Description

Theory
2

Theory/Practice
4

Instructors

Alcinda Barreiras

Contents

(CP1) Functions several variables (from 30% to 35%)
1.1. Definition.
1.2. Continuity.
1.3. Partial derivative, matrix of partial derivatives. Differentiability, differentials.
1.4. The chain rule.
1.5. Directional derivative.
1.6. Implicit derivative.
1.7. Maxima and minima.

(CP2)Ordinary differential equations (from 30% to 35%)
2.1. Basic concepts and ideas
2.2. First order equations
2.2.1. Separable differential equations
2.2.2. Linear differential equations
2.2.3. Variable change
2.3. Second order equations:
2.3.1. Reducible to a first order equation.
2.3.2. Linear differential equations

(CP3 )Laplace Transforms (from 15% to 25%)
3.1. Definition
3.2. Heaviside´s unit step.The impulse function.
3.3. Properties of the Laplace Transform.
3.4. Inverse Laplace Transform.
3.5. Cases of differential equations solvable by Laplace transform.

(CP4) Multiple Integrals (from 15% to 20%)
3.1 Double integrals
3.1.1. Definition, properties.
3.1.2. Evaluate
3.1.3. Applications.
 

Learning Outcomes

After the frequency with the 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.
The student should be able, also to identify and resolve first and second ordinary differential equations.
Calculate the Laplace transform by definition. Identify the properties of the direct and inverse Laplace transform and know how to apply them in the resolution of differential equations.
Recognize the importance and apply the different mathematical techniques studied in this Mathematical Analysis course on formulating and resolving other problems (OB3).
This knowledge should be applied to specific problems in their Engineering area (OB4).