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Joseph W. Cutrone, PhD
This first course on concepts of single variable calculus will introduce the notions of limits of a function to define the derivative of a function. In mathematics, the derivative measures the sensitivity to change of the function. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. This fundamental notion will be applied through the modelling and analysis of data.
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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.
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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.
Read more
Traffic lights
Traffic lights
Read about what's good
what should give you pause 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
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Reviews summary
Practical calculus with data applications
According to learners, this course offers a highly relevant and practical introduction to calculus, uniquely integrating data modeling throughout the curriculum. Students found the lectures to be clear, concise, and engaging, particularly appreciating how the course demystifies abstract mathematical concepts by showing their real-world applications. The final project is highlighted as a significant strength, effectively solidifying understanding. While generally well-structured, some found the pace challenging or felt the quizzes could be improved.
Quizzes can be tricky; assignments vary in clarity.
"Sometimes the quizzes felt a bit disconnected from the lecture examples."
"The quizzes were tough and often had tricky wording."
"Some homework assignments were a bit unclear, but overall, the problems were challenging but fair."
Lectures are well-structured and easy to follow.
"The material is presented very clearly, and the explanations were always helpful."
"This course is incredibly well-structured and the lectures are clear and concise."
"I found the instructor did an excellent job explaining complex topics and was very knowledgeable and passionate."
Integrates data modeling to make calculus practical.
"The integration of data modeling throughout was brilliant and made calculus feel very practical."
"As someone who struggles with abstract math, the data-driven approach of this course was a game-changer. It really helped me visualize the concepts."
"The focus on data modeling is a unique selling point, and this course certainly made calculus highly relevant for today's world."
Forum discussions could be more active.
"The forum discussions weren't very active, which made it hard to get quick answers to questions."
Some needed extra resources for core concepts.
"I needed to supplement heavily with external resources for basic understanding."
"Sometimes I wished for more traditional examples to build foundational understanding before jumping into complex data scenarios."
Some learners found the course pace challenging.
"I found the course quite challenging, especially the later modules on derivatives."
"My main criticism is that the pace can be quite fast at times, especially if you're new to calculus."
"I struggled with this course, and sometimes felt the pace could be uneven."
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
Show steps
Review and enhance your understanding of the mathematical foundations of calculus by compiling a collection of relevant resources.
Browse courses on
Functions
Show steps
-
Gather materials
-
Organize and group resources
-
Create a comprehensive resource guide
-
Make personal notes and observations
Read Stewart's Calculus
Show steps
Strengthen your comprehension of calculus concepts by reading and engaging with Stewart's Calculus: Concepts and Contexts.
View
Algebra and Trigonometry
on Amazon
Show steps
-
Read each chapter thoroughly
-
Take notes and highlight important concepts
-
Complete end-of-chapter exercises
Khan Academy: Calculus
Show steps
Supplement your learning by following guided tutorials from Khan Academy to reinforce foundational concepts in calculus.
Browse courses on
Calculus
Show steps
-
Explore video tutorials and interactive exercises
-
Practice solving calculus problems
-
Test your understanding through quizzes and assessments
Four other activities
Expand to see all activities and additional details
Show all seven activities
Derivatives Practice
Show steps
Enhance your understanding of derivatives by engaging in targeted practice exercises.
Browse courses on
Derivatives
Show steps
-
Identify different types of derivatives
-
Practice finding derivatives using various techniques
-
Analyze the behavior of functions using derivatives
Calculus Study Group
Show steps
Form a study group with peers to collaboratively work on calculus problems and reinforce concepts through discussions.
Browse courses on
Calculus
Show steps
-
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
Show steps
Solidify your understanding of derivatives by creating an interactive visualization tool that demonstrates how derivatives affect the behavior of functions.
Browse courses on
Derivatives
Show steps
-
Choose a programming language and environment
-
Design and implement graphical elements
-
Incorporate mathematical calculations
-
Test and refine your visualization
Calculus Application Project
Show steps
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
Show steps
-
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
Mathematical Foundations
Show steps
Review and enhance your understanding of the mathematical foundations of calculus by compiling a collection of relevant resources.
