Calculus through Data & Modeling: Applying Differentiation from Coursera

What's inside

Syllabus

Linear Approximations and Tangent Planes

In single variable calculus, the derivative computes the slope of the tangent line where defined. This is then used to create the equation of the tangent line at a point, which can be used as an accurate estimation tool for complicated functions. This theory generalizes to lines in space which are used to create tangent planes. In this module, we work through the formulas and applications of these notions, using our developed theory of derivatives and partial derivatives.

Maxima and Minima of Single-Variable Functions

Some of the most important applications of differential calculus are optimization problems in which the goal is to find the optimal (best) solution. For example, problems in marketing, economics, inventory analysis, machine learning, and business are all concerned with finding the best solution. These problems can be reduced to finding the maximum or minimum values of a function using our notions of the derivative.

Maxima and Minima of Multivariable Functions

As models become more complicated, the functions used to describe them do as well. Many functions require more than one input to describe their output. These multivariable functions also contain maximum and minimum values that we seek to find using the tools of calculus. In this module, we will extend our optimization techniques to multivariable functions.

Lagrange Multipliers

In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints. It is named after the mathematician Joseph-Louis Lagrange. In this module, we develop the theory and work through examples of this powerful tool which converts a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a usually easier reformulation of the original problem.

Final Project - Optimization

We now put all our theory and practice to use in a real world problem to model the costs associated to a construction project in an effort to find the best possible price point. This project is challenging and answers may vary slightly based on the assumptions you use. Be thoughtful and clear in your report about any assumptions you make along the way.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops solid foundation in mathematical keystones, including limits and derivatives

Strengthens existing foundation in single-variable and multi-variable calculus

Provides a strong and useful foundation for both academia and industry roles

Teaches tools that are essential to all fields, including data analysis and the natural sciences

Builds a strong base for optimization techniques, which are crucial for decision making

Taught by an experienced and accomplished PhD holder

Reviews summary

Calculus through data & modeling: challenging differentiation concepts

Learners say this course is a challenging but rewarding introduction to using differentiation for modeling. The lectures are engaging and cover a range of topics, including extrema for multivariable functions, Lagrange multipliers, tangent lines, and tangent planes. The quizzes are difficult, but students appreciate the opportunity to get answers after taking them. While some learners wish there was a textbook, others find the notes and sample problems to be helpful. Overall, this course is well-received and is a good option for students who want to learn more about advanced calculus.

Professor Cutrone is engaging and easy to follow.

"Prof. Cutrone is pleasant and easy to follow."

"nice class with professor Joesph, he is a fantastic mathematics professor, as he can translate complex definition of mathematics into simple and clear functions with the same meaning."

There is no textbook assigned.

"I really think that is a weakness of the course."

The quizzes are difficult.

"The quizzes are also significantly harder than those in previous courses and could take you more time than expected."

"My only complaint is that the tests almost always seem to include significant amounts of material that was only briefly covered in the lectures or practice sets."

This course is more on the difficult end of the specialization.

"The lagrangian exercises are really tough."

"This is a well developed course. It is interestingg that Professor Cutrone chose to integrate single variable and multivariable functions. I'm certainly no expert, but I would have rather studied single variable functions alone and taken a multivariable calculus course later."

"I think that some additionak comments are in order:1. Professor Cutrone has an engaging style but his board work frequently has typos."

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 through Data & Modeling: Applying Differentiation with these activities:

Review Calculus Fundamentals

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Understand the core concepts of calculus necessary for this course

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Review the definition of a function
Practice finding the limit of a function
Review the definition of a derivative
Practice applying the derivative to find the slope of a function

Review 'Single Variable Calculus' by James Stewart

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Reinforce differentiation concepts through a comprehensive textbook

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Read the relevant chapters on differentiation
Solve the practice problems in the textbook

Watch Video Tutorials on Differentiation

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Gain a visual understanding of differentiation concepts

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Search for online video tutorials on differentiation
Choose a tutorial that aligns with your learning style
Take notes on the key concepts covered in the tutorial

Four other activities

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Solve Differentiation Practice Problems

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Apply and reinforce differentiation skills

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Find practice problems from textbooks or online resources
Solve the problems without using a calculator
Check your answers and identify areas for improvement

Create a Concept Map of Differentiation

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Visualize and connect different concepts related to differentiation

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Identify the main concepts of differentiation
Draw a mind map or diagram connecting these concepts
Add details and examples to illustrate each concept

Participate in a Study Group for Differentiation

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Collaborate with peers to clarify concepts and improve understanding

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Find a study group or create one with classmates
Discuss differentiation concepts, ask questions, and work on problems together

Contribute to an Open-Source Differentiation Project

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Develop practical skills and contribute to the community

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Identify open-source projects related to differentiation
Contribute code, documentation, or other resources to the project

Career center

Learners who complete Calculus through Data & Modeling: Applying Differentiation will develop knowledge and skills that may be useful to these careers:

Data Analyst

Data Analysts gather, organize, and interpret large amounts of data. As the data landscape rapidly changes, so does the need to develop new tools and techniques for collecting and understanding data. The methods and concepts covered in the course “Calculus through Data & Modeling: Applying Differentiation” will help provide a foundation for your work in this field. Specifically, the course’s emphasis on applying calculus through data and modeling will provide you with a strong foundation in the mathematical tools essential to the success of any Data Analyst, such as linear approximations, maxima and minima of single- and multivariable functions, and Lagrange multipliers.

