Checking date: 23/07/2020

Course: 2020/2021

Calculus II
Study: Bachelor in Aerospace Engineering (251)

Coordinating teacher: MUÑOZ GARCIA, JAVIER MANUEL

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

The aim of this course is to provide students the basic tools of differential and integral calculus of several variables. To achieve this goal students must acquire a range of expertise and capabilities. SPECIFIC LEARNING OBJECTIVES (PO a): - To understand the n-dimensional Euclidean space and in more depth n = 2 and 3. - To know the properties of scalar and vector functions of several variables. - To understand the concepts of continuity, differentiability and integrability. - To be able to handle optimization problems using optimization techniques. - To understand how to calculate double, triple, line and surface integrals. - To know and apply the main theorems of vector calculus: Green, Gauss, Stokes. - To understand how to apply the integral to calculate surface areas, volumes and solve some basic problems of Mathematical-Physics. - To know what are linear ordinary differential equations and learn techniques for solving equations of first and second order. SPECIFIC ABILITIES (PO a, k): - To be able to work with functions of several variables given in terms of a graphical, numerical or analytical description. - To understand the concept of differentiable function and ability to solve problems involving the concept. - To understand the concept of multiple integral, line and surface integral and its practical applications. - To understand what is an ordinary differential equation and know how to apply techniques of solving differential equations in different contexts. GENERAL ABILITIES (PO a, g, k): - To understand the necessity of abstract thinking and formal mathematical proofs. - To acquire communicative skills in mathematics. - To acquire the ability to model real-world situations mathematically, with the aim of solving practical problems. - To improve problem-solving skills. - To be able to use mathematical software in specific situations.
Description of contents: programme
1 .- The n-dimensional Euclidean space. Cartesian, polar, cylindrical and spherical coordinates. 2 .- Scalar and vector functions of several variables. Limits, continuity and differentiability. 3 .- Taylor's theorem. Optimization problems with and without constraints. 4 .- Double, triple, line and surface integral. 5 .- Theorems of Green, Gauss, Stokes and its applications .
Learning activities and methodology
Theory (3.0 credits. PO a). Problem sessions working individually and in groups (3.0 credits. PO a).
Assessment System
  • % end-of-term-examination 40
  • % of continuous assessment (assigments, laboratory, practicals...) 60
Basic Bibliography
  • James Stewart . Multivariable calculus . Cengage Learning. 8th ed 2016

The course syllabus and the academic weekly planning may change due academic events or other reasons.