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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 second part--part two of five--we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators.
Register for this course and see more details by visiting:
OpenCourser.com/course/q1nciv/calculus
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What's inside
Syllabus
A New Look at Differentiation
Think derivatives mean "slopes"? Not anymore... In this module, we will reconsider what a derivative is and means in terms of the asymptotic (or big-O) notation from the previous chapter. This will give us a new language for describing and understanding rates of change and the rules that govern them.
Read more
Syllabus
A New Look at Differentiation
Think derivatives mean "slopes"? Not anymore... In this module, we will reconsider what a derivative is and means in terms of the asymptotic (or big-O) notation from the previous chapter. This will give us a new language for describing and understanding rates of change and the rules that govern them.
Read more
Putting Derivatives to Work
Why exactly are derivatives so central to calculus? In part, it is because they are so ubiquitously useful! In this module, we will recall a few core applications of derivatives. In so doing, we'll see exactly how having an understanding of the asymptotics assists in building applications of the derivative.
Differentials and Operators
There is much more to derivatives than simply their computation and applications. So much of how they arise is calculus is in the mysterious guise of *differentials*. These arise from implicit differentiation, which in turn reveals a deeper level of understanding of what differentiation means.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Provides a clear understanding of calculus concepts with emphasis on conceptual understanding and applications
Covers core ideas of single-variable Calculus, making it suitable for students in engineering, physical, and social sciences
Incorporates Taylor series and approximations from the beginning, providing a deeper understanding of calculus
Introduces a novel synthesis of discrete and continuous forms of Calculus, enhancing conceptual understanding
Emphasizes conceptual understanding over computational aspects, facilitating a deeper grasp of the subject
Facilitates a clear and dynamic approach to learning Calculus, making it accessible and engaging
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Save Calculus: Single Variable Part 2 - Differentiation to your list so you can find it easily later:
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Reviews summary
Highly rated calculus differentiation course
According to students, Calculus: Single Variable Part 2 - Differentiation is a well-received course. The course features engaging assignments, lectures from knowledgeable instructors, and clear explanations with helpful visuals. Students report that the course is challenging but well organized, making it a suitable choice for those with a strong foundation in calculus.
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 2 - Differentiation with these
activities:
Review prerequisite math
Show steps
Calculus relies on a strong foundation in mathematics. Revisiting prerequisite math will ensure you have a strong foundation in place before beginning this course.
Browse courses on
Pre-Calculus
Show steps
-
Review basic algebra concepts, such as linear equations, quadratic equations, and polynomials.
-
Practice solving trigonometric equations and identities.
-
Review the concept of limits and how they are used to define derivatives.
Review key concepts from prerequisite courses
Show steps
Calculus builds on concepts from prerequisite courses. Reviewing these concepts will strengthen your foundation and make learning calculus easier.
Browse courses on
Pre-Calculus
Show steps
-
Review your notes or textbooks from prerequisite courses.
-
Focus on understanding the core concepts and their relevance to calculus.
-
Practice solving problems related to these concepts.
Form a study group with classmates
Show steps
Collaboration and discussion can enhance understanding. A study group provides a platform to share knowledge, ask questions, and learn from peers.
Show steps
-
Identify classmates who are also taking the course.
-
Schedule regular study sessions to discuss course material and work on problems together.
-
Take turns explaining concepts and solving problems.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Follow online tutorials on differentiation rules
Show steps
Differentiation rules are essential for solving derivatives. Tutorials provide a structured approach to learning and practicing these rules.
Browse courses on
Differentiation Rules
Show steps
-
Find online tutorials that cover the chain rule, product rule, and quotient rule.
-
Follow the tutorials and take notes on the steps involved in applying each rule.
-
Practice applying the rules to solve differentiation problems.
Practice differentiating functions
Show steps
Practice is key to mastering differentiation. This activity provides an opportunity to apply your understanding and improve your skills.
Browse courses on
Differentiation
Show steps
-
Find a collection of differentiation problems.
-
Attempt to solve the problems on your own.
-
Check your answers and identify areas where you need improvement.
Create visual aids for understanding derivatives
Show steps
Visual aids can enhance understanding and retention. Creating your own visual aids will reinforce your learning and provide a valuable resource for review.
Browse courses on
Differentiation
Show steps
-
Identify key concepts in differentiation that you find challenging.
-
Create diagrams, graphs, or other visual representations to illustrate these concepts.
-
Use your visual aids to explain differentiation to a peer or family member.
