Description

Theory
2

Theory/Practice
2

Instructors

Isabel Figueiredo

Contents

1. Functions of Several Variables (CP1)
1.1 Definition and forms of representation. Contours.
1.2 Partial derivatives and the differential.
1.3 Derivative of composite function and implicit function.
1.4 Optimization: Computing extremes.

2. Double Integrals (CP2)
2.1 Definition and properties.
2.2 Calculation and application to the calculation of areas and volumes.
2.3 Polar coordinates. Calculation of areas and volumes.

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

4. Laplace Transform (CP4)
4.1 The calculation of the Laplace Transform using the definition.
4.2 Properties of the Laplace Transform.
4.3 Laplace Transform of elementary functions and special functions.
4.4 Inverse Laplace Transform.
4.5 Solving differential equations using Laplace Transform.

Learning Outcomes

OB1: Analyse and manipulate functions of several variables using multivariable calculus techniques.

OB2: Calculate double integrals and apply them to determine areas and volumes.

OB3: Identify, formulate, and solve ordinary differential equations.

OB4: Calculate and apply Laplace transforms in the solution of mathematical and engineering problems.

OB5: Apply multivariable calculus, differential equations, and Laplace transform techniques to engineering problems.

OB6: Demonstrate rigour and clarity in problem-solving through structured reasoning, result simplification, and critical interpretation of solutions.