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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/integration-calculus
课程评论：没有评论
课程名称: 微积分：单变量第三部分 - 积分 概述: 微积分是人类思想的伟大成就之一，解释了从行星轨道到城市最佳规模再到心跳的周期性等各种现象。本课程覆盖单变量微积分的核心理念，强调概念理解和应用，非常适合工程、自然科学和社会科学的初学者。课程的独特之处包括：1) 从一开始就引入和使用泰勒级数和近似值；2) 对离散和连续微积分形式进行新颖的综合；3) 强调概念而非计算；4) 明确、动态的统一方法。 在本课程的第三部分，我们将讨论以下内容：积分微分方程、积分技巧、积分微积分基本定理和复杂积分。 课程大纲: 1. **积分微分方程** - 描述事物随时间演变的过程自然引出反导数的概念，并探讨平衡解的稳定性标准。 2. **积分技巧** - 由于不定积分本质上是反导数，因此我们将学习最基本和重要的积分技巧，这些规则是微分法则的逆过程。 3. **积分微积分基本定理** - 不定积分只是故事的一部分；定积分则是通过极限求和来理解的。基本定理提供了不定积分和定积分之间的桥梁，使我们能够将积分技巧应用于定积分的实际问题中。 4. **处理复杂积分** - 虽然课程初期讨论的内容相对简单，但在现实世界中，积分并不总是表现良好。这一部分将介绍常见问题及其解决方法，并强调在面对困难时大-O符号的重要性。 本课程通过动态的教学方式，帮助学生更好地理解和应用微积分的概念。
Name:Integrating Differential Equations
Description: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.
Name:Techniques of Integration
Description: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.
Name:The Fundamental Theorem of Integral Calculus
Description: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.
Name:Dealing with Difficult Integrals
Description: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.
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. In this third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals.
