We may earn an affiliate commission when you visit our partners.

Precalculus

Mathematical Modeling

Joseph W. Cutrone, PhD

4.7

Based on 85 ratings

, see reviews

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.

Enroll now

Or subscribe to Coursera Plus

And get unlimited access to Coursera

What's inside

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.

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

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

Save this course

Create your own learning path. Save this course to your list so you can find it easily later.

Save

Reviews summary

Precalculus for real-world application

According to learners, this course offers a highly effective approach to precalculus by emphasizing mathematical modeling and real-world applications. Students frequently highlight the clear explanations and tangible examples, particularly within the linear and exponential modeling modules. It's considered an excellent foundation for STEM fields, bridging high school math to university-level concepts. However, a few students noted that later modules, like Dimensional Analysis, felt less developed or paced quickly, potentially requiring supplementary study for some, especially those with weaker prior mathematical backgrounds.

Assessments and exercises reinforce learning effectively.

"The exercise sets were challenging but fair."

"The course material was presented clearly, and the assessments genuinely helped reinforce learning."

"The exercises were helpful, though some solutions could use more step-by-step detail."

"I found the regular assessments to be a valuable way to check my understanding."

Instructor provides clear and engaging explanations of complex topics.

"The instructor's delivery was engaging and clear."

"The course material was presented clearly, and the assessments genuinely helped reinforce learning."

"Instructor was top-notch."

"I found the explanations to be very solid and easy to follow throughout the course."

Emphasizes applying precalculus to real-world problems and data.

"The mathematical modeling aspect was truly insightful. The real-world examples in linear and exponential functions made the concepts tangible and applicable."

"The emphasis on practical applications of functions was exactly what I needed. Understanding how to model real-world data is crucial."

"This course reframes precalculus in a way that makes it immediately relevant. The mathematical modeling approach is brilliant, transforming abstract concepts into practical tools."

"I really valued learning how precalculus applies to real problems and data analysis."

Early modules are strong; later ones may need more depth.

"The linear and exponential modules were solid."

"I found the dimensional analysis module a bit rushed compared to the others, but still beneficial."

"I felt some parts, especially later modules, lacked sufficient depth or examples."

"The 'Modeling with Other Functions' and 'Dimensional Analysis' felt less developed than the initial topics."

Course requires a solid foundation in math for optimal learning.

"It definitely helped bridge the gap between high school math and university-level concepts."

"I struggled with this course. It didn't feel suitable for someone without a strong prior grasp of math."

"It sometimes assumes prior knowledge, which can be tough if you're truly starting from scratch."

"I found it challenging to follow without a very strong prior mathematical background."

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

Show steps

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

Browse courses on Functions

Show steps

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

Show steps

Practice graphing functions to visualize their behavior and properties.

Browse courses on Functions

Show steps

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

Show steps

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

Show steps

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

Seven other activities

Expand to see all activities and additional details

Show all ten activities

Review pre-calculus principles

Show steps

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

Browse courses on Pre-Calculus

Show steps

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

Show steps

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

Browse courses on Functions

Show steps

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

Show steps

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

Show steps

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

Show steps

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

Show steps

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

Show steps

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

Browse courses on Dimensional Analysis

Show steps

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

Show steps

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

Show steps

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

Show steps

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

Show steps

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

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

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

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

Save

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

What's inside

Syllabus

Traffic lights

Save this course

Reviews summary

Precalculus for real-world application

Activities

Career center

Reading list

Share

Similar courses