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Machine Learning Engineer

Machine Learning Engineers design, build, and maintain machine learning models. Machine Learning is a subfield of Artificial Intelligence that gives computers the ability to learn without being explicitly programmed. Calculus plays a significant role in understanding and applying Machine Learning algorithms, particularly those that use gradient-based optimization techniques. The course “Calculus through Data & Modeling: Applying Differentiation” provides a strong foundation in calculus that will be essential for your success as a Machine Learning Engineer. This includes learning about linear approximations, maxima and minima of single- and multivariable functions, and Lagrange multipliers.

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Data Scientist

Data Scientists design, implement, and evaluate systems and algorithms that can be used to extract value from data. Calculus is an essential mathematical tool for data scientists, as it provides a way to model complex relationships and solve optimization problems. The course “Calculus through Data & Modeling: Applying Differentiation” aims to provide you with the necessary skills in applying calculus to data analysis and modeling. This includes understanding linear approximations, maxima and minima of single- and multivariable functions, and Lagrange multipliers. These concepts are essential for developing and analyzing data-driven models in various domains such as natural sciences, machine learning, and finance.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to solve complex problems in business and industry. Calculus is an essential tool for Operations Research Analysts in areas such as optimization, scheduling, and forecasting. The course “Calculus through Data & Modeling: Applying Differentiation” will help provide you with a strong foundation in the mathematical tools needed for success in this field. In particular, the course’s focus on applying calculus to data and modeling will be very valuable for understanding and solving real-world problems.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

Financial Analysts use mathematical and analytical skills to evaluate and make recommendations on investments. Calculus is an important tool for Financial Analysts, as it can be used to model and analyze financial data. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving financial problems.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze and predict financial data. Calculus is an essential tool for Quantitative Analysts, as it provides a way to model complex financial relationships and solve optimization problems. The course “Calculus through Data & Modeling: Applying Differentiation” can help builda foundation in the mathematical tools that are essential for success in this field. The course’s focus on applying calculus to data and modeling will be particularly valuable for understanding and solving financial problems.

See salaries and explore the career path for Quantitative Analyst

Statistician

Statisticians use mathematical and statistical models to collect, analyze, and interpret data. Calculus is an essential tool for Statisticians, as it provides a way to model complex relationships and solve optimization problems. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving statistical problems.

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Actuary

Actuaries use mathematical and statistical models to assess risk and uncertainty. Calculus is an essential tool for Actuaries, as it provides a way to model complex relationships and solve optimization problems. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving problems related to risk and uncertainty.

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Economist

Economists use mathematical and statistical models to analyze economic data and make predictions about the economy. Calculus is an essential tool for Economists, as it provides a way to model complex economic relationships and solve optimization problems. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving economic problems.

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Operations Manager

Operations Managers plan and oversee the operations of organizations. Calculus can be a valuable tool for Operations Managers, as it can be used to optimize processes and improve efficiency. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s focus on applying calculus to data and modeling will be particularly valuable for understanding and solving operational problems.

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Market Researcher

Market Researchers use mathematical and statistical models to collect, analyze, and interpret market data. Calculus can be a valuable tool for Market Researchers, as it provides a way to model complex market relationships and solve optimization problems. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving market research problems.

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Business Analyst

Business Analysts use mathematical and analytical skills to solve business problems. Calculus can be a valuable tool for Business Analysts, as it can be used to model and analyze business data. The course “Calculus through Data & Modeling: Applying Differentiation” can help builda foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving business problems.

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Financial Planner

Financial Planners use mathematical and analytical skills to help clients plan for their financial future. Calculus can be a valuable tool for Financial Planners, as it can be used to model and analyze financial data. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving financial planning problems.

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Software Engineer

Software Engineers design, develop, and maintain software systems. Calculus can be a valuable tool for Software Engineers, as it can be used to model and analyze software systems. The course “Calculus through Data & Modeling: Applying Differentiation” can help provide you with a strong foundation in the mathematical tools that are essential for success in this field. The course’s emphasis on applying calculus to data and modeling will be particularly valuable for understanding and solving software engineering problems.

See salaries and explore the career path for Software Engineer