Mathematical Analysis

Mathematics of secondary school.

The teaching methodology is based on theoretical-practical classes that combine the presentation of concepts with critical discussion and the resolution of real-world problems, promoting the practical application of knowledge. It is complemented by individualised support to foster critical thinking and creativity, in line with a student-centred pedagogical model oriented towards active learning.

After completing the curricular unit, the student should achieve the following objectives:

Knowledge – Recall and understand the fundamental concepts of differential and integral calculus, as well as ordinary differential equations.

Skills – Apply these concepts to solve practical problems, analyse solution methods and assess their suitability.

Competences – Create strategies to solve problems involving integrals and differential equations, developing autonomy and critical thinking.

The teaching method, based on the immediate application of concepts and detailed discussion in class, is compatible with these objectives as it promotes active learning, consolidation of knowledge and the development of competences such as analysis, evaluation and creation. This approach enables understanding of concepts, application of strategies to problem-solving and the development of autonomy and critical thinking, ensuring coherence with the defined objectives.

Competence 1 – 1.1. Derivatives; 1.2. Antiderivative; 1.3. Definite integrals; 1.4. Areas and volumes using definite integrals; 1.5. Improper integrals

Competence 2 – 2.1. Ordinary differential equations of separable variables; 2.2. Linear ordinary differential equations; 2.3. Bernoulli ordinary differential equations

Continuous Assessment

Part 1

Test 1 (T1) - written test, weight: 35%

Performance Assessment (PA1) in TP classes for Part 1 - weight: 10%

Part 2

Test 2 (T2) - written test, weight: 45%

Performance Assessment (PA2) in TP classes for Part 2 - weight: 10%

The performance assessments (PA1 and PA2) include class participation and the completion of in-class tasks.

Test 1 will assess the following syllabus topics: Competences 1.1 and 1.2.

Test 2 will assess the following syllabus topics: Competences 1.3 to 2.3.

The final grade (on a scale from 0 to 20) is the weighted average of the two parts (1 and 2), rounded to two decimal places:

Part 1 = max { 0.45 × T1 ; 0.35 × T1 + 0.10 × PA1 }

Part 2 = max { 0.55 × T2 ; 0.45 × T2 + 0.10 × PA2 }

Final Grade = Part 1 + Part 2

The student passes if the final grade is greater than or equal to 9.50.

Final Examination Assessment

Assessment is based on a single written exam, consisting of two parts: Part 1 (weight: 45%) and Part 2 (weight: 55%).

The student passes if the grade is greater than or equal to 9.50.

Conditions for the use of artificial intelligence (AI) systems:

The use of AI systems is governed by the Regulation on the Use of Artificial Intelligence Systems at IPC and by the AI Use Scale set out in its Annex I.

- In Tests 1 and 2 and in final examination, Level 0 of the IPC AI Use Scale applies, meaning that the use of AI systems is not allowed.

- In tasks carried out for the purposes of performance assessment (PA1 and PA2), Level 0 also applies, unless expressly stated otherwise by the lecturer for a specific activity.

- In all other learning activities of the course unit, limited-risk uses corresponding to Levels 2 to 4 are allowed, according to the student’s needs, particularly as a complementary learning resource to obtain alternative explanations, generate practice exercises, clarify doubts and critically analyse solutions. The use of AI should not, however, replace the student’s own work.

NAO