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

Back to all courses

Multivariable Calculus

Calculus of many variables, from vectors to volume.

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Change is an essential part of our world, and calculus helps us quantify it. The change that most interests us happens in systems with more than one variable: weather depends on time of year and location on the Earth, economies have several sectors, important chemical reactions have many reactants and products.

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Multivariable calculus continues the story of calculus. Learn how tools like the derivative and integral generalize to functions depending on several independent variables, and discover some of the exciting new realms in physics and pure mathematics they unlock.

Interactive
quizzes

44

Concepts and
exercises

505+
  1. 1

    Introduction

    Double the variables, double the fun.

    1. Many Variables in a Nutshell

      Take a lightning tour of calculus with several variables.

    2. Finding Extrema

      Learn how partial derivatives can solve important real-world problems.

    3. Coordinates in 3D

      Explore new ways to navigate in three dimensions.

    4. 3D Volumes

      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Bridge the gap between geometry and multiple integrals with Riemann sums.

  2. 2

    Vector Bootcamp

    Master vectors, the basic building blocks of multivariable calculus.

    1. Included with
      Brilliant Premium

      Vector Arithmetic

      Work hands-on with vectors, the building blocks of multivariable calculus.

    2. Included with
      Brilliant Premium

      Vector Properties

      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Continue to build your vector intuition by approaching it geometrically!

    3. Included with
      Brilliant Premium

      Equations of Lines

      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Apply your vector knowledge to the motion of heavenly bodies.

    4. Included with
      Brilliant Premium

      Dot Product Definition and Properties

      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Use geometry to make the dot product, an essential way of multiplying vectors.

  3. 3

    Multivariable Functions

    Take the first step into higher dimensions.

    1. Included with
      Brilliant Premium

      Multivariable Functions

      Explore functions of several variables and discover what they're good for.

    2. Included with
      Brilliant Premium

      Function Domains

      Connect multivariable functions with set geometry.

    3. Included with
      Brilliant Premium

      Basic Graphing

      Learn to capture the most important qualities of a function with a 3D picture.

    4. Included with
      Brilliant Premium

      Graphs by Slices

      Develop skills to visualize the shape of a function and to think in higher dimensions.

  4. 4

    Limits with Many Variables

    Uncover unexpected function properties with limits.

    1. Included with
      Brilliant Premium

      Searching Square Lake

      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Begin to uncover the mysteries of limits with the search for a mythical beast.

    2. Included with
      Brilliant Premium

      Multivariable Limits

      Connect limits with many variables to limits with just one.

    3. Included with
      Brilliant Premium

      Shock Waves and Discontinuities

      Learn to visualize limits and apply them to the real world.

    4. Included with
      Brilliant Premium

      Extreme Value Theorem (Part I)

      Get a bird's-eye view of a crucial calculus theorem.

  5. 5

    Derivatives

    Measuring rates of change is just the beginning...

    1. Included with
      Brilliant Premium

      Basic Partial Derivatives

      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Master the mechanics of multivariable rates of change.

    2. Included with
      Brilliant Premium

      Higher-Order Partials

      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 about the uses of a derivative's derivative, like the wave equation.

    3. Included with
      Brilliant Premium

      Under the Microscope: Tangent Planes

      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Zoom in on a function's graph and see its tangent planes up close.

    4. Included with
      Brilliant Premium

      Directional Derivatives

      Dive beneath Square Lake to develop directional rates of change.

  6. 6

    Optimization

    Put derivatives to work finding and classifying extreme values.

    1. Included with
      Brilliant Premium

      Local Maxima and Minima

      Use gradient geometry to find the highs and lows of a graph.

    2. Included with
      Brilliant Premium

      Back Under the Microscope: Quadrics

      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Dust off your function microscope and see the basic shape of a graph near a critical point.

    3. Included with
      Brilliant Premium

      Back Under the Microscope: Hessian Test

      Use the microscope to come up with a simple test to classify local extrema.

    4. Included with
      Brilliant Premium

      Boundary Extrema

      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Discover how functions can achieve extreme values on exotic shapes.

  7. 7

    Multiple Integrals

    Become a master of multivariable integration.

    1. Included with
      Brilliant Premium

      Double Integrals (Part I)

      Gain double integral intuition through Riemann sums.

    2. Included with
      Brilliant Premium

      Double Integrals (Part II)

      Evaluate simple double integrals with geometric reasoning.

    3. Included with
      Brilliant Premium

      Fubini's Theorem (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Break difficult double integrals down into bite-sized pieces.

    4. Included with
      Brilliant Premium

      Fubini's Theorem (Part II)

      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Master the art of integral domain slicing.