Browse courses on
Functions
Show steps
Show steps
Show steps
- Gather materials
- Organize and group resources
- Create a comprehensive resource guide
- Make personal notes and observations
Read Stewart's Calculus
Show steps
Strengthen your comprehension of calculus concepts by reading and engaging with Stewart's Calculus: Concepts and Contexts.
View
Algebra and Trigonometry
on Amazon
Show steps
Show steps
Show steps
- Read each chapter thoroughly
- Take notes and highlight important concepts
- Complete end-of-chapter exercises
Khan Academy: Calculus
Show steps
Supplement your learning by following guided tutorials from Khan Academy to reinforce foundational concepts in calculus.
Browse courses on
Calculus
Show steps
Show steps
Show steps
- Explore video tutorials and interactive exercises
- Practice solving calculus problems
- Test your understanding through quizzes and assessments
Four other activities
Expand to see all activities and additional details
Show all seven activities
Derivatives Practice
Show steps
Enhance your understanding of derivatives by engaging in targeted practice exercises.
Browse courses on
Derivatives
Show steps
Show steps
Show steps
- Identify different types of derivatives
- Practice finding derivatives using various techniques
- Analyze the behavior of functions using derivatives
Calculus Study Group
Show steps
Form a study group with peers to collaboratively work on calculus problems and reinforce concepts through discussions.
Browse courses on
Calculus
Show steps
Show steps
Show steps
- 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
Show steps
Solidify your understanding of derivatives by creating an interactive visualization tool that demonstrates how derivatives affect the behavior of functions.
Browse courses on
Derivatives
Show steps
Show steps
Show steps
- Choose a programming language and environment
- Design and implement graphical elements
- Incorporate mathematical calculations
- Test and refine your visualization
Calculus Application Project
Show steps
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
Show steps
Show steps
Show steps
- 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 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.
Statistician
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.
Financial Analyst
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.
Economist
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.
Operations Research Analyst
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.
Software Engineer
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.
Actuary
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.
Quantitative Analyst
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.
Data Scientist
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.
Market Research Analyst
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.
Business Analyst
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.
Investment Analyst
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.
Risk Manager
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.
Financial Planner
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.
Teacher
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.
For more career information including salaries, visit:
OpenCourser.com/course/l10lc3/calculus
Reading list
We've selected seven 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
Calculus through Data & Modeling: Limits & Derivatives.
Classic calculus textbook that provides a comprehensive overview of the subject. It good choice for students who want a solid foundation in calculus. The book good as a reference book due to its thorough explanations and worked-out examples.
More advanced calculus textbook. It good choice for students who want to learn more about the theoretical foundations of calculus.
More theoretical approach to calculus. It good choice for students who want a deeper understanding of the subject. This can supplement the theoretical component of the course and serve as a reference tool.
More theoretical approach to calculus. It good choice for students who want a deeper understanding of the subject. This book is good as a supplementary reference source.
Save
More concise and accessible introduction to calculus. It good choice for students who are new to the subject or who need a refresher. It is good reference book for this course.
Save
More intuitive and physical approach to calculus. It good choice for students who want to understand the concepts of calculus in a more concrete way. This can help provide additional depth to the course.
Calculus textbook that is specifically designed for students in the managerial, life, and social sciences. It good choice for students who want to see how calculus is used in their field of study.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/l10lc3/calculus
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Johns Hopkins University
Instructor
Joseph W. Cutrone, PhD
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This course belongs to a
collection
called
Differential Calculus through Data and Modeling. It's comprised of four courses:
- Calculus through Data & Modeling: Applying Differentiation
- Calculus through Data & Modeling: Differentiation Rules
- Calculus through Data & Modeling: Precalculus Review
- Calculus through Data & Modeling: Limits & Derivatives (viewing)
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