What will I learn?
The online derivatives course (available in free or paid mode), Mathematical Foundations: Derivatives, offers you an introduction to differential calculus from both a theoretical and practical perspective. You will learn the basic concepts of differential calculus, such as the derivative of a function, the chain rule, higher-order derivatives, implicit differentiation, derivatives of trigonometric, exponential, and logarithmic functions, as well as Rolle’s Theorem and the Mean Value Theorem. Additionally, you will have the opportunity to work through 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 calculus but wish to deepen their understanding of differential calculus and its applications. It follows a rigorous and didactic approach, combining clear and detailed explanations with examples and activities that will help you consolidate your learning. It 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 completed entirely for free or by paying a small fee.
Contents of the online derivatives course Mathematical Foundations: Derivatives
These are the contents of the course, which will allow you to learn the fundamental concepts and methods of differential calculus:
- Derivative of a function: the concept of the derivative of a function is defined, interpreted geometrically and physically, calculated using the limit of the difference quotient, and its properties are studied.
- Chain rule and higher-order derivatives: it explains how to derive composite functions using the chain rule, introduces the concept of higher-order derivatives, and calculates higher-order derivatives of simple and composite functions.
- Implicit derivatives: teaches how to derive implicit functions, that is, those that cannot be explicitly expressed as a function of one variable, and solves examples of implicit differentiation.
- Derivatives of trigonometric, exponential, and logarithmic functions: presents the formulas for deriving trigonometric, exponential, and logarithmic functions, and applies them to exercises and problems.
- Rolle’s Theorem and Mean Value Theorem: states and proves Rolle’s Theorem and the Mean Value Theorem, which relate the value of a function’s derivative to the function’s behavior in an interval, and applies them to examples and problems.
Free or paid derivatives course
The course has two modes: free and paid. The free derivatives course mode allows you to access all course content, including videos, readings, exercises, and discussion forums.
The paid mode also offers 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 for your resume, as it demonstrates your interest and competence in using differential calculus. Furthermore, by paying for the course, you will be contributing to the Universitat Politècnica de València and edX’s ability to continue offering quality and accessible courses for everyone. If you want to know more about the cost and benefits of this mode, I invite you to visit the course page on edX, where you will find all the information you need.
In conclusion, the online derivatives course (free or paid mode), Mathematical Foundations: Derivatives, is a course that provides you with an excellent opportunity to learn the foundations and applications of differential 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.
