Calculus through Data & Modeling: Limits & Derivatives from Coursera

What's inside

Syllabus

The Limit of a Function

One of the goals in studying Calculus is to analyze rates of change and movement. In this module, we introduce the central ideas which will help us achieve this goal: the notions of the limit and the derivative. Rather than evaluating a function at a single point, the limit allows for the study of the behavior of a function in an interval around that point. In this module, you will find limits of functions by a variety of methods, both visually and algebraically. Finally, we will apply limits to define the key idea of Differentiable Calculus, the derivative.

The Limit Laws

Using calculators or graphs is an imprecise way to find the limit of a function. In this module, we will state and use algebraic properties of limits, called the Limit Laws, to calculate the exact values of limits. A solid understanding of these laws will allow us to derive theorems which in turn can be used to study the behavior of more advanced functions.

Continuity

In the last module, there were several types of functions where the limit of a function as x approaches a number could be found by simply calculating the value of the function at the number. Functions with this property will be called continuous and in this module, we use limits to define continuity. We will see that the mathematical definition of continuity will correspond closely with the English meaning of the word continuity used in every day language.

Limits at Infinity

In this module, we allow for x to become arbitrarily large in the positive or negative direction to understand the end-behaviors of functions. This will allow for the formal definition of a horizontal asymptote and to provide classifications of end-behavior of certain types of functions.

Derivatives

The problem of finding the slope of the tangent line to a curve and the problem of finding the instantaneous velocity of an object both involve finding the same type of limit. This special type of limit is called the derivative and in this module, we will see that this notion of the derivative can be interpreted as a rate of change in any of the natural or social sciences or engineering.

Final Project

In this final project, we will apply the tools and language of differentiable calculus to analyze trends in data. This project will focus on modelling and analyzing gender ratios in educational attainment over time in several regions of the world.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores concepts of Calculus, which is highly relevant in science, technology, engineering, and mathematics (STEM) fields

Teaches fundamental notions of Calculus, such as limits and derivatives, which are essential for understanding the behavior of functions

Taught by Joseph W. Cutrone, PhD, who has extensive experience in teaching Calculus

Requires a strong foundation in Algebra and Trigonometry

May require additional resources or support for learners who need to refresh their Algebra and Trigonometry skills

Reviews summary

Calculus through calculus through data & modeling

Learners say this course is an excellent review of limits and derivatives. Interactive lectures are clear and concise, although they lack opportunities for dynamic discussion. According to students, the course requires mathematical reasoning skills, and the final project may involve tasks not entirely related to calculus, such as data description and peer review in Excel. Yet, many learners appreciate the easy-to-understand teaching style of Professor Cutrone.

Progressive content with practice opportunities.

"The course is an excellent way to review limits and derivatives."

"The content is provided progressively and with some opportunity for practice."

Engaging and easy to follow.

"The lectures were fun and interactive."

"It may be asynchronous, but the lectures are clear and concise."

"The instructor also gave an insight using real-world scenarios."

Unrelated tasks and time-consuming.

"The course was OK, but the final project spoiled it all."

"I needed to spend tons of time on things which were irrelevant in terms of Calculus, like describing the data in my own words."

"In total, I spent one full day on this assignment (which was supposed to take an hour) most of the time I wasn't practicing Calculus, but either writing a wordy description or reading a wordy description that my peer wrote."

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: Limits & Derivatives with these activities:

Mathematical Foundations

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Review and enhance your understanding of the mathematical foundations of calculus by compiling a collection of relevant resources.

Browse courses on Functions

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Gather materials
Organize and group resources
Create a comprehensive resource guide
Make personal notes and observations

Read Stewart's Calculus

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Strengthen your comprehension of calculus concepts by reading and engaging with Stewart's Calculus: Concepts and Contexts.

View Algebra and Trigonometry on Amazon

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Read each chapter thoroughly
Take notes and highlight important concepts
Complete end-of-chapter exercises

Khan Academy: Calculus

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Supplement your learning by following guided tutorials from Khan Academy to reinforce foundational concepts in calculus.

Browse courses on Calculus

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Explore video tutorials and interactive exercises
Practice solving calculus problems
Test your understanding through quizzes and assessments

Four other activities

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Derivatives Practice

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Enhance your understanding of derivatives by engaging in targeted practice exercises.

Browse courses on Derivatives

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Identify different types of derivatives
Practice finding derivatives using various techniques
Analyze the behavior of functions using derivatives

Calculus Study Group

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Form a study group with peers to collaboratively work on calculus problems and reinforce concepts through discussions.

