Key Information
About the content
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.
Syllabus
- Week 1 - 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 ... - Week 2 - 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 ass... - Week 3 - 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 understan...
Instructors
Robert Ghrist
Professor
Mathematics and Electrical & Systems Engineering
Content Designer
The University of Pennsylvania (commonly known as Penn), founded in 1740, is a private university located in Philadelphia, Pennsylvania, USA. A member of the Ivy League, Penn is the fourth oldest institution of higher learning in the United States and considers itself the first university in the United States to offer both undergraduate and graduate degrees.
Platform
Coursera is a digital company offering massive open online course founded by computer teachers Andrew Ng and Daphne Koller Stanford University, located in Mountain View, California.
Coursera works with top universities and organizations to make some of their courses available online, and offers courses in many subjects, including: physics, engineering, humanities, medicine, biology, social sciences, mathematics, business, computer science, digital marketing, data science, and other subjects.
