Enroll Course: https://www.coursera.org/learn/calculo-diferencial
Traditional calculus courses often separate differential and integral calculus, introducing the derivative first and then the integral, with the Fundamental Theorem of Calculus (TFC) bridging the gap. However, the Coursera course ‘Cálculo Diferencial e Integral unidos por el Teorema Fundamental del Cálculo’ (Differential and Integral Calculus United by the Fundamental Theorem of Calculus) offers a refreshing and integrated approach.
This course breaks away from the conventional sequence by introducing the derivative and integral as interconnected concepts from the outset. It begins by exploring the prediction of changing magnitudes, starting with the simplest case of variation to establish the Linear Model. The course then delves into numerical strategies for approximating accumulated change, using the Method of Euler as a key tool. This practical application, supported by digital tools like spreadsheets, helps solidify understanding before moving to exact values.
The syllabus progressively introduces polynomial models, starting with quadratic and cubic functions, and analyzing how their rates of change relate to simpler models. This visual and analytical approach to graphs helps in understanding the behavior of changing quantities. The course also tackles exponential and trigonometric models, linking them to real-world scenarios and differential equations, and revisiting trigonometric fundamentals.
The latter modules revisit the core concepts of derivative and integral from both Newtonian and Leibnizian perspectives, discussing their advantages in problem-solving. Algorithmic aspects of calculating derivatives and integrals are reinforced, with an emphasis on algebraic manipulation and the utility of digital technologies. The course concludes by exploring new mathematical models derived from the basic ones and applying these concepts to various real-world prediction problems.
Overall, this course provides a more intuitive and connected understanding of calculus. By integrating concepts early and utilizing practical examples and digital tools, it makes the often-daunting subject of calculus more accessible and engaging. I highly recommend this course for anyone looking to grasp the essence of calculus through a unified and insightful perspective.
Enroll Course: https://www.coursera.org/learn/calculo-diferencial