4.- El Cálculo - Otros Modelos

Go to Course: https://www.coursera.org/learn/calculo-4

Introduction

### Course Review: "4.- El Cálculo - Otros Modelos" **Overview:** "4.- El Cálculo - Otros Modelos" is a specialized online course offered through Coursera, framed within the broader context of pre-university mathematics as a stepping stone toward university-level mathematics. The course focuses on linking mathematical concepts to real-world applications and embedding digital technologies into the learning experience. It specifically explores mathematical models involving radicals and exponents through the lens of differential calculus, effectively serving as a bridge to more advanced subjects. **Course Syllabus:** The course is comprehensive, with a syllabus divided into four main modules: 1. **Rules of Derivation:** This module delves into the fundamental rules of differentiation, including the Product, Quotient, and Chain Rules. The objective is to equip students with the algebraic tools necessary for understanding more complex mathematical models that feature negative and fractional exponents. Through practical exercises, learners will appreciate the integration of specialized technology in tracing and executing these rules. 2. **Practice of Derivation and Comparison with Technology:** This section emphasizes hands-on practice with function derivation, ensuring that students recognize the importance of algebraic processes in calculus. By utilizing specialized technology, learners will compare different methods of derivation, enhancing their algebraic and graphical skills in a way that reflects real-world technological applications. 3. **Algebraic Insights on Derivatives and Classical Graphs:** Here, students will uncover the algebraic processes involved in calculating derivatives while addressing common complications that may arise. The module aims to minimize these difficulties through practical advice. Additionally, classical mathematical models related to well-known curves like parabolas, circles, and ellipses are explored, tying theoretical concepts to familiar geometrical shapes. 4. **Optimization:** The course culminates in a practical application of optimization of functions, grounded in real-life contexts. Students will learn to employ various mathematical representations—numerical, algebraic, and graphical—to tackle optimization problems effectively, broadening their understanding of practical applications of calculus. **Review:** "4.- El Cálculo - Otros Modelos" stands out as an excellent preparatory course for those looking to solidify their understanding of calculus and its associated concepts. The course is well-structured, promoting an integrative approach to learning that combines traditional mathematical theory with innovative technology. The emphasis on practical applications and real-world modeling makes complex topics more relatable and comprehensible. Participants will benefit from the engaging content, supportive instructional design, and the opportunity to learn at their own pace. The incorporation of technology to visualize and manipulate mathematical concepts enhances the learning experience, especially for students who may struggle with abstract algebraic principles. **Recommendation:** I highly recommend "4.- El Cálculo - Otros Modelos" for anyone preparing to advance their studies in mathematics, particularly those who may be transitioning from high school to college. Whether you are a student looking to enhance your mathematical prowess or an educator seeking resources to supplement your curriculum, this course offers valuable insights and practical skills that will serve you well in higher education. Furthermore, the course's focus on real-world applications ensures that participants will not only learn theoretically but also understand the relevance of calculus in everyday life. Enroll today and take a significant step toward mastering these essential mathematical concepts!

Syllabus

Reglas de derivación

Hablaremos de las Reglas del Producto, Cociente y Cadena para dar cabida al estudio de otros modelos matemáticos en cuya representación algebraica aparecen exponentes negativos y/o fraccionarios. Practicaremos con las Reglas y apreciaremos los aportes de tecnología especializada en este proceso.

Practicaremos con la derivación de funciones para revisar la importancia de ciertos procesos algebraicos cuando estudiamos Cálculo. Utilizaremos la tecnología especializada para comparar procesos y adquirir habilidades algebraicas y gráficas de una manera relacionada con el uso de tecnología.

Hablaremos del proceso algebraico de cálculo de derivadas y de las complicaciones a que da lugar con el fin de minimizar dificultades seguiendo los consejos planteados. Hablaremos además de modelos matemáticos clásicos cuya gráfica se asocia con curvas clásicas como parábolas, círculos y elipses.

Retomaremos la aplicación de optimización de funciones considerando un contexto real en el que aparecen los nuevos modelos matemáticos. Hablaremos de estrategias de solución que utilizan las diferentes representaciones matemáticas: numérica, algebraica y gráfica.