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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Single Variable Calculus
Пенсильванский университетОб этом курсе
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Прибл. 14 часов на выполнение
Английский
Субтитры: Французский, Португальский (Европа), Русский, Английский, Испанский
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Прибл. 14 часов на выполнение
Английский
Субтитры: Французский, Португальский (Европа), Русский, Английский, Испанский
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Пенсильванский университет
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.
Программа курса: что вы изучите
4 ч. на завершение
A Calculus for Sequences
It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>.
4 ч. на завершение
4 видео ((всего 53 мин.)), 2 материалов для самостоятельного изучения, 5 тестов
1 ч. на завершение
Introduction to Numerical Methods
That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations.
1 ч. на завершение
2 видео ((всего 34 мин.))
4 ч. на завершение
Series and Convergence Tests
In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or <b>series</b>. The determination of convergence for such will occupy our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!
4 ч. на завершение
4 видео ((всего 65 мин.))
3 ч. на завершение
Power and Taylor Series
This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series.
3 ч. на завершение
4 видео ((всего 59 мин.))
Рецензии
Лучшие отзывы о курсе SINGLE VARIABLE CALCULUS
от партнера PC14 сент. 2019 г.
Loved it ! I've grown attached to Prof. Ghrist's lectures, so it is with a heavy heart that I took the final exam and finished this course. I xould really love to take another !
от партнера SC9 апр. 2020 г.
A fantastic course. Kudos to Prof. Ghrist for making this a fun, interesting and challenging ride at the same time. Looking forward to Multivariable Calculus by Prof. Ghrist.
от партнера RB10 февр. 2017 г.
Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus. Looking forward to Multi Variable Calculus.
от партнера XL3 дек. 2017 г.
Again and again and again ... love the bonus lectures! Really enlightening! Please release the Multi-variable Calculus ASAP! Can't wait to take it!
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