Calculus: Single Variable Part 3 - Integration

位教师：Robert Ghrist

访问权限由 Coursera Learning Team 提供

44,551 人已注册

4个模块

深入了解一个主题并学习基础知识。

548 条评论

1 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

94%

大多数学生喜欢此课程

4个模块

深入了解一个主题并学习基础知识。

548 条评论

1 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

94%

大多数学生喜欢此课程

您将获得的技能

要了解的详细信息

作业

26 项作业

授课语言：英语（English）

了解顶级公司的员工如何掌握热门技能

了解关于 Coursera for Business 的更多信息

Petrobras, TATA, Danone, Capgemini, P&G 和 L'Oreal 的徽标

该课程共有4个模块

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.

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

5个视频总计75分钟

Indefinite Integrals 17分钟
A Simple O.D.E. 17分钟
More O.D.E.s 16分钟
O.D.E. Linearization 17分钟
BONUS! 9分钟

2篇阅读材料总计20分钟

How Grading Works 10分钟
Your Guide to Getting Started in this Course 10分钟

9个作业总计234分钟

Core Homework: Indefinite Integrals 30分钟
Core Homework: A Simple O.D.E. 30分钟
Core Homework: More O.D.E.s 10分钟
Core Homework: O.D.E. Linearization 14分钟
Learning Style Preference Survey 30分钟
Challenge Homework: Indefinite Integrals 30分钟
Challenge Homework: A Simple O.D.E. 30分钟
Challenge Homework: More O.D.E.s 30分钟
Challenge Homework: O.D.E. Linearization 30分钟

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.

涵盖的内容

6个视频8个作业

6个视频总计76分钟

Integration by Substitution 14分钟
Integration by Parts 17分钟
Trig Substitution 15分钟
BONUS! 7分钟
Partial Fractions 16分钟
BONUS! 7分钟

8个作业总计170分钟

Core Homework: Integration by Substitution 12分钟
Core Homework: Integration by Parts 14分钟
Core Homework: Trig Substitution 12分钟
Core Homework: Partial Fractions 12分钟
Challenge Homework: Integration by Substitution 30分钟
Challenge Homework: Integration by Parts 30分钟
Challenge Homework: Trig Substitution 30分钟
Challenge Homework: Partial Fractions 30分钟

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.

涵盖的内容

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.