Un acercamiento divertido al cálculo de una variable

El curso de Calculus: Single Variable de Robert Ghrist (Universidad de Pennsylvania) se ofrece de forma gratuita en la plataforma Coursera.

Una imagen del video de presentación

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El curso comienza el 7 de enero, y pretende dar una introducción rápida y entretenida al cálculo diferencial e integral, con énfasis en la comprensión conceptual y las aplicaciones a la ingeniería, la física y las ciencias sociales.

Los cinco capítulos de los que consta el curso son:

CHAPTER 1: Functions
After a brief review of the basics, we will dive into Taylor series as a way of working with and approximating complicated functions. The chapter will use a series-based approach to understanding limits and asymptotics.

CHAPTER 2: Differentiation
Though you already know how to differentiate some functions, you may not know what differentiation means. This chapter will emphasize conceptual understanding and applications of derivatives.

CHAPTER 3: Integration
We will use the indefinite integral (an anti-derivative) as a motivation to look at differential equations in applications ranging from population models to linguistics to coupled oscillators. Techniques of integration up to and including computer-assisted methods will lead to Riemann sums and the definite integral.

CHAPTER 4: Applications
We will get busy in this chapter with applications of the definite integral to problems in geometry, physics, economics, biology, probability, and more. You will learn how to solve a wide array of problems using a consistent conceptual approach.

CHAPTER 5: Discretization
Having covered Calculus for functions with a single real input and a single real output, we turn to functions with a discrete input and a real output: sequences. We will re-develop all of Calculus (limits, derivatives, integrals, differential equations) in this new context, and return to the beginning of the course with a deeper consideration of Taylor series.

Unos 60 videos de 15 minutos de duración durante 13 semanas… y foros de discusión abiertos… para aprender cálculo y practicarlo en inglés.

http://www.math.upenn.edu/~ghrist/FLCT/FLCT.pdf

Para empezar a trabajar, el profesor recomienda su libro [R. Ghrist, FLCT: the Funny Little Calculus Text, 2012], que puede descargarse en formato pdf. En él, con divertidas imágenes, repasa las ideas centrales del curso.

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