Description

Theory
2

Theory/Practice
2

Instructors

Alcinda Barreiras

Contents

(CP1) Ordinary differential equations (from 35% to 45%)
1.1. Basic concepts and ideas
1.2. First order equations
1.2.1. Separable differential equations
1.2.2. Linear differential equations
1.3. Second order equations:
1.3.1. Reducible to a first order equation.
1.3.2. Linear differential equations

(CP2). Functions several variables (from 35% to 45%)
2.1. Definition. Domain. Graphic.
2.2. Limits and continuity.
2.3. Partial derivative, matrix of partial derivatives. Differentiability, differentials.
2.4. The chain rule.
2.5. Directional derivative. Gradients
2.6. Implicit derivative.
2.7. Maxima and minima.
2.8. Divergence and rotation of a vector field.

(CP3). Multiple Integrals (from 15% to205)
3.1 Double integrals
3.1.1. Definition, properties and geometric interpretation.
3.1.2. Evaluate
3.1.3. Applications.
3.2 Triple Integrals
3.2.1. Definition, properties, geometric and physical interpretation.
3.2.2. Evaluate
3.2.3. Applications.

Learning Outcomes

After the frequency with success of this course, the student should be able to perform the fundamental operations of multivariable differential and integral calculus and implement its applications on several engineering issues(OB1).
The student should be able, also to identify and resolve first and second ordinary differential equations (OB2).
Recognize the importance and apply the different mathematical techniques studied on this Mathematical Analysis course on the formulation and in the resolution of different problem (OB3).
These knowledge should be applied to specific problems in their area of Engineering (OB4).