Online courses directory (19947)

Podemos afirmar sin temor a equivocarnos que un buen curso de Cálculo amplía la visión del estudiante en su campo y en su área de estudio, que no pertenece necesariamente al área de física o matemática, por ejemplo en fisiología para estudiantes de medicina.

El Cálculo Diferencial es el lenguaje en el que algunas leyes de la naturaleza se expresan, por ejemplo: nos permite describir el movimiento y el cálculo de trayectorias en dinámica, nos ayuda a resolver problemas de áreas y volúmenes, a resolver problemas extremales en campos como economía y matemática financiera.

En este curso se presentan los conceptos y demostraciones con extrema precisión y cuidado; se hace énfasis en los fundamentos del Cálculo para que lo que se enseña quede fundamentado y claramente explicado.

Se estudia el cálculo diferencial de funciones de variable real, por lo tanto, se parte de una estructura algebraica de los números reales, Se utilizan conceptos puramente métricos, se introduce el concepto de distancia para explicar que nos vamos acercando a algo, es decir, se define la estructura del espacio métrico que da paso al primer tema sucesiones de números reales continúa con sucesiones convergentes, límite funcional, continuidad y la derivada de una función hasta llegar a problemas de aplicación.

Este curso está en modalidad “self-paced”, es decir, “a tu propio ritmo de aprendizaje”. ¿Qué significa esto? Que puedes empezar el curso cuando quieras y seguirlo a tu ritmo ya que no hay fecha prevista de cierre o apertura de lecciones, no sigue un calendario establecido; los trabajos y exámenes no tienen fecha de inicio o entrega, puedes enviarlos en cualquier momento antes de la fecha de finalización del curso.

Esperamos que este curso de Cálculo Diferencial logre cambiar la percepción de los estudiantes en cuanto a su aplicación e importancia.

Curso sobre todos los temas referentes a calculo vectorial

Learn about how use derivatives to solve real-world problems.

Derivatives answer calculus' first major question, which is, "how do you find the rate of change of a function?"

Learn everything about these foundational calculus concepts: the limit of a function, and the continuity of a function.

How does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters?  What is the accuracy of a GPS position measurement?  How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative. 

But what is the derivative?  You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative.  You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions.  You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior.  You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.  

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1B: Integration

Calculus 1C: Coordinate Systems & Infinite Series

This course was funded in part by the Wertheimer Fund.

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral. 

But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative.  You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.

1. Modeling the Integral

1. Differentials and Antiderivatives
2. Differential Equations
3. Separation of Variables

2. Theory of Integration

1. Mean Value Theorem
2. Definition of the Integral and the First Fundamental Theorem
3. Second Fundamental Theorem

3. Applications

1. Areas and Volumes
2. Average Value and Probability
3. Arc Length and Surface Area

4. Techniques of Integration

1. Numerical Integration
2. Trigonometric Powers, Trig Substitutions, Completing the Square
3. Partial Fractions, Integration by Parts

This course, in combination with Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.

This course was funded in part by the Wertheimer Fund.

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1A: Differentiation

Calculus 1C: Coordinate Systems & Infinite Series

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

How did Newton describe the orbits of the planets? To do this, he created calculus.  But he used a different coordinate system more appropriate for planetary motion.  We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.

How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.

1. Changing Perspectives
   1. Parametric Equations
   2. Polar Coordinates
2. Series and Polynomial Approximations
   1. Series and Convergence
   2. Taylor Series and Power Series

This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1A: Differentiation

Calculus 1B: Integration

This course was funded in part by the Wertheimer Fund.

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

Learn how to use integrals to solve real-world problems.

Integrals answer calculus' second major question, which is, "how do you find the area underneath a function?"

Learn everything about polar coordinate space and how to deal with parametric curves.

Learn the difference between a sequence and a series, how to test convergence, and how to find limits and sums.

Learn everything about differential equations in calculus 1, 2 and 3, plus the beginning of a introductory DE course.

Upgrade your understanding of integrals in two dimensions (area) to integrals in three dimensions (volume).

Learn the basics of multivariable functions, and everything you need to know about partial derivatives.

Learn everything you ever wanted to know about vector calculus.

In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work.

Through a series of case studies, you’ll learn:

• How standardized test makers use functions to analyze the difficulty of test questions;
• How economists model interaction of price and demand using rates of change, in a historical case of subway ridership;
• How an x-ray is different from a CT-scan, and what this has to do with integrals;
• How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks;
• How the Lotka-Volterra predator-prey model was created to answer a biological puzzle;
• How statisticians use functions to model data, like income distributions, and how integrals measure chance;
• How Einstein’s Energy Equation, E=mc² is an approximation to a more complicated equation.

With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions.

This course provides a unique supplement to a course in single-variable calculus. Key topics include application of derivatives, integrals and differential equations, mathematical models and parameters.

This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms.

This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!

Using Desmos in this Course This course uses Desmos (https://www.desmos.com/), an online graphing calculator, to illustrate examples. Your use of the Desmos platform or any content hosted by Desmos is subject to the Desmos terms of service at https://www.desmos.com/terms and privacy policy at https://www.desmos.com/privacy.

If you do not wish to use the Desmos platform or view content hosted by Desmos, you may not be able to complete the course. This course does NOT require you to make your own individual user account on Desmos. Desmos is a separate entity and is not directly affiliated with HarvardX or edX.

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Videos on a first course in calculus (Differential Calculus).

Covering the basics of Calculus I

Videos on a second course in calculus (Integral Calculus).