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Precalculus

Mathematical Modeling

Joseph W. Cutrone, PhD

This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses. Students interested in the natural sciences, computer sciences, psychology, sociology, or similar will genuinely benefit from this introductory course, applying the skills learned to their discipline to analyze and interpret their subject material. Students will be presented with not only new ideas, but also new applications of an old subject. Real-life data, exercise sets, and regular assessments help to motivate and reinforce the content in this course, leading to learning and mastery.

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Syllabus

Module 1: Linear Modeling

Data is all around us, Trillions of terabytes of data are generated and recorded daily by just using a smartphone, driving a car, or using a credit card. In this course, students examine how data is created, obtained, examined, and used to shape everyday life. To understand an analyze this data, researchers in diverse fields conjecture models based on their data. With more data, they modify and update the model accordingly. The model is then tested to validate results and conclusions. This module will help you to visualize large data sets, present different models for data, and statistics to measure how good the model is to the data. We will also focus on how to communicate the results of the models and common pitfalls to avoid overreaching or overstating your conclusions.

Module 2: Exponential Modeling

Perhaps the most important function of this course and your future courses in calculus, the exponential function is introduced to model many natural phenomena. For example, this function is used to measure population growth, the spread of a disease, and the elimination of drug from the body. Types of interest and present value calculations will require the understanding and use of the exponential functions. We will allow the exponential to have any positive base, but the natural exponential, that with e = 2.718.. will be our main object of study.

Modeling with Other Functions

In this module, we will use other functions to model specific behavior, such as polynomial, periodic and power functions.

Module 4: Dimensional Analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. In this module, we will study dimensional analysis, or more specifically the factor-label method and apply it to measure the strength of an explosion.

Good to know

Know what's good

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Builds a foundation for further science and calculus courses

Introduces the exponential function, which is crucial for modeling natural phenomena

Develops skills and knowledge relevant to various disciplines, including natural sciences, computer science, psychology, and sociology

Taught by Joseph W. Cutrone, PhD, who has expertise in the field

Explores data analysis and modeling techniques that are widely used in industry and research

Reviews dimensional analysis methods, which are essential in engineering and science

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Reviews summary

Precalculus mathematical modeling essentials

Learners say this Coursera course from John's Hopkins University is a great way to learn the basics of mathematical modeling. Mathematical Modeling can help you better understand statistics and solve problems involving advanced mathematics. Most students say that the quizzes and assignments are helpful for learning, but a few mention that some of the quizzes are difficult. Overall, learners say that Professor Cutrone is engaging and that the course is well-worth the time and effort.

Course is well-worth the time and effort.

"Great course, great instructor."

"I found the course valuable and feel more prepared to take Calculus this semester after a long break from math."

"I believe it will inspire people to explore the beauty of math."

Professor Cutrone is engaging.

"Professor Cutrone's videos are pretty helpful."

"A fairly challenging yet thorough course."

"Excellent course and MOOC specialization."

Quizzes are helpful for learning.

"The quizzes are helpful for learning."

"I recommend going through all of the materials and doing all the quizzes."

"The sample problems and quizzes are also very useful."

Course is not for non-math people.

"It is definitely NOT for non-math people."

"For those with advanced knowledge it maybe a good course to review the subject."

Some quizzes are difficult.

"Love this, but test sometimes almost impossible with learned material"

"Some tests are difficult to understand due to lack of explanation in problems or questions."

"It took me 2 months to finish the final quiz since I stuck in 1 question and couldn't find how to write the answer."

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 Precalculus: Mathematical Modeling with these activities:

Understand Terminology

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Review the terminology used in functions to understand the core concepts of this course.

Browse courses on Functions

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Read the course syllabus and make a list of unfamiliar terms.
Use online resources or a textbook to define each term.
Create a glossary of terms for future reference.

Graphing Functions

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Practice graphing functions to visualize their behavior and properties.

Browse courses on Functions

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Find a set of practice problems from your textbook or online.
Plot the points for each function.
Connect the points to create a graph.
Analyze the graph to identify key features.