Browse courses on Calculus

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Find a group of interested classmates
Establish regular meeting times and locations
Set goals and prepare discussion topics
Take turns presenting and explaining solutions

Interactive Derivative Visualizer

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Solidify your understanding of derivatives by creating an interactive visualization tool that demonstrates how derivatives affect the behavior of functions.

Browse courses on Derivatives

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Choose a programming language and environment
Design and implement graphical elements
Incorporate mathematical calculations
Test and refine your visualization

Calculus Application Project

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Apply your calculus knowledge to a real-world problem by initiating a project that involves data analysis, modeling, and problem-solving.

Browse courses on Calculus

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Identify a problem or scenario to investigate
Gather data and conduct research
Develop a mathematical model using calculus
Analyze and interpret results
Present findings and conclusions

Career center

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

Data Analyst

Data Analysts use mathematical and statistical techniques to extract meaningful insights from data. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing data. By completing this course, you will gain the skills necessary to interpret data, identify trends, and make informed decisions, which are highly sought-after skills in the field of data analytics.

See salaries and explore the career path for Data Analyst

Statistician

Statisticians apply mathematical and statistical principles to solve problems in various fields, including healthcare, finance, and market research. The course, *Calculus through Data & Modeling: Limits & Derivatives,* provides a strong foundation in calculus, which is essential for understanding statistical concepts and performing statistical analyses. The course covers topics such as limits and derivatives, which are used to model and analyze data, and will help you develop the skills necessary to succeed as a Statistician.

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Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing financial data. By completing this course, you will gain the skills necessary to interpret financial data, identify trends, and make informed investment decisions.

See salaries and explore the career path for Financial Analyst

Economist

Economists use mathematical and statistical models to analyze economic data and make predictions about the economy. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing economic data. By completing this course, you will gain the skills necessary to interpret economic data, identify trends, and make informed economic decisions.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve problems in business and industry. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing operational data. By completing this course, you will gain the skills necessary to interpret operational data, identify trends, and make informed decisions.

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Software Engineer

Software Engineers design, develop, and maintain software applications. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are used to model and analyze software performance. By completing this course, you will gain the skills necessary to understand and analyze software performance, and develop more efficient and effective software applications.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing financial data. By completing this course, you will gain the skills necessary to interpret financial data, identify trends, and make informed investment decisions.

See salaries and explore the career path for Quantitative Analyst

Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing risk and uncertainty. By completing this course, you will gain the skills necessary to quantify risk, develop risk management strategies, and make informed decisions.

See salaries and explore the career path for Actuary

Data Scientist

Data Scientists use mathematical and statistical techniques to extract meaningful insights from data. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing data. By completing this course, you will gain the skills necessary to interpret data, identify trends, and make informed decisions, which are highly sought-after skills in the field of data science.

See salaries and explore the career path for Data Scientist

Market Research Analyst

Market Research Analysts use mathematical and statistical techniques to analyze market data and make recommendations about marketing strategies. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing market data. By completing this course, you will gain the skills necessary to interpret market data, identify trends, and make informed marketing decisions.

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Financial Planner

Financial Planners use mathematical and statistical techniques to develop financial plans for individuals and families. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing financial data. By completing this course, you will gain the skills necessary to interpret financial data, identify trends, and make informed financial decisions.

See salaries and explore the career path for Financial Planner

Business Analyst

Business Analysts use mathematical and statistical techniques to analyze business data and make recommendations about business strategies. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing business data. By completing this course, you will gain the skills necessary to interpret business data, identify trends, and make informed business decisions.

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Investment Analyst

Investment Analysts use mathematical and statistical techniques to analyze investment data and make recommendations about investment strategies. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing investment data. By completing this course, you will gain the skills necessary to interpret investment data, identify trends, and make informed investment decisions.

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Risk Manager

Risk Managers use mathematical and statistical techniques to assess risk and uncertainty. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and analyzing risk and uncertainty. By completing this course, you will gain the skills necessary to quantify risk, develop risk management strategies, and make informed decisions.

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Teacher

Teachers use mathematical and statistical techniques to teach mathematics and statistics to students. The course, *Calculus through Data & Modeling: Limits & Derivatives,* introduces the fundamental concepts of calculus, including limits and derivatives, which are essential for understanding and teaching calculus. By completing this course, you will gain the skills necessary to teach calculus to students in a clear and engaging way.

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