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
Недавно просмотрено: 44 036
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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
Назначьте сроки сдачи в соответствии со своим графиком.
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
Лучшие отзывы о курсе CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
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 NK22 февр. 2016 г.
Would have preferred accompanying solutions. Just getting the answer ain't enough. Making sure my approach is correct is essential as well considering the course touches upon the absolute basics.
от партнера NL9 февр. 2021 г.
Excellent introduction to Calculus, I wanted to review the material to tutor my child but I am very happy that I learned a whole new way of looking at Calculus. Thank you so much Prof. Ghrist.
от партнера KR17 авг. 2020 г.
Very good and challenging material! This motivated me to do better in my Calculus Courses. Would definitely have more of these courses soon, as this is suited for higher mathematics in college.
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