Apply differentiation to real-world problems
Show steps
Applying differentiation to real-world problems demonstrates its practical significance. This project will challenge you to use your understanding to solve meaningful problems.
Browse courses on
Differentiation
Show steps
-
Identify a real-world problem that can be solved using differentiation.
-
Develop a mathematical model that describes the problem.
-
Use differentiation to find the solution to the problem.
Review prerequisite math
Show steps
Calculus relies on a strong foundation in mathematics. Revisiting prerequisite math will ensure you have a strong foundation in place before beginning this course.
Browse courses on
Pre-Calculus
Show steps
Show steps
Show steps
- Review basic algebra concepts, such as linear equations, quadratic equations, and polynomials.
- Practice solving trigonometric equations and identities.
- Review the concept of limits and how they are used to define derivatives.
Review key concepts from prerequisite courses
Show steps
Calculus builds on concepts from prerequisite courses. Reviewing these concepts will strengthen your foundation and make learning calculus easier.
Browse courses on
Pre-Calculus
Show steps
Show steps
Show steps
- Review your notes or textbooks from prerequisite courses.
- Focus on understanding the core concepts and their relevance to calculus.
- Practice solving problems related to these concepts.
Form a study group with classmates
Show steps
Collaboration and discussion can enhance understanding. A study group provides a platform to share knowledge, ask questions, and learn from peers.
Show steps
Show steps
Show steps
- Identify classmates who are also taking the course.
- Schedule regular study sessions to discuss course material and work on problems together.
- Take turns explaining concepts and solving problems.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Follow online tutorials on differentiation rules
Show steps
Differentiation rules are essential for solving derivatives. Tutorials provide a structured approach to learning and practicing these rules.
Browse courses on
Differentiation Rules
Show steps
Show steps
Show steps
- Find online tutorials that cover the chain rule, product rule, and quotient rule.
- Follow the tutorials and take notes on the steps involved in applying each rule.
- Practice applying the rules to solve differentiation problems.
Practice differentiating functions
Show steps
Practice is key to mastering differentiation. This activity provides an opportunity to apply your understanding and improve your skills.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Find a collection of differentiation problems.
- Attempt to solve the problems on your own.
- Check your answers and identify areas where you need improvement.
Create visual aids for understanding derivatives
Show steps
Visual aids can enhance understanding and retention. Creating your own visual aids will reinforce your learning and provide a valuable resource for review.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Identify key concepts in differentiation that you find challenging.
- Create diagrams, graphs, or other visual representations to illustrate these concepts.
- Use your visual aids to explain differentiation to a peer or family member.
Apply differentiation to real-world problems
Show steps
Applying differentiation to real-world problems demonstrates its practical significance. This project will challenge you to use your understanding to solve meaningful problems.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Identify a real-world problem that can be solved using differentiation.
- Develop a mathematical model that describes the problem.
- Use differentiation to find the solution to the problem.
Career center
Learners who complete Calculus: Single Variable Part 2 - Differentiation will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
A Data Scientist uses mathematical and statistical techniques to extract knowledge from data. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for data analysis and modeling. The course's emphasis on conceptual understanding and applications will also be beneficial for Data Scientists who need to apply calculus to real-world problems.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software applications. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing efficient and reliable software. The course's emphasis on conceptual understanding and applications will also be beneficial for Software Engineers who need to apply calculus to real-world problems.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for financial modeling and analysis. The course's emphasis on conceptual understanding and applications will also be beneficial for Financial Analysts who need to apply calculus to real-world problems.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical techniques to solve business problems. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing mathematical models. The course's emphasis on conceptual understanding and applications will also be beneficial for Operations Research Analysts who need to apply calculus to real-world problems.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing actuarial models. The course's emphasis on conceptual understanding and applications will also be beneficial for Actuaries who need to apply calculus to real-world problems.
Statistician
Statistician
Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing statistical models. The course's emphasis on conceptual understanding and applications will also be beneficial for Statisticians who need to apply calculus to real-world problems.
Economist
Economist
Economists use mathematical and statistical techniques to analyze economic data and make policy recommendations. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing economic models. The course's emphasis on conceptual understanding and applications will also be beneficial for Economists who need to apply calculus to real-world problems.
Physicist
Physicist
Physicists use mathematical and statistical techniques to study the laws of nature. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing physical models. The course's emphasis on conceptual understanding and applications will also be beneficial for Physicists who need to apply calculus to real-world problems.
Engineer
Engineer
Engineers use mathematical and statistical techniques to design and build structures and machines. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing engineering models. The course's emphasis on conceptual understanding and applications will also be beneficial for Engineers who need to apply calculus to real-world problems.
