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Robert Ghrist
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.
Read more
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.
Read more
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.
In this fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability.
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What's inside
Syllabus
Computing Areas and Volumes
Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and volume elements, we will see how to tackle tough geometry problems in a principled manner.
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Syllabus
Computing Areas and Volumes
Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and volume elements, we will see how to tackle tough geometry problems in a principled manner.
Read more
Other Geometric Applications
There's more to geometry than just area and volume! In this module, we will take things "to the next level", ascending to higher dimensions. Coming back to the 3-d world, we will return to problems of length and area, but this time in the context of curves and surfaces. As always, the emphasis will be on how to construct the appropriate differential element for integrating.
Physical Applications
There is so much more to applications of integrals than geometry! So many subjects, from physics to finance, have, at heart, the need for setting up and computing definite integrals. In this short but intense module, we will cover applications including work, force, torque, mass, and present & future value.
Averages and Mass
There is a statistical aspect to integrals that has not yet been brought up in this course: integrals are ideal for computing averages. Motivated by physical problems of mass, centroid, and moments of inertia, we will cover applications of integrals to averages.
An Introduction to Probability
This capstone module gives a very brief introduction to probability, using what we know about integrals and differential elements. Beginning with common-sense uniform probabilities, we move on to define probability density functions and the corresponding probability element. Building on the physical intuition obtained from centers of mass and moments of inertia, we offer a unique perspective on expectation, variance, and standard deviation.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Suitable for those new to engineering or physical sciences
Well-suited for learners in social sciences and other disciplines who seek a foundation in calculus
Provides a unique perspective on probability
Led by a highly respected and experienced instructor, Robert Ghrist
No prior calculus knowledge is required for this course
Emphasizes conceptual understanding over rote memorization
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Reviews summary
Highly praised calculus
Learners say Robert Ghrist's Calculus: Single Variable Part 4 - Applications course is well presented. It covers functions, Taylor series, differentiation, integration, limits, convergence, and sums. Students appreciate Ghrist's active engagement on forums. Overall, this engaging course is recommended for those with prior calculus knowledge looking for a beautiful learning experience.
Learners may benefit from some prior calculus knowledge.
"Though accessible for beginners (like myself), it presents the material in a way that makes you curious and eager to dig deeper."
"Better you have some prior knowledge of the stuff to deeply learn from this course."
Professor Ghrist is an excellent teacher.
"Professor Ghrist is a great teacher."
"Robert Ghrist produced the most beautiful course I've seen on Coursera."
"Robert Ghrist is so nice and clever while explaining difficult concept."
Vast majority of reviews praise the course.
"It is simply the best mooc course I had ever seen."
"This is the best course on Calculus Single Variable I have ever followed."
"This is definitely one of the most exciting courses around."
The course moves at a fast pace and includes challenging quizzes.
"Prof G covers material very quickly."
"The quizzes near the end of the course include quiz questions that require getting 10 - 16 answers correct within a question in order to score that question correctly."
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: Single Variable Part 4 - Applications with these
activities:
Organize and review course materials
Show steps
Keeping your course materials organized and easily accessible will facilitate your learning and help you stay on top of the coursework.
Show steps
-
Create a dedicated study space or folder for your Calculus materials.
-
Organize your notes, assignments, and quizzes by topic or date.
-
Review your materials regularly to reinforce your understanding and identify areas for improvement.
Review Calculus prerequisites
Show steps
Brushing up on your prior Calculus knowledge will provide a solid foundation for this course.
Show steps
-
Review the basics of functions, limits, and derivatives.
-
Practice solving derivative problems.
-
Review integration techniques.
Explore online Calculus tutorials
Show steps
Seeking out additional Calculus tutorials can reinforce your understanding of the course material.
Show steps
-
Identify reputable online Calculus resources.
-
Watch video tutorials on specific Calculus topics.
-
Practice solving problems using the techniques presented in the tutorials.
Five other activities
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Show all eight activities
Join a Calculus study group
Show steps
Engaging with peers in a study group can help you understand different perspectives and improve your communication skills.
Show steps
-
Find classmates or online communities interested in forming a study group.
-
Establish regular meeting times and a study schedule.
-
Discuss course material, solve problems together, and support each other's learning.
