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Introducción a las ecuaciones diferenciales

Alberth Alvarado, Ph.D. and Henry Campos

Las ecuaciones diferenciales son parte fundamental del estudio tanto de la matemática como de la ingeniería y la ciencia en general. Muchas leyes y fenómenos físicos pueden ser descritos mediante ellas. En otras palabras, el estudio de estos fenómenos requiere de la creación de un modelo matemático capaz de describirlo, el cual, generalmente se compone de una o varias ecuaciones diferenciales. De allí la importancia de contar con un sólido conocimiento en este tema.

Este curso en línea se centra en el estudio de las ecuaciones diferenciales ordinarias (EDOs) de primer orden y consta de una introducción a la terminología y teoría, haciendo especial énfasis en la solución analítica de las mismas, sus propiedades y su aplicación en el modelado y resolución de problemas en física e ingeniería, entre otros.

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Learning objectives

Terminología y conceptos elementales del lenguaje de las ecuaciones diferenciales
Métodos analíticos de solución de distintos tipos de ecuaciones diferenciales ordinarias de primer orden

Modelación y resolución de problemas de aplicación en áreas diversas

Terminología y conceptos elementales del lenguaje de las ecuaciones diferenciales
Métodos analíticos de solución de distintos tipos de ecuaciones diferenciales ordinarias de primer orden
Modelación y resolución de problemas de aplicación en áreas diversas

Syllabus

Semana 1 - Introducción a las EDOs • ¿Por qué y para qué un curso de Ecuaciones Diferenciales Ordinarias (EDOs)?• Definición de ecuación diferencial y terminología.• ¿A qué nos referimos con resolver una ecuación diferencial?• Interpretación geométrica de una EDO de primer orden: campo direccional.

Semana 2 - EDO Separable• Introducción a las EDOs de primer orden. • EDO Separable. • Introducción a la modelación mediante EDOs.

Semana 3 - EDO Homogénea• EDO Homogénea. • EDO Casi Homogénea.• Aplicaciones Geométricas, incluyendo trayectorias ortogonales e isogonales.

Semana 4 - EDO Lineal• EDO Lineal.

Semana 5 - Modelación mediante EDOs de Primer Orden • Aplicaciones a la mecánica: movimiento libre y movimiento con limitantes.• Modelación de circuitos eléctricos. • Diluciones.

Semana 6 - EDO Exacta• EDO Exacta. • EDO Exacta por factor integrante.

Semana 7 - Otros tipos de EDOs de Primer Orden Relevantes• EDOs reducibles a lineales.o EDO de Bernoulli.o EDO de Riccati.• EDO de Clairaut. o Definición y algoritmo de solución.o Envolvente de una familia de curvas.o Ejemplos.

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Ideal para estudiantes de primer semestre de licenciaturas en física e ingeniería

Familiza a los estudiantes con las EDOs básicas, sentando una base para cursos avanzados

Refuerza los conceptos matemáticos fundamentales utilizados en física e ingeniería

Incorpora aplicaciones prácticas a problemas de física e ingeniería, lo que hace que el aprendizaje sea relevante

Puede ser útil para estudiantes que buscan una comprensión más profunda de los fundamentos de las EDOs

El curso es impartido por instructores experimentados, lo que garantiza la calidad del contenido

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Reviews summary

Sólido conocimiento de edo

Los alumnos están muy satisfechos con este curso. Aprecian su enfoque en los fundamentos y su cobertura de una amplia gama de tipos de ecuaciones diferenciales ordinarias de primer orden. Los alumnos encuentran que el material es claro y completo, y aprecian la inclusión de ejemplos y aplicaciones del mundo real. También valoran la oportunidad de aplicar sus conocimientos a través de problemas y proyectos.

Base sólida en los conceptos básicos de las EDO

"... me a permitido mejorar en mis conocimientos en las EDO, ..."

Aplicaciones prácticas y ejemplos del mundo real

Amplia gama de tipos de EDO cubiertos

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Introducción a las ecuaciones diferenciales with these activities:

Complete an online tutorial on solving first-order differential equations

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Completing an online tutorial will provide you with a structured approach to learning how to solve first-order differential equations.

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Find an online tutorial
Complete the tutorial

Review the textbook chapter on first-order differential equations

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Reviewing the textbook chapter will help you familiarize yourself with the concepts and techniques used to solve first-order differential equations.

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Read the chapter
Take notes
Review your notes

Solve 10 practice problems on first-order differential equations

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Solving practice problems will help you develop your problem-solving skills and improve your understanding of the techniques used to solve first-order differential equations.

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Find a set of practice problems
Solve the practice problems
Check your answers

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Create a visual representation of a solution to a differential equation

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Creating a visual representation of a solution to a differential equation can help you visualize the behavior of the solution and understand how it changes over time.

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Choose a differential equation to solve
Solve the differential equation
Create a visual representation of the solution

Participate in a peer study group for first-order differential equations

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Working with other students to solve problems and discuss concepts will help you deepen your understanding of first-order differential equations.

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Find a peer study group
Attend the study group
Participate actively

Attend a workshop on first-order differential equations

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Attending a workshop will give you the opportunity to learn from experts in the field and to ask questions about specific topics.

