Calculus Applied! from edX

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!

What's inside

Learning objectives

Authentic examples and case studies of how calculus is applied to problems in other fields
How to analyze mathematical models, including variables, constants, and parameters

Appreciation for the assumptions and complications that go into modeling real world situations with mathematics

Authentic examples and case studies of how calculus is applied to problems in other fields
How to analyze mathematical models, including variables, constants, and parameters
Appreciation for the assumptions and complications that go into modeling real world situations with mathematics

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Read about what's good

what should give you pause

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This course complements an introductory Calculus course

Useful for students who have just finished an introductory Calculus course or teachers seeking real-world examples

Taught by instructors recognized for their expertise in calculus and its applications

Provides authentic examples and case studies of calculus applications across various fields

Develops skills in analyzing mathematical models and understanding their assumptions and limitations

Requires prior knowledge of calculus basics, including derivatives, integrals, and differential equations

Reviews summary

Applied calculus case studies

Learners say that Calculus Applied! is a fantastic supplement to traditional calculus courses, offering real-world applications through engaging case studies like economics and biology. Students appreciated how it brought calculus to life and reinforced theoretical understanding. However, a frequent point raised is that it assumes a strong prerequisite knowledge of single-variable calculus, and some found the pace fast or the explanations occasionally rushed, making it potentially challenging even for those who have finished the basics. It is clearly not for beginners but highly valuable for those seeking practical context.

Assignments are demanding but useful practice.

"The assignments were challenging but rewarding."

"Some assignments were quite demanding."

"Assignments were useful practice."

Provides practical context for calculus.

"This course is exactly what I needed to see how calculus applies to real-world problems. The case studies were fascinating..."

"Absolutely brilliant! This course brought calculus to life for me. The connection to real-world scenarios... was eye-opening."

"Fantastic supplement to my university calculus course. The case studies provided real-world relevance that lectures often miss."

"Provides crucial context for why we learn calculus. The case studies are the highlight. Engaging and well-explained."

Some found the explanations rushed or lacking depth.

"Some parts were a bit fast-paced, assuming prior knowledge, which is fair given the description."

"I struggled with some of the math needed for the case studies... Maybe needs a bit more review of the math basics..."

"Lectures were mostly clear, but some case study analyses could have been broken down more."

"Felt like it skimmed over some mathematical details necessary to fully grasp the models."

Assumes solid single-variable calculus background.

"...Highly recommend if you have a strong calculus background and want to see practical uses."

"The prerequisite knowledge listed felt underestimated. The pace was too fast, and I got lost quickly."

"...The difficulty level felt appropriate for someone who has completed calculus, but it's definitely not for beginners."

"Felt like it required more than just basic single-variable calculus familiarity."

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 Calculus Applied! with these activities:

Analyze Geometric Figures

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Review the basic properties and formulas for geometric figures to strengthen your foundation in geometry.

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Revisit definitions of basic geometric shapes (e.g., triangle, circle, square)
Practice calculating the area and perimeter of different geometric figures
Solve problems involving geometric relationships and properties (e.g., Pythagorean theorem)

Read 'Calculus: Early Transcendentals' by Briggs, Cochran, and Gillett

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Supplement your course material with a comprehensive textbook that provides in-depth explanations and practice problems to strengthen your understanding of calculus concepts.

View Calculus on Amazon

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Read through the relevant chapters corresponding to the course material
Work through the practice problems and examples provided in the book
Use the book as a reference for challenging concepts and additional clarification

Explore Real-World Calculus Applications

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Delve into real-world examples and case studies to witness how calculus is applied in various fields, deepening your appreciation for its practical relevance.

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Explore online resources and videos showcasing calculus applications in science, engineering, and economics
Attend guest lectures or webinars featuring industry professionals discussing real-world applications
Identify and analyze the role of calculus in solving real-world problems

One other activity

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Develop a Calculus-Based Project

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Apply your calculus knowledge to a hands-on project, such as designing a roller coaster or modeling population growth, to demonstrate your understanding and creativity.

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Identify a real-world problem or phenomenon that can be analyzed using calculus
Develop a mathematical model based on calculus principles to address the problem
Collect and analyze data to support your model and draw conclusions

Career center

Learners who complete Calculus Applied! will develop knowledge and skills that may be useful to these careers:

Data Scientist

**Data Scientists** analyze business data to help companies understand operations and predict future trends. This course provides the foundation needed for understanding how to apply calculus to model a wide range of data and situations. With this course, you will be well-prepared to enter the field of Data Science.

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Statistician

**Statisticians** help organizations make data-driven decisions. The skills you learn in this course will help you use calculus to analyze data, model outcomes, and communicate findings to help professionals make better decisions.

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Mathematician

**Mathematicians** use advanced math skills to solve problems. This course provides you with a foundation in applied calculus, which will be critical to your success in this field. With this course, you will be more prepared to engage with research and publish your findings.

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Physics Professor

**Physics Professors** teach concepts of physics at the postsecondary level. This course will help you develop the skills needed to understand how calculus is applied to real-world physics problems.

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Economist

**Economists** analyze economic data to help governments, businesses, and individuals understand trends. This course will teach you how to apply the principles of calculus to study the relationship between price and demand and other economic phenomena.

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Biologist

**Biologists** study living things. This course may be helpful for your training as a Biologist since it provides foundations for understanding how calculus is used to model the spread of disease and growth of populations.

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Biostatistician

**Biostatisticians** apply statistical methods to biological data. This course may be helpful for your training as a Biostatistician since it provides foundations for understanding how calculus is used to model the spread of disease and growth of populations, as well as how to analyze data on biological systems.

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Financial Analyst

**Financial Analysts** use data to make recommendations on stocks and other investments. This course provides the mathematical foundation you need to understand how calculus is used to model financial markets and interpret data in order to give clients solid advice.

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Actuary

**Actuaries** use mathematical and statistical skills to assess risk. This course will help you develop a strong foundation in applied calculus. With this course, you will be able to understand how calculus is used to create financial models and analyze economic data in this field.

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Computer Scientist

**Computer Scientists** design software and create computer systems. This course may be helpful for your training as a Computer Scientist as it will give you a deeper understanding of the mathematical techniques used to create computer programs.

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Software Engineer

**Software Engineers** use programming languages to build software programs. This course may be helpful for your training as a Software Engineer as it covers concepts of calculus that are often used in software engineering. For example, this course covers differential equations, which are used in computer graphics.

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Quantitative Analyst

**Quantitative Analysts** use mathematical and statistical techniques to analyze data and make predictions. This course will give you the foundation in calculus you need to succeed in this role. You will learn how to apply calculus to real-world problems and develop financial models.

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Operations Research Analyst

**Operations Research Analysts** use analytical methods to solve business problems. This course will give you the skills needed to collect data, build models, and analyze solutions. This course will help you get the most out of existing operations and prepare for future growth.

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Market Research Analyst

**Market Research Analysts** study market conditions to help businesses make informed decisions. This course will give you the foundation in calculus you need to succeed in this role. You will learn how to apply calculus to analyze market data and make predictions.

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Data Analyst

**Data Analysts** collect, process, and analyze data to help businesses make decisions. This course will give you the foundation in calculus you need to succeed in this role. You will learn how to apply calculus to analyze data and make predictions.

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