Solve Calculus practice problems
Show steps
Regular practice with Calculus problems will enhance your problem-solving skills and solidify your understanding of the concepts.
Show steps
-
Find practice problems from textbooks, online resources, or your instructor.
-
Work through the problems step-by-step.
-
Check your answers and identify areas where you need improvement.
Create Calculus concept maps
Show steps
Visualizing Calculus concepts through concept maps can enhance your understanding and retention of the material.
Show steps
-
Identify the main concepts and subtopics of a Calculus topic.
-
Use a tool like Miro or MindMeister to create a visual map.
-
Connect the concepts with arrows or lines.
-
Add descriptions or examples to each concept.
Develop a Calculus cheat sheet
Show steps
Creating a comprehensive cheat sheet will force you to synthesize and condense your Calculus knowledge.
Show steps
-
Identify the key formulas, theorems, and concepts from the course.
-
Organize the information into categories.
-
Write down the formulas and key points in a clear and concise manner.
-
Review and update your cheat sheet regularly.
Volunteer as a Calculus tutor
Show steps
Sharing your knowledge with others through tutoring can reinforce your own understanding and build your confidence.
Show steps
-
Contact local schools or tutoring centers to inquire about volunteer opportunities.
-
Prepare lesson plans and materials to help students understand Calculus concepts.
-
Work with students one-on-one or in small groups.
Organize and review course materials
Show steps
Keeping your course materials organized and easily accessible will facilitate your learning and help you stay on top of the coursework.
Show steps
Show steps
Show steps
- Create a dedicated study space or folder for your Calculus materials.
- Organize your notes, assignments, and quizzes by topic or date.
- Review your materials regularly to reinforce your understanding and identify areas for improvement.
Review Calculus prerequisites
Show steps
Brushing up on your prior Calculus knowledge will provide a solid foundation for this course.
Show steps
Show steps
Show steps
- Review the basics of functions, limits, and derivatives.
- Practice solving derivative problems.
- Review integration techniques.
Explore online Calculus tutorials
Show steps
Seeking out additional Calculus tutorials can reinforce your understanding of the course material.
Show steps
Show steps
Show steps
- Identify reputable online Calculus resources.
- Watch video tutorials on specific Calculus topics.
- Practice solving problems using the techniques presented in the tutorials.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Join a Calculus study group
Show steps
Engaging with peers in a study group can help you understand different perspectives and improve your communication skills.
Show steps
Show steps
Show steps
- Find classmates or online communities interested in forming a study group.
- Establish regular meeting times and a study schedule.
- Discuss course material, solve problems together, and support each other's learning.
Solve Calculus practice problems
Show steps
Regular practice with Calculus problems will enhance your problem-solving skills and solidify your understanding of the concepts.
Show steps
Show steps
Show steps
- Find practice problems from textbooks, online resources, or your instructor.
- Work through the problems step-by-step.
- Check your answers and identify areas where you need improvement.
Create Calculus concept maps
Show steps
Visualizing Calculus concepts through concept maps can enhance your understanding and retention of the material.
Show steps
Show steps
Show steps
- Identify the main concepts and subtopics of a Calculus topic.
- Use a tool like Miro or MindMeister to create a visual map.
- Connect the concepts with arrows or lines.
- Add descriptions or examples to each concept.
Develop a Calculus cheat sheet
Show steps
Creating a comprehensive cheat sheet will force you to synthesize and condense your Calculus knowledge.
Show steps
Show steps
Show steps
- Identify the key formulas, theorems, and concepts from the course.
- Organize the information into categories.
- Write down the formulas and key points in a clear and concise manner.
- Review and update your cheat sheet regularly.
Volunteer as a Calculus tutor
Show steps
Sharing your knowledge with others through tutoring can reinforce your own understanding and build your confidence.
Show steps
Show steps
Show steps
- Contact local schools or tutoring centers to inquire about volunteer opportunities.
- Prepare lesson plans and materials to help students understand Calculus concepts.
- Work with students one-on-one or in small groups.
Career center
Learners who complete Calculus: Single Variable Part 4 - Applications will develop knowledge and skills
that may be useful to these careers:
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use advanced analytical techniques to help businesses make better decisions. They may use calculus to model and solve problems related to resource allocation, logistics, and inventory management. This course can help Operations Research Analysts develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Operations Research Analysts, who often need to be able to think critically and solve complex problems.
