Numerical Integration with Problem-Based Learning: Theory, Exercises, and Engineering Applications

The book Numerical Integration with Problem-Based Learning proposes an innovative and meaningful approach to classical numerical integration methods within the engineering context. Through a balanced combination of theory, practice, and contextualization, the book allows the reader to understand not only the formulas and algorithms that underpin integration, but also their application in solving real-life problems in the professional environment.

The text progressively develops the fundamental integration methods—the Trapezium Rule, Simpson 1/3, Simpson 3/8, and Romberg—presenting for each the theoretical foundations, deductions, advantages, limitations, and carefully designed examples using the Problem-Based Learning (PBL) methodology. This structure encourages autonomy, critical reasoning, and the application of knowledge in interdisciplinary contexts.

In this sense, the book integrates complementary digital resources, such as interactive Python notebooks and methodological guides, which expand the learning experience through computational experimentation. With a practical and pedagogical approach, the book becomes an essential support tool for students and teachers of engineering, applied sciences, and related fields interested in strengthening their analytical and technological skills.

This book is an invitation to connect mathematics with reality, promoting active, reflective learning that is consistent with the challenges of contemporary higher education.

In this scenario, being literate doesn't just mean reading or writing. Literacy, in the digital environment, has expanded: it now also involves using technological tools and judiciously understanding the information circulating in virtual environments. Digital competence has become one of those key, essential skills that allow people to navigate a world where everything is connected, or at least almost everything. Education, work, civic life: everything is touched by the digital world.

Despite these advances, the digital divide remains. It is a problem not only measured by the lack of access to devices or networks. It is also—and perhaps above all—a question of knowledge, of skills that many people have not been able to acquire. And this, in the end, deepens existing inequalities: economic, social, and educational.

This book aims to examine this entire landscape closely. It presents a detailed analysis of how digital literacy has evolved, why it is so important, and what effects it has had on different fields. Based on a review of academic studies, theoretical models such as DigComp and TPACK, and concrete experiences such as Uruguay's Plan Ceibal, it offers a broad overview. The intention is clear: to better understand how to develop digital skills and reduce the barriers that still impede access to technology.

Eleven chapters address central topics. It analyzes how digital literacy is applied in education, how it impacts the workplace, and what its role is in developing critical citizens who can make informed decisions within a digital society. It also proposes ideas for strengthening digital education in schools, promoting inclusive public policies, and developing skills that will help people find jobs in today's global economy, which waits for no one.

This book is aimed at a wide range of people: teachers, researchers, educational policymakers, institutional leaders, and anyone interested in the changes brought about by the digital transformation. It offers a combination of theory, concrete data, and practical proposals. All with a common goal: to bridge the digital divide and harness the real potential that technology has to improve our societies.