Funciones algebraicas y trascendentes from Coursera

En este curso estudiarás las funciones algebraicas y trascendentes desde su definición y notación.

Resolverás problemas de la vida cotidiana que se modelan a través de funciones:

Polinomiales

Racionales

Con Radicales

Exponenciales

Logarítmicas

Trigonométricas

Para las cuales utilizarás conceptos y procedimientos de aritmética, álgebra y trigonometría, así como de la geometría euclidiana y de la analítica.

Utilizarás un Software dinámico (libre) que te apoyará en la exploración de la representación gráfica de la función para comprender las relaciones entre los parámetros de la representación algebraica.

Realizarás generalizaciones para obtener la regla de correspondencia de la función.

Deducirás e inferirás gracias a este estudio apoyado siempre en las tres representaciones:

Tablas numéricas

Gráfica

Expresión algebraica

What's inside

Syllabus

Función polinomial

Hola, soy el Profesor Ernesto Márquez Fragoso. En este primer módulo abordaremos contenidos generales de las funciones tales como los conceptos de dominio y rango, además de revisar funciones polinomiales de distintos grados: lineal, cuadrática y superior. Aprenderás algunas técnicas exploratorias que te servirán para realizar todos los módulos y participarás en actividades creadas para involucrarte en la reflexión y construcción de tu conocimiento con respecto a este tema. ¡Mucha suerte!

Función racional y con radicales. Parte 1

¡Hola! Soy María del Carmen Martínez, y te doy la más cordial bienvenida al módulo 2. Funciones racionales y funciones con radicales. En este módulo revisaremos la importancia del estudio de las funciones racionales y con radicales. Posiblemente, en alguna ocasión te encuentres con un problema cuya representación matemática sea una función racional o con radicales. Quizás nunca necesites resolver problemas en los que se involucran este tipo de funciones, pero es muy importante que sepas que existen y cuáles son sus características. Es como saber para qué se consulta a un dermatólogo, aunque nunca necesites uno en tu vida. Además, requieres de estos conocimientos para continuar con el estudio del cálculo.

Función racional y con radicales. Parte 2

¡Hola! Soy María del Carmen Martínez, y te doy la más cordial bienvenida al módulo 2. Funciones racionales y funciones con radicales.En este módulo revisaremos la importancia del estudio de las funciones racionales y con radicales. Posiblemente, en alguna ocasión te encuentres con un problema cuya representación matemática sea una función racional o con radicales. Quizás nunca necesites resolver problemas en los que se involucran este tipo de funciones, pero es muy importante que sepas que existen y cuáles son sus características. Es como saber para qué se consulta a un dermatólogo, aunque nunca necesites uno en tu vida. Además, requieres de estos conocimientos para continuar con el estudio del cálculo.

Función Exponencial y logaritmica

¡Hola! Soy Claudia Morales y les doy la más cordial bienvenida al módulo 3. Funciones exponencial y logarítmica. Para las funciones exponenciales, analizaremos diversas problemáticas realizando un estudio gráfico y analítico mediante la relación de sus parámetros auxiliándonos de su representación gráfica. Después estudiaremos la función inversa de la función exponencial, es decir: la función logaritmo.

Función Trigonométrica

¡Hola! ¡Bienvenidos al módulo 4! En éste revisaremos información relacionada con las funciones trigonométricas y su comportamiento gráfico respecto a sus parámetros. ¡Adelante!

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores functions, which is standard in math curricula

Uses multiple representations to build understandings, which is core to math

Introduces tools that support learning, which can help students in foundational math

Emphasizes exploration, which is key to developing mathematical thinking

Teaches concepts that are foundational across many math disciplines

Could benefit from more hands-on examples to aid beginners

Reviews summary

Comprehensive algebra and transcendental functions

This course provides a comprehensive review of algebraic and transcendental functions, covering polynomials, rational functions, radical functions, exponential functions, logarithmic functions, and trigonometric functions. It uses a dynamic software to support exploration of the graphical representation of functions and to understand the relationships between the parameters of algebraic representation. The course is highly rated by students, with many finding it to be an excellent resource for reinforcing their understanding of functions. Overall, this course is highly recommended for students looking to strengthen their knowledge of algebraic and transcendental functions.

Activities involve students in the learning process.

"Activities created to involve you in reflecting and building your knowledge on this topic."

Shows how functions are used in real-life situations.

"In addition to explaining the theoretical part, some examples or applications in everyday life, or in specific situations, are portrayed."

Students grade each other's work, providing feedback and learning from others.

"The course has a good peer evaluation system and a well-structured syllabus."

Explanations of concepts and examples are clear and easy to understand.

"The way the teachers explain things is awesome. Don't even mention the activities, because they are very concise, and since they are practical examples, they help a lot."

"I really liked the way the teachers explained."

"Examples are very relevant and supportive to theoretical part."

Covers a wide range of topics related to functions.

"The truth is, the course is quite complete and all the tasks and questionnaires are attached to what is taught in the videos."

Grading peers' work can be time-consuming and may delay progress.

"Very tedious to grade three assignments of so many topics."

Some errors in content and assessments.

"Many mistakes in the evaluation options of the questionnaires that have already been reported and that have not been addressed."

"There are many technical errors in the evaluation by questionnaires and even in the videos themselves."

May be challenging for students with no prior knowledge of functions.

"If you are looking to learn these topics from scratch, I do not recommend it, since it can be confusing where certain methods to solve a problem come from because nothing is ever demonstrated due to the short duration of it."

