Description

Theory
2

Theory/Practice
2

Instructors

Gisela Vieira Ramadas

Contents

1. Functions of two or more variables(2,5weeks)
1.1. Definition and forms of representation. Contour lines.
1.2. Partial derivatives. Differentials.
1.3. The chain rule. Implicit differentiation.
1.4. Gradients.
1.5. Maxima and minima.

2. Ordinary Differential Equations(5weeks)
2.1. Introduction. Meaning and interpretation of a solution.
2.2. First-order differential equations.
2.3. Second-order differential equations.
2.4. Brief reference to systems of differential equations.

3. Laplace Transforms(5weeks)
3.1. Definition and region of convergence.
3.2. Heaviside´s unit step. The impulse function.
3.3. Properties of the Laplace Transform.
3.4. Inverse Laplace Transform.
3.5. Solving differential equations by the Laplace transform.

4. Double integrals(2,5weeks)
4.1. Definition, geometric interpretation, properties.
4.2. Evaluate. Polar coordinates.
4.3. Applications.

Learning Outcomes

OB1: Analyse real functions of several variables and apply differential calculus techniques.

OB2: Identify and solve different types of ordinary differential equations using appropriate methods.

OB3: Calculate Laplace transforms and apply their properties to solve differential equations.

OB4: Apply double integral techniques to solve problems involving areas and volumes of solids.

OB5: Apply mathematical concepts and techniques from this course unit to problems in Chemical Engineering.

OB6: Develop structured problem-solving skills, including analysis, simplification, and critical interpretation of mathematical results.