Mathematician
Mathematician
Mathematicians use mathematical and statistical techniques to study the nature of numbers, quantities, and space. This course can help build a foundation for this career by providing a deep understanding of calculus, which is a core area of mathematics. The course's emphasis on conceptual understanding and applications will also be beneficial for Mathematicians who need to apply calculus to real-world problems.
Computer Scientist
Computer Scientist
Computer Scientists use mathematical and statistical techniques to design and develop computer systems. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing computer algorithms. The course's emphasis on conceptual understanding and applications will also be beneficial for Computer Scientists who need to apply calculus to real-world problems.
Biostatistician
Biostatistician
Biostatisticians use mathematical and statistical techniques to analyze biological data. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing biostatistical models. The course's emphasis on conceptual understanding and applications will also be beneficial for Biostatisticians who need to apply calculus to real-world problems.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing quantitative models. The course's emphasis on conceptual understanding and applications will also be beneficial for Quantitative Analysts who need to apply calculus to real-world problems.
Market Researcher
Market Researcher
Market Researchers use mathematical and statistical techniques to collect and analyze data about consumer behavior. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing market research models. The course's emphasis on conceptual understanding and applications will also be beneficial for Market Researchers who need to apply calculus to real-world problems.
Epidemiologist
Epidemiologist
Epidemiologists use mathematical and statistical techniques to study the causes and patterns of disease. This course can help build a foundation for this career by providing a deep understanding of calculus, which is essential for developing and analyzing epidemiological models. The course's emphasis on conceptual understanding and applications will also be beneficial for Epidemiologists who need to apply calculus to real-world problems.
For more career information including salaries, visit:
OpenCourser.com/course/q1nciv/calculus
Reading list
We've selected 15 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 2 - Differentiation.
Classic calculus textbook that provides a comprehensive overview of the subject. It is well-written and easy to follow, and it provides a good foundation for students who are new to calculus.
Takes a more modern approach to Calculus than most other texts. It considers calculus from a viewpoint that integrates discrete and continuous forms. Ideal for physical and life sciences.
Popular calculus textbook that provides a good balance of theory and applications. It good choice for students who are looking for a book that is both comprehensive and accessible.
Save
This textbook provides a comprehensive introduction to multivariable calculus. This may be of interest to those seeking further depth in the subject.
Save
More concise and accessible introduction to calculus than Stewart's book. It good choice for students who are looking for a book that is easy to read and understand.
This classic calculus textbook is known for its clear and concise explanations and rigorous approach. Useful for students looking to deepen their understanding of the subject.
More intuitive approach to calculus than most other textbooks. It good choice for students who are looking for a book that is easy to read and understand.
More conceptual approach to calculus than Stewart's other book. It good choice for students who are interested in understanding the underlying concepts of calculus.
For those seeking a more theoretical treatment of calculus, this book provides an introduction to real analysis. This may be of interest to those seeking a deeper understanding of the foundations of calculus.
Save
This textbook covers a variety of numerical methods used in applied mathematics. This may be of interest to those seeking to apply calculus to practical problems.
Provides an introduction to a variety of mathematical methods used in the physical sciences. This may be of interest to those seeking to apply calculus to physics and other physical sciences.
Provides an introduction to a variety of applied mathematics topics. This may be of interest to those seeking to apply calculus to practical problems in a variety of fields.
Provides an introduction to measure theory and integration. This may be of interest to those seeking a deeper understanding of the theoretical foundations of calculus.
Provides an introduction to partial differential equations. This may be of interest to those seeking to apply calculus to problems in physics, engineering, and other fields.
Provides an introduction to ordinary differential equations. This may be of interest to those seeking to apply calculus to problems in physics, engineering, and other fields.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/q1nciv/calculus
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Effort
6-8 hours/week
Via
Coursera
Institution
University of Pennsylvania
Instructor
Robert Ghrist
Language
English
Transcripts
Español
Français
中文
Pусский
Good to know
Provides a clear understanding of calculus concepts with emphasis on conceptual understanding and applications
Covers core ideas of single-variable Calculus, making it suitable for students in engineering, physical, and social sciences
Incorporates Taylor series and approximations from the beginning, providing a deeper understanding of calculus
Introduces a novel synthesis of discrete and continuous forms of Calculus, enhancing conceptual understanding
Emphasizes conceptual understanding over computational aspects, facilitating a deeper grasp of the subject
Facilitates a clear and dynamic approach to learning Calculus, making it accessible and engaging
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