Financial Analyst
Financial Analyst
Financial Analysts use calculus to value stocks, bonds, and other financial instruments. They also use calculus to develop and test financial models. This course can help Financial Analysts develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Financial Analysts, who often need to be able to think critically and solve complex problems.
Actuary
Actuary
Actuaries use calculus to assess and manage risk. They may use calculus to model the probability of events, such as accidents, illnesses, or deaths. They also use calculus to develop and test insurance products. This course can help Actuaries develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Actuaries, who often need to be able to think critically and solve complex problems.
Data Scientist
Data Scientist
Data Scientists use calculus to analyze data and develop predictive models. They may use calculus to identify trends, patterns, and relationships in data. They also use calculus to develop and test machine learning algorithms. This course can help Data Scientists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Data Scientists, who often need to be able to think critically and solve complex problems.
Engineer
Engineer
Engineers use calculus to design and analyze engineering systems. They may use calculus to develop and test engineering models, or to design experiments. This course can help Engineers develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Engineers, who often need to be able to think critically and solve complex problems.
Statistician
Statistician
Statisticians use calculus to analyze data and draw conclusions. They may use calculus to develop and test statistical models, or to design experiments. This course can help Statisticians develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Statisticians, who often need to be able to think critically and solve complex problems.
Software Engineer
Software Engineer
Software Engineers use calculus to develop and test software. They may use calculus to model the behavior of software systems, or to develop algorithms for solving problems. This course can help Software Engineers develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Software Engineers, who often need to be able to think critically and solve complex problems.
Economist
Economist
Economists use calculus to model and analyze economic data. They may use calculus to develop and test economic models, or to forecast economic trends. This course can help Economists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Economists, who often need to be able to think critically and solve complex problems.
Physicist
Physicist
Physicists use calculus to model and analyze physical phenomena. They may use calculus to develop and test physical theories, or to design experiments. This course can help Physicists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Physicists, who often need to be able to think critically and solve complex problems.
Environmental Scientist
Environmental Scientist
Environmental Scientists use calculus to model and analyze environmental processes. They may use calculus to develop and test environmental models, or to design experiments. This course can help Environmental Scientists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Environmental Scientists, who often need to be able to think critically and solve complex problems.
Computer Scientist
Computer Scientist
Computer Scientists use calculus to model and analyze the performance of computer systems. They may use calculus to develop and test computer models, or to design experiments. This course can help Computer Scientists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Computer Scientists, who often need to be able to think critically and solve complex problems.
Geologist
Geologist
Geologists use calculus to model and analyze geological processes. They may use calculus to develop and test geological models, or to design experiments. This course can help Geologists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Geologists, who often need to be able to think critically and solve complex problems.
Biologist
Biologist
Biologists use calculus to model and analyze biological processes. They may use calculus to develop and test biological models, or to design experiments. This course can help Biologists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Biologists, who often need to be able to think critically and solve complex problems.
Materials Scientist
Materials Scientist
Materials Scientists use calculus to model and analyze the properties of materials. They may use calculus to develop and test materials models, or to design experiments. This course can help Materials Scientists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Materials Scientists, who often need to be able to think critically and solve complex problems.
Chemist
Chemist
Chemists use calculus to model and analyze chemical processes. They may use calculus to develop and test chemical models, or to design experiments. This course can help Chemists develop the skills they need to succeed in their roles by providing them with a strong foundation in calculus and its applications. The course's emphasis on conceptual understanding and problem-solving will be particularly valuable for Chemists, who often need to be able to think critically and solve complex problems.
For more career information including salaries, visit:
OpenCourser.com/course/jfknlq/calculus
Reading list
We've selected 24 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: Single Variable Part 4 - Applications.
Provides a mathematically rigorous and in-depth treatment of calculus and real analysis. It great choice for students who are looking for a more advanced and theoretical approach to calculus.
This textbook provides a comprehensive and rigorous treatment of single-variable calculus, covering all the topics included in the course. It is written in a clear and concise style, with numerous examples and exercises to help students understand the concepts. It is commonly used as a textbook for calculus courses at universities and colleges.
