Description

Theory
2

Theory/Practice
2

Instructors

Isabel Pinto

Contents

1. Differential calculus in R^n (CP1)
1.1 Scalar and vector fields
1.3 Partial derivatives; the differential; Chain rule; implicit function
1.4 Directional derivatives and Gradient
1.5 Extreme values. Lagrange multipliers

2. Integral calculus in R^n (CP2)
2.1 Double and triple integrals.
2.2 Change of variables.
2.3 Application to the calculation of areas and volumes.
2.4 Line integrals.

3. Ordinary Differential Equations (CP3)
3.1 Ordinary Differential Equations of 1st order
3.2 Differential equations of 2nd order

Learning Outcomes

The course is geared towards developing the capacity of abstraction when solving engineering problems, strengthen and complement the previously acquired mathematical training and obtain training in the field of multivariable differential and integral calculus and ordinary differential equations.
It is intended that the student could be able to:
- Manipulate multi-variable functions, in particular scalar and vector functions in R^2 and R^3. (OB1)
- Determine double and triple integrals and apply it to compute areas and volumes. Solve line integrals. (OB2)
- Identify differential equations and determine its general and particular solutions. (OB3)
- Use rigour and detail in the presentation of the resolution of the exercises, namely using the structured presentation of the reasoning underlying the problem solving, the simplification of the result obtained and the presentation of an interpretative and critical comment on the solution obtained. (OB4)