一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本

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Vector Calculus

Complete the multivariable calculus saga with vector fields.

Change is deeply rooted in the natural world. Fluids, electromagnetic fields, the orbits of planets, the motion of molecules; all are described by vectors and all have characteristics depending on where we look and when.

一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本In this course, you'll learn how to quantify such change with calculus on vector fields. Go beyond the math to explore the underlying ideas scientists and engineers use every day.

Interactive
quizzes

35

Concepts and
exercises

420+
  1. 1

    Introduction

    Vector fields, surface integrals, div and curl.

    1. Vector Calculus in a Nutshell

      Explore the possibilities that come from combining calculus and vectors.

  2. 2

    Vector-valued Functions

    Force fields, motion through space, and much, much more...

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      Calculus of Motion

      一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本Look at the world in motion through the lens of vector calculus.

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      Space Curves

      Fly along curves through three dimensions.

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      Integrals and Arc Length

      Exactly how long is a space curve?

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      Frenet Formulae

      Measure the shape of space curves with vector calculus.

  3. 3

    Surface Integrals and Divergence

    Part I of the essential vector calculus toolbox.

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      Introducing Surface Integrals

      Mix vectors with integrals to uncover an essential tool for applications.

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      Flux (Part I)

      一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本Experiment with charges moving in electric field and discover the concept of flux.

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      Flux (Part II)

      Use flux to uncover surface integrals and see how they're used to solve important problems.

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      Surface Integrals

      Master integrals of functions on parametrized surfaces.

  4. 4

    Line Integrals & Curl

    Part II of the essential vector calculus toolbox.

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      Work (Part I)

      一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本Explore an important physics application of vector calculus.

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      Work (Part II)

      Unveil a new kind of integral by delving into a familiar physics concept.

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      Line Integrals

      一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本Learn how to integrate along space curves and why it's so useful.

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      Path Independence

      一点不卡视频观看一区_一点都不卡的中文视频_中文字幕一本到无线_2017中文字字幕一本Journey to where calculus and topology meet to discover a crucial property of vector fields.

  5. 5

    Advanced Applications

    Solve important real-world problems with vector calculus.

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      The Laplacian

      Apply a new derivative to problems in electrostatics and fluid dynamics.

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      Gaussian Integrals (Part I)

      Detour into the world of multivariable calculus to compute an integral crucial for applications.

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      Gaussian Integrals (Part II)

      Use linear algebra and a change of variables to find the most general Gaussian integral.

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      Fourier Transform

      Apply Gaussian integrals to understand the Fourier transform, a powerful way to solve pdes.