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.
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Calculus: Single Variable Part 2 - Differentiation
宾夕法尼亚大学課程信息
您將獲得的技能
- Differential (Mathematics)
- Newton'S Method
- Linear Approximation
- Differential Calculus
- Derivative
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宾夕法尼亚大学
The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.
授課大綱 - 您將從這門課程中學到什麼
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.
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.
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- 5 stars84.01%
- 4 stars13.07%
- 3 stars1.69%
- 2 stars0.84%
- 1 star0.36%
來自CALCULUS: SINGLE VARIABLE PART 2 - DIFFERENTIATION的熱門評論
This module is great. The thing I like most is how professor implements the theory into Physics and other realistic models. Ive also begun liking statistics a little bit. Now, part 3.
Explanations are crystal clear, with a strong emphasis on developing a deep conceptual understanding of math rather than "calculating derivatives"
Very nice course. It served as a good refresher, and was not hard for me. The material is presented in a different way than a typical college course.
This course is highly interactive. You'll never experience boredom. This is recommendable to learners of standard level. Remember you should have at least studied calculus at high school.
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