Read 'Mathematics for the Life Sciences' by Michael R. Cullen

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Supplement your course materials with a comprehensive book that provides a detailed exploration of mathematical concepts relevant to the life sciences.

View Linear Models in Biology on Amazon

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Obtain a copy of the book.
Read the relevant chapters and take notes.
Complete the practice exercises provided in the book.

Seven other activities

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Show all ten activities

Review pre-calculus principles

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Reinforce the foundational mathematical concepts that will be built upon throughout the course.

Browse courses on Pre-Calculus

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Review the unit circle and trigonometric functions.
Practice solving equations involving logarithms and exponentials.
Work through practice problems on polynomials and rational functions.

Function Family Overview

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Create a visual or written summary of the different function families, highlighting their characteristics and applications.

Browse courses on Functions

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Research the different function families.
Identify the key characteristics of each family.
Create a table or diagram to summarize the information.
Share your summary with classmates for feedback.

Attend a study group or tutoring session

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Enhance your understanding and reinforce concepts by collaborating with peers in a study group or tutoring session.

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Identify classmates or friends who are also taking the course.
Schedule regular study sessions to discuss course material, solve problems, and quiz each other.

Solve exponential and logarithmic equations

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Gain proficiency in solving equations involving exponential and logarithmic functions, a key skill for modeling natural phenomena.

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Practice solving equations of the form a^x = b.
Practice solving equations of the form log_a(x) = b.
Work through practice problems that combine exponential and logarithmic functions.

Explore online tutorials on dimensional analysis

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Supplement your understanding of dimensional analysis by exploring online tutorials that provide step-by-step guidance and interactive exercises.

Browse courses on Dimensional Analysis

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Search for online tutorials on dimensional analysis.
Choose a tutorial that aligns with your learning style and pace.
Follow the tutorial's instructions and complete the practice exercises.

Develop a visual representation of a real-life data set

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Enhance understanding of data analysis and interpretation by creating a visual representation of a real-life data set, such as a graph, chart, or infographic.

Browse courses on Data Visualization

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Identify a real-life data set that is relevant to your interests.
Choose an appropriate visual representation for the data.
Create the visual representation using a tool such as Excel, Google Sheets, or Tableau.
Analyze the visual representation and draw conclusions from the data.

Design a mathematical model to predict the spread of a disease

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Apply the concepts of exponential modeling to a real-world scenario by developing a mathematical model to predict the spread of a disease.

Browse courses on Mathematical Modeling

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Research the spread of diseases and identify the factors that influence it.
Develop a mathematical model that incorporates these factors.
Use the model to predict the spread of the disease under different scenarios.
Evaluate the accuracy of the model and make adjustments as needed.

Career center

Learners who complete Precalculus: Mathematical Modeling will develop knowledge and skills that may be useful to these careers:

Data Analyst

**Data Analysts** use data to make informed decisions. Gaining insight into data on a large scale is a challenge that requires understanding the best methods for collecting, modeling, and visualizing data. This course provides the tools and techniques necessary for data analysis, including examining how data is created, obtained, and examined. You will also learn how to present different models as well as the pitfalls to avoid when communicating your findings.

See salaries and explore the career path for Data Analyst

Statistician

**Statisticians** apply mathematical and statistical techniques to solve real-world problems. Understanding data is a critical part of this process and is something that is taught in-depth in this course. You will learn how to visualize large data sets and use statistics to measure how good a model is to the data.

See salaries and explore the career path for Statistician

Operations Research Analyst

**Operations Research Analysts** use advanced analytical techniques to help organizations make better decisions. This includes the development of mathematical models to represent real-world systems. This course will provide you with the foundational knowledge to pursue this field. You will gain an understanding of linear modeling, as well as exponential modeling. Additionally, you will learn how to apply dimensional analysis to measure the strength of an explosion. These are essential skills for those who wish to work as Operations Research Analysts.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

**Financial Analysts** use mathematical and statistical techniques to analyze financial data. This course provides a strong foundation for a career in financial analysis. You will learn how to model exponential functions and use dimensional analysis to solve problems, which will prove essential as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Actuary

**Actuaries** use mathematical and statistical techniques to assess risk and uncertainty. This course will help you develop the skills necessary to succeed in this field. You will learn how to use mathematical and statistical techniques to model and solve real-world problems, as well as how to communicate your findings to decision-makers. All of these are essential skills for Actuaries.

