Fundamentals of Mathematics and Physics

5 ECTS / Semestral / Português

Objectives and method

It is intended that the student:

  • masters some basic techniques of linear algebra (operations with vectors and matrices) and recognizes some of its applications;
  • masters some basic techniques of differential and integral calculus of one variable (calculation of derivatives, primitives and integrals, solution of differential equations) and recognizes some of their applications;
  • acquires knowledge of diverse fields of physics, namely in statics and the dynamics of a particle, work and energy, and thermodynamics;
  • applies the mathematical knowledge acquired to practical problem-solving situations in the fields of physics addressed.

The curricular unit is structured in theoretical-practical classes where theoretical contents will be presented, with examples of application. It is intended to combine a theoretical exposure of contents with problem-solving strategies. Students are encouraged to independently solve proposed exercises that are compiled into worksheets aligned with the syllabus taught.



I - Fundamentals of Mathematics
I.1 - Linear Algebra
1. Fundamental concepts and structures; basic operations with vectors and matrices
I.2 - Calculus
2. Polynomial, exponential, logarithmic, and trigonometric functions; inverse trigonometric functions and their derivatives
3. Primitive calculus: integration by substitution and by parts; integration of rational functions
4. Area and definite integrals; Fundamental Theorem of Calculus
5. First-order differential equations: separable and linear

II - Fundamentals of Physics
II.1 - Statics and the Dynamics of a particle
1. The concept of force
2. Newton's Laws of motion and their applications
II.2 - Work and energy
3. Work done by constant forces and variable forces
4. Kinetic energy and work-energy theorem
5. Conservative and non-conservative forces
6. The law of conservation of energy
II.3 - Temperature, Heat and the First Law of Thermodynamics