This textbook classic in the field of calculus. It is written in a clear and concise style, and it includes numerous examples and exercises. It is commonly used as a textbook for calculus courses at universities and colleges.
Save
This textbook provides a comprehensive and rigorous treatment of single-variable and multivariable calculus. The book has been widely used as a textbook for introductory calculus courses at the university level.
Save
Comprehensive and well-written resource for students who are looking for a thorough introduction to calculus. It covers a wide range of topics, from the basics of limits and derivatives to more advanced topics such as integration and differential equations.
This textbook comprehensive and well-respected resource for introductory calculus courses. It provides a thorough treatment of the fundamental concepts of calculus, with a focus on early transcendentals.
Is an excellent resource for students who are looking for practice problems and solutions. It includes over 1,000 problems, with detailed solutions. It good choice for students who are preparing for a calculus exam or who need extra practice.
Provides a clear and concise introduction to the calculus of variations. It great choice for students who are interested in learning about the applications of calculus to optimization problems.
Provides a comprehensive introduction to probability and statistics, with a focus on applications in engineering and science. It includes numerous examples and exercises, and it is written in a clear and concise style.
This textbook classic and widely used resource for introductory calculus courses. It provides a clear and accessible introduction to the fundamental concepts of calculus, with a focus on early transcendentals.
Comprehensive and well-respected resource for students who are looking for a thorough review of calculus. It provides a wide range of practice problems and solved examples, making it a great choice for students who are preparing for exams or who want to brush up on their calculus skills.
Unique and insightful introduction to calculus. It takes a more intuitive and physical approach to the subject, making it a great choice for students who are interested in understanding the underlying concepts of calculus.
This textbook is designed specifically for students in the life sciences, and it covers the topics of single-variable calculus that are most relevant to their field of study. It includes numerous examples and applications from biology, chemistry, and other life sciences.
Good choice for students who are taking a calculus course for the first time. It provides a clear and comprehensive introduction to the concepts of calculus, and it includes numerous examples and practice problems.
This textbook is designed to help students develop a strong understanding of the concepts of calculus. It includes numerous examples and applications, and it is written in a clear and engaging style. It good choice for students who are taking a calculus course for the first time.
Good choice for students who are struggling with calculus. It provides a clear and concise explanation of the concepts of calculus, and it includes numerous examples and practice problems. It is written in a friendly and engaging style.
Good choice for students who are taking a calculus course for the first time. It provides a clear and comprehensive introduction to the concepts of calculus, and it includes numerous examples and practice problems.
Clear and accessible introduction to calculus for students who are new to the subject. It provides a step-by-step approach to the fundamental concepts of calculus, making it a great choice for students who want to learn calculus at their own pace.
Save
This textbook provides a comprehensive and accessible introduction to single-variable calculus. It is written in a clear and engaging style, and it includes numerous worked examples and practice problems. It good choice for students who are new to calculus or who need a refresher.
Good choice for students who are taking a calculus course for the first time. It provides a clear and concise introduction to the concepts of calculus, and it includes numerous examples and practice problems.
Save
Good choice for students who are struggling with calculus. It provides a clear and concise explanation of the concepts of calculus, and it includes numerous examples and practice problems. It is written in a friendly and engaging style.
Save
Good choice for students who are new to calculus. It provides a gentle introduction to the concepts of calculus, and it includes numerous examples and practice problems. It is written in a clear and engaging style.
Good choice for students who are new to calculus. It provides a gentle introduction to the concepts of calculus, and it includes numerous examples and practice problems. It is written in a clear and engaging style.
This textbook provides a solid foundation in single-variable calculus. It is written in a clear and concise style, and it includes numerous examples and exercises. It good choice for students who are taking a calculus course for the first time.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/jfknlq/calculus
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Effort
6-8 hours/week
Via
Coursera
Institution
University of Pennsylvania
Instructor
Robert Ghrist
Language
English
Transcripts
Español
Français
Pусский
Good to know
Suitable for those new to engineering or physical sciences
Well-suited for learners in social sciences and other disciplines who seek a foundation in calculus
Provides a unique perspective on probability
Led by a highly respected and experienced instructor, Robert Ghrist
No prior calculus knowledge is required for this course
Emphasizes conceptual understanding over rote memorization
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