See salaries and explore the career path for Actuary

Market Research Analyst

**Market Research Analysts** use data to understand consumer behavior. This course will help you build a solid understanding of how to collect, analyze, and interpret data. You will also learn how to communicate your findings to decision-makers. These are all essential skills for Market Research Analysts.

See salaries and explore the career path for Market Research Analyst

Business Analyst

**Business Analysts** use data to solve business problems. This course will provide you with a solid foundation in data analysis, including how to collect, analyze, and interpret data. You will also learn how to communicate your findings to decision-makers. These are all essential skills for Business Analysts.

See salaries and explore the career path for Business Analyst

Software Engineer

**Software Engineers** design, develop, and maintain software systems. This course will help you develop the mathematical and analytical skills necessary to succeed in this field. You will learn how to use mathematical and statistical techniques to model and solve real-world problems, as well as how to communicate your findings to decision-makers. These are all essential skills for Software Engineers.

See salaries and explore the career path for Software Engineer

Economist

**Economists** use mathematical and statistical techniques to analyze economic data. This course provides a solid foundation for a career in economics. You will learn how to use mathematical and statistical techniques to model and solve real-world problems, as well as how to communicate your findings to decision-makers.

See salaries and explore the career path for Economist

Data Scientist

**Data Scientists** use data to solve complex business problems. This course will provide you with a solid foundation in data analysis and machine learning. You will learn how to collect, analyze, and interpret data, as well as how to build and deploy machine learning models. These are all essential skills for Data Scientists.

See salaries and explore the career path for Data Scientist

Quantitative Analyst

**Quantitative Analysts** use mathematical and statistical techniques to solve complex financial problems. This course will provide you with a solid foundation in mathematics and statistics, as well as in financial modeling. You will learn how to use mathematical and statistical techniques to model and solve real-world problems, as well as how to communicate your findings to decision-makers. These are all essential skills for Quantitative Analysts.

See salaries and explore the career path for Quantitative Analyst

Risk Analyst

**Risk Analysts** use data to identify and manage risk. This course will provide you with a solid foundation in data analysis and risk management. You will learn how to collect, analyze, and interpret data, as well as how to develop and implement risk management strategies. These are all essential skills for Risk Analysts.

See salaries and explore the career path for Risk Analyst

Mathematician

**Mathematicians** solve problems using mathematical techniques. This course will help you develop the mathematical skills necessary to succeed in this field. You will learn how to use mathematical and statistical techniques to model and solve real-world problems.

See salaries and explore the career path for Mathematician

Physicist

**Physicists** study the fundamental laws of nature. This course will help you develop the mathematical and analytical skills necessary to succeed in this field. You will learn how to use mathematical and statistical techniques to model and solve real-world problems. This course will also introduce you to the exponential function, which is of critical importance to the study of physics.

See salaries and explore the career path for Physicist

Engineer

**Engineers** design, develop, and maintain machines and systems. This course will help you develop the mathematical and analytical skills necessary to succeed in this field. You will learn how to use mathematical and statistical techniques to model and solve real-world problems. Additionally, you will learn how to apply dimensional analysis to measure the strength of an explosion. This is a critical skill for Engineers.

See salaries and explore the career path for Engineer

Reading list

We've selected 11 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 Precalculus: Mathematical Modeling.

Precalculus

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This textbook is written by the same author of the Calculus textbooks many students are familiar with. provides a strong foundation for students entering calculus.

Precalculus

Mathematical Modeling

Three deals to help you save

What's inside

Syllabus

Good to know

Save this course

Reviews summary

Precalculus mathematical modeling essentials

Activities

Career center

Reading list

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