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 Funciones algebraicas y trascendentes with these activities:

Explorar tutoriales en línea sobre Derivadas e Integrales

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Amplía tus conocimientos sobre funciones y sus aplicaciones mediante la exploración de tutoriales en línea sobre derivadas e integrales.

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Busca tutoriales en línea sobre derivadas e integrales.
Sigue los tutoriales y completa los ejercicios de práctica.
Aplica tus nuevos conocimientos a problemas del mundo real.

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Career center

Learners who complete Funciones algebraicas y trascendentes will develop knowledge and skills that may be useful to these careers:

Machine Learning Engineer

Machine Learning Engineers design and implement machine learning algorithms and models. They work with large datasets and use their knowledge of mathematics and computer science to build systems that can learn from data and make predictions. The course's content on functions, probability distributions, and statistical inference will provide you with a solid foundation in the mathematical and statistical concepts used by Machine Learning Engineers, enhancing your chances of success in this field.

See salaries and explore the career path for Machine Learning Engineer

Data Scientist

Data Scientists use their expertise in mathematics, statistics, and computer science to extract insights from large amounts of data. They develop models and algorithms to solve complex problems and drive decision-making. The course's content on functions, probability distributions, and statistical inference will provide you with a strong foundation in the mathematical and statistical concepts used by Data Scientists, enhancing your chances of success in this field.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians collect, analyze, interpret, and present data. They work in various industries, including healthcare, finance, and marketing. The course's emphasis on probability distributions, statistical inference, and data analysis will provide you with a solid foundation in the methods used by statisticians, increasing your chances of success in this field.

See salaries and explore the career path for Statistician

Economist

Economists study the production, distribution, and consumption of goods and services. They use their knowledge of mathematics and statistics to analyze economic data and make predictions about the economy. The course's content on functions, probability distributions, and statistical inference will provide you with a solid foundation in the mathematical and statistical concepts used by economists, enhancing your chances of success in this field.

See salaries and explore the career path for Economist

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They play a critical role in risk management and portfolio optimization. The course's content on functions, probability distributions, and statistical inference will provide you with a solid foundation in the quantitative methods used in this field, increasing your chances of success as a Quantitative Analyst.

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Risk Manager

Risk Managers identify, assess, and manage risks within organizations. They develop strategies to mitigate potential losses and ensure business continuity. The course's content on probability distributions and statistical inference provides a strong foundation for understanding risk assessment and management techniques, which are essential for a successful career in risk management.

See salaries and explore the career path for Risk Manager

Actuary

Actuaries use mathematical and statistical skills to assess risk and uncertainty, especially in the insurance and finance industries. They develop models to predict the likelihood and financial impact of events. The course's content on probability distributions and statistical inference provides a strong foundation for the skills required to succeed as an actuary.

See salaries and explore the career path for Actuary

Operations Research Analyst

Operations Research Analysts use mathematical models and techniques to optimize business processes and decision-making. They work in various industries, including manufacturing, logistics, and healthcare. The course's focus on functions and their applications in modeling real-world problems provides a valuable foundation for understanding the techniques used by Operations Research Analysts, enhancing your chances of success in this field.

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Software Engineer

Software Engineers design, develop, and maintain software systems. They must have a strong understanding of computer science fundamentals, including mathematics and algorithms. The course's content on functions, particularly polynomial and rational functions, can help you build a foundation in the mathematical concepts used in software development, enhancing your chances of success in this field.

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Business Analyst

Business Analysts use their knowledge of business processes and data analysis techniques to identify and solve business problems. They work closely with stakeholders to understand their needs and develop solutions that meet those needs. The course's emphasis on problem-solving and data analysis will provide you with a strong foundation for the skills required to succeed as a Business Analyst, particularly in industries that rely heavily on mathematical and statistical modeling.

See salaries and explore the career path for Business Analyst

Financial Planner

Financial Planners help individuals and families plan for their financial future. They develop personalized financial plans that consider factors such as income, expenses, savings, and investments. The course's content on functions, particularly exponential and logarithmic functions, can help you build a foundation in the mathematical concepts used in financial planning, enhancing your chances of success in this field.

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Market Researcher

Market Researchers gather and analyze data about consumer behavior and market trends. They use their findings to help businesses make informed decisions about product development, marketing campaigns, and pricing strategies. The course's content on functions, particularly exponential and logarithmic functions, can help you build a foundation in the mathematical concepts used in market research, enhancing your chances of success in this field.

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Database Administrator

Database Administrators maintain and secure an organization's databases, ensuring that they run efficiently. They must have a solid understanding of database systems, including their design, implementation, and maintenance. The course's content, in particular the module on algebra and arithmetic operations, will help you build a foundation in the mathematical principles used in database management, which is essential for success in this role.

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Financial Analyst

Financial Analysts apply their understanding of mathematics, statistics, and economics to evaluate investments and make recommendations to clients. They need a deep understanding of financial markets and the factors that affect them. The course's content on functions and their applications in modeling real-world problems can help you build a foundation for comprehending the complex interactions within financial markets, essential for success in this field.

See salaries and explore the career path for Financial Analyst

Data Analyst

Data Analysts combine their knowledge of statistics, analytical tools, and computer programming to gather and interpret large amounts of data. Their ultimate goal is to uncover trends that can help organizations make decisions. The course's content on solving problems by modeling them as functions is essential for understanding how complex systems operate and is a crucial skill in data analysis. This course may help you succeed in this field.

See salaries and explore the career path for Data Analyst