals. Moreover, they will apply also these skills to solve optimization problems.

Description of contents: programme

1.- Vectors and scalar product. Basic topological concepts.
2.- Functions of several variables. Graphs and level sets. Limits and continuity.
3.- Partial derivatives. Directional derivatives. Differentiability: Tangent plane.
4.- Chain rule. Higher order derivatives.
5.- Double and triple integrals: properties. Iterated integrals. Changes of variables.
6.- Applications of double and triple integrals.
7.- Quadratic approximation: Taylor's theorem.
8.- Maxima and minima. Lagrange multipliers.

Learning activities and methodology

The course will be taught mostly through lectures, with supporting material available on the web. These classes should be complemented with the students' autonomous reading on some aspects of the syllabus, especially concerning motivation and applications.
Some of the lectures will be devoted to solving exercises singled out from the collection of exercises the students will be given at the beginning of the semester. Two partial exam.

Assessment System

- % end-of-term-examination 50
- % of continuous assessment (assigments, laboratory, practicals...) 50

Basic Bibliography

- James Stewart. Cálculo multivariable. Thomson.
- Jerrold E. Marsden, Anthony J. Tromba. Cálculo Vectorial. Pearson Educación. 2004
- Ron Larson y Bruce H. Edwards. Cálculo 2. Mc Graw Hill. 9ª edición 2010

The course syllabus may change due academic events or other reasons.