Universidad Carlos III de Madrid
Area of Study
Taught In English
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
Calculus II (251 - 15324)
Study: Bachelor in Aerospace Engineering
Semester 2/Spring Semester
1ST Year Course/Lower Division
Competences and skills that will be acquired and learning results:
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:
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).
We follow a continuous-assessment system plus a final exam:
- The continuous-assessment part consists in a written examination
contributing with weight 40% to the final mark. The mid-term examination
will take place, approximately, at two thirds of the semester and it
will be held in regular class hours, according to the current regulations.
- The final exam (contributing with weight 60% to the final mark) will
be held at the end of the semester. (PO: a.)
Courses and course hours of instruction are subject to change.
ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.