What will I learn?
The online integral course (in its free or paid mode), Mathematical Foundations: Integrals, offers an introduction to integral calculus from both a theoretical and practical perspective. You will learn the basic concepts of integral calculus, such as the indefinite integral, the definite integral, the fundamental theorem of calculus, integration techniques, improper integrals, and the applications of the integral. Furthermore, you will have the opportunity to perform exercises and problems that will allow you to apply what you have learned and develop your mathematical reasoning. The course is designed for individuals who have prior knowledge of algebra and differential calculus, but who wish to delve deeper into integral calculus and its applications. The course has a rigorous and didactic approach that combines clear and detailed explanations with examples and activities that will help you consolidate your learning. The course also offers additional resources, such as readings, videos, and links of interest, which you can consult to expand your knowledge and explore the topics that interest you most. This course is available on the edX platform, one of the most prestigious in the world for online education, founded by MIT and Harvard University. It can be taken entirely for free or by paying a small fee.
Contents of the Mathematical Foundations: Integrals course
These are the contents of the course, which will allow you to learn the fundamental concepts and methods of integral calculus:
- Indefinite integral: the concept of the indefinite integral is defined, interpreted geometrically and physically, calculated using the method of antiderivation, and the properties of the indefinite integral are studied.
- Definite integral: the concept of the definite integral is defined, interpreted geometrically and physically, calculated using the Riemann sums method, and the properties of the definite integral are studied.
- Fundamental theorem of calculus: the fundamental theorem of calculus is stated and proven, which relates the indefinite integral and the definite integral, and is applied to examples and problems.
- Integration techniques: the most common integration techniques are presented, such as change of variable, integration by parts, trigonometric substitution, partial fraction decomposition, and rational substitution, and are applied to exercises and problems.
- Improper integrals: the concept of the improper integral is introduced, improper integrals are classified according to their type, convergence and divergence criteria are established, and examples of improper integrals are solved.
- Applications of the integral: applications of the integral to problems in geometry, physics, economics, and other areas are shown, such as the calculation of areas, volumes, lengths, work, pressure, force, consumption, income, cost, profit, etc.
Free or paid integral course
The course has two modalities: free and paid. The free integral course mode allows you to access all course content, including videos, readings, exercises, and discussion forums. The paid modality also offers you the possibility of obtaining a verified certificate from edX, which accredits your participation and completion of the course. This certificate can be of great value to your curriculum vitae, as it demonstrates your interest and competence in the use of integral calculus. Additionally, by paying for the course, you are contributing to enabling the Universitat Politècnica de València and edX to continue offering quality and accessible courses for everyone. If you want to know more about the cost and benefits of this modality, I invite you to visit the course page on edX, where you will find all the information you need. In conclusion, the online integral course (in its free or paid mode), Mathematical Foundations: Integrals, is a course that provides you with an excellent opportunity to learn the foundations and applications of integral calculus, one of the most relevant and versatile disciplines in mathematics. If you are interested in this topic, do not hesitate to register and start enjoying this course. I am sure you will not regret it.
