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.
Calculus: Single Variable Part 3 - Integration
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要了解的详细信息
作业
26 项作业
授课语言：英语（English）
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该课程共有4个模块
Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions.
涵盖的内容
5个视频2篇阅读材料9个作业
Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques.
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6个视频8个作业
Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals.
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3个视频3个作业
The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need.
涵盖的内容
4个视频1篇阅读材料6个作业
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授课教师评分
4.8 (71个评价)
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状态：免费University of Pennsylvania
状态：免费University of Pennsylvania
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状态：免费University of Pennsylvania
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BP
5
已于 Dec 8, 2016审阅
excellent course ..please guys enroll and learn with best prof...Robert Ghrist....
RB
5
已于 Feb 7, 2017审阅
I will be sad when I finish Chapter 5. Cant wait for Multi variable calculus
WT
5
已于 Sep 28, 2020审阅
UN CURSO EXCELENTE, CON METODOLOGIAS ACORDES A LA ACTUALIDAD Y APLICACIONES AFINES.Un consulta. ¿Cómo accedo al Certificado? Gracias
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