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Find a workshop
Register for the workshop
Attend the workshop

Contribute to an open-source project related to differential equations

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Contributing to an open-source project will give you hands-on experience with solving differential equations and working with others in the field.

Browse courses on Differential Equations

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Contribute to the project

Create a blog post or video tutorial on a topic related to first-order differential equations

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Creating a blog post or video tutorial will help you solidify your understanding of the topic and share your knowledge with others.

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Research the topic
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Career center

Learners who complete Introducción a las ecuaciones diferenciales will develop knowledge and skills that may be useful to these careers:

Physicist

Physicists study the fundamental laws of nature. Differential equations are a fundamental tool in physics, and they are used to describe the motion of objects, the interactions of forces, and the behavior of matter and energy. This course in differential equations can help you develop the skills you need to be successful as a physicist.

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Mathematician

Mathematicians study the properties of numbers, shapes, and other mathematical objects. Differential equations are a fundamental tool in mathematics, and they are used to solve a wide variety of problems in pure and applied mathematics. This course in differential equations can help you develop the skills you need to be successful as a mathematician.

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Actuary

Actuaries use mathematical and statistical models to help businesses and individuals manage risk and uncertainty. The ability to solve differential equations is essential for actuaries, as they use these models to predict future events and assess the likelihood of different outcomes. This course in differential equations can help you develop the skills you need to be successful as an actuary.

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Mechanical Engineer

Mechanical engineers design and build machines and other mechanical devices. Differential equations are used in mechanical engineering to model the motion of objects, the forces acting on objects, and the performance of mechanical systems. This course in differential equations can help you develop the skills you need to be successful as a mechanical engineer.

See salaries and explore the career path for Mechanical Engineer

Electrical Engineer

Electrical engineers design and build electrical systems and devices. Differential equations are used in electrical engineering to model the flow of electricity, the behavior of circuits, and the performance of electrical machines. This course in differential equations can help you develop the skills you need to be successful as an electrical engineer.

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Biostatistician

Biostatisticians apply statistical methods to data from biological and medical research. Differential equations are used in biostatistics to model the growth and spread of diseases, the effects of drugs and treatments, and other biological processes. This course in differential equations can help you develop the skills you need to be successful as a biostatistician.

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Chemical Engineer

Chemical engineers design and operate chemical plants and processes. Differential equations are used in chemical engineering to model the flow of fluids, the transfer of heat and mass, and the reactions of chemicals. This course in differential equations can help you develop the skills you need to be successful as a chemical engineer.

See salaries and explore the career path for Chemical Engineer

Operations Research Analyst

Operations research analysts use mathematical and statistical models to solve problems in business and industry. Differential equations are used in operations research to model the flow of goods and services, the scheduling of production, and the allocation of resources. This course in differential equations can help you develop the skills you need to be successful as an operations research analyst.

See salaries and explore the career path for Operations Research Analyst

Data Scientist

Data scientists use statistical and machine learning methods to analyze data and extract insights. Differential equations are used in data science to model the evolution of data over time, the relationships between different variables, and the effects of different interventions. This course in differential equations can help you develop the skills you need to be successful as a data scientist.

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Environmental Engineer

Environmental engineers design and implement solutions to environmental problems. Differential equations are used in environmental engineering to model the transport of pollutants, the fate of chemicals in the environment, and the effects of human activities on the environment. This course in differential equations can help you develop the skills you need to be successful as an environmental engineer.

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Industrial Engineer

Industrial engineers design and improve production systems. Differential equations are used in industrial engineering to model the flow of materials, the scheduling of production, and the performance of production systems. This course in differential equations can help you develop the skills you need to be successful as an industrial engineer.

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Economist

Economists study the production, distribution, and consumption of goods and services. Differential equations are used in economics to model the growth of economies, the effects of government policies, and the behavior of financial markets. This course in differential equations can help you develop the skills you need to be successful as an economist.

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Financial Analyst

Financial analysts evaluate investments and make recommendations to clients. Differential equations are used in financial analysis to model the growth of investments, the effects of interest rates, and the behavior of financial markets. This course in differential equations can help you develop the skills you need to be successful as a financial analyst.

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Software Engineer

Software engineers design, develop, and maintain software systems. Differential equations are used in software engineering to model the behavior of software systems, the performance of algorithms, and the interactions between software components. This course in differential equations can help you develop the skills you need to be successful as a software engineer.

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Civil Engineer

Civil engineers design and construct infrastructure projects such as bridges, roads, and buildings. Differential equations are used in civil engineering to model the forces acting on structures, the flow of water and other fluids, and the stability of soil and other materials. This course in differential equations can help you develop the skills you need to be successful as a civil engineer.

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Reading list

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Introducción a las ecuaciones diferenciales.

Matemáticas avanzadas para ingeniería

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Este libro de texto clásico proporciona una introducción completa a las ecuaciones diferenciales ordinarias. Cubre una amplia gama de temas relevantes para el curso, incluidos los métodos analíticos para resolver EDO de primer orden y aplicaciones en modelado.

Introducción a las ecuaciones diferenciales

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What's inside

Learning objectives

Syllabus

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Reviews summary

Sólido conocimiento de edo

Activities

Career center

Reading list

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