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 1 - Functions
Пенсильванский университетОб этом курсе
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Прибл. 14 часов на выполнение
Английский
Субтитры: Арабский, Французский, Португальский (Европа), Китайский (упрощенное письмо), Итальянский, Вьетнамский, Немецкий, Русский, Английский, Испанский
Приобретаемые навыки
- Series Expansions
- Calculus
- Series Expansion
Гибкие сроки
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100% онлайн
Начните сейчас и учитесь по собственному графику.
Прибл. 14 часов на выполнение
Английский
Субтитры: Арабский, Французский, Португальский (Европа), Китайский (упрощенное письмо), Итальянский, Вьетнамский, Немецкий, 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
1 ч. на завершение
Introduction
Welcome to Calculus: Single Variable! below you will find the course's diagnostic exam. if you like, please take the exam. you don't need to score a minimal amount on the diagnostic in order to take the course. but if you do get a low score, you might want to readjust your expectations: this is a very hard class...
1 ч. на завершение
1 видео ((всего 8 мин.)), 2 материалов для самостоятельного изучения, 1 тест
3 ч. на завершение
A Review of Functions
This module will review the basics of your (pre-)calculus background and set the stage for the rest of the course by considering the question: just what <i>is</i> the exponential function?
3 ч. на завершение
3 видео ((всего 36 мин.)), 1 материал для самостоятельного изучения, 4 тестов
5 ч. на завершение
Taylor Series
This module gets at the heart of the entire course: the Taylor series, which provides an approximation to a function as a series, or "long polynomial". You will learn what a Taylor series is and how to compute it. Don't worry! The notation may be unfamiliar, but it's all just working with polynomials....
5 ч. на завершение
5 видео ((всего 69 мин.))
5 ч. на завершение
Limits and Asymptotics
A Taylor series may or may not converge, depending on its limiting (or "asymptotic") properties. Indeed, Taylor series are a perfect tool for understanding limits, both large and small, making sense of such methods as that of l'Hopital. To solidify these newfound skills, we introduce the language of "big-O" as a means of bounding the size of asymptotic terms. This language will be put to use in future Chapters on Calculus.
5 ч. на завершение
4 видео ((всего 62 мин.)), 1 материал для самостоятельного изучения, 7 тестов
Рецензии
- 5 stars80,20 %
- 4 stars15,46 %
- 3 stars2,24 %
- 2 stars0,69 %
- 1 star1,39 %
Лучшие отзывы о курсе CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
от партнера YF19 сент. 2020 г.
There were certain advanced concepts that could have had a better and clearer explanation such as the “big O”. But on the whole it was a very good course and very much recommendable.
от партнера YG2 июля 2018 г.
Very well structured for a refresher course. Thank you Professor Ghrist for your effort in putting this course together. A little additional outside research was required but well worth the effort.
от партнера AT13 авг. 2020 г.
Very insightful. However, I believe (although I may be wrong) that certain methods and techniques required to solve the homework problems weren't explained in the course material.
от партнера NL27 окт. 2016 г.
What can I say? It is so good that I watch the lectures when I have dinner alone. Prof Ghrist absolutely has presented calculus so well that it becomes such an entertainment!
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