Surface integrals and Stokes' theorem | Multivariable Calculus | Khan Academy

由曲面的参数化来推导单位法向量 观看下一节课：https://www.khanacademy.org/math/mult... 错过上一节课？https://www.khanacademy.org/math/mult... 可汗学院的多变量微积分：想想微积分。 然后想想代数 II 里我们在一个方程中处理两个变量。 现在我们把它抽象化并结合这两个数学概念，您将开始看到多变量微积分所包含的一些内容，到现在才包括的多维思维。 典型的概念或运算可能包括：极限和连续性、偏微分、多重积分、标量函数和多维微积分基本定理。 关于可汗学院：可汗学院提供练习，教学视频和个性化的学习进度表，使学习者可以在教室内外按自己的步调学习。我们提供数学，科学，计算机编程，历史，艺术史，经济学等等学科的内容。我们的数学任务使用最先进的自适应技术来指导学生从幼儿园到微积分的学习。 这些技术可以识别学习中的优势和差

表面积积分计算立体 第2部分 观看下一节课：https://www.khanacademy.org/math/mult... 错过上一节课？https://www.khanacademy.org/math/mult... 可汗学院的多变量微积分：想想微积分。 然后想想代数 II 里我们在一个方程中处理两个变量。 现在我们把它抽象化并结合这两个数学概念，您将开始看到多变量微积分所包含的一些内容，到现在才包括的多维思维。 典型的概念或运算可能包括：极限和连续性、偏微分、多重积分、标量函数和多维微积分基本定理。 关于可汗学院：可汗学院提供练习，教学视频和个性化的学习进度表，使学习者可以在教室内外按自己的步调学习。我们提供数学，科学，计算机编程，历史，艺术史，经济学等等学科的内容。我们的数学任务使用最先进的自适应技术来指导学生从幼儿园到微积分的学习。 这些技术可以识别学习中的优势和差距。

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/mult... The beginning of a proof of Stokes' theorem for a special class of surfaces. Finding the curl of our vector field. Watch the next lesson: https://www.khanacademy.org/math/mult... Missed the previous lesson? https://www.khanacademy.org/math/mult... Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning das

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/mult... Determining a Position Vector-Valued Function for a Parametrization of Two Parameters Watch the next lesson: https://www.khanacademy.org/math/mult... Missed the previous lesson? https://www.khanacademy.org/math/mult... Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners t

写出曲面的参数方程，并表示出 dS 在这里观看下一课：https://www.khanacademy.org/math/mult... 错过了上一课吗？ https://www.khanacademy.org/math/mult... 可汗学院的多元微积分：先想想微积分，再想想代数 II 里学的多变量方程，然后把这两个数学概念合并起来，你就明白什么是多变量微积分了——当然还需要把各个概念推广到多维度，包括：极限和连续性，偏微分，多重积分，标量函数，还有多维度版本的微积分基本定理。 关于可汗学院：可汗学院提供练习习题, 教学视频和个性化的学习界面, 让学习者能够在课堂内外按照自己的进度学习. 内容涉及数学, 科学, 计算机编程, 历史, 艺术史, 经济学等. 其中数学方面的内容涵盖了从幼儿园的基础知识到大学的微积分, 并采用了最先进的可识别学习强度和学习障碍的自适应技术. 可汗学院还与NASA, The Museum of Modern Art, T

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/mult... Using Green's Theorem to complete the proof Watch the next lesson: https://www.khanacademy.org/math/mult... Missed the previous lesson? https://www.khanacademy.org/math/mult... Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside

将表面积分转化为双重积分 观看下一节课：https://www.khanacademy.org/math/mult... 错过上一节课？https://www.khanacademy.org/math/mult... 可汗学院的多变量微积分：想想微积分。 然后想想代数 II 里我们在一个方程中处理两个变量。 现在我们把它抽象化并结合这两个数学概念，您将开始看到多变量微积分所包含的一些内容，到现在才包括的多维思维。 典型的概念或运算可能包括：极限和连续性、偏微分、多重积分、标量函数和多维微积分基本定理。 关于可汗学院：可汗学院提供练习，教学视频和个性化的学习进度表，使学习者可以在教室内外按自己的步调学习。我们提供数学，科学，计算机编程，历史，艺术史，经济学等等学科的内容。我们的数学任务使用最先进的自适应技术来指导学生从幼儿园到微积分的学习。 这些技术可以识别学习中的优势和差距。我

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/mult... Determining the proper orientation of a boundary given the orientation of the normal vector Watch the next lesson: https://www.khanacademy.org/math/mult... Missed the previous lesson? https://www.khanacademy.org/math/mult... Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower lea

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/mult... Seeing that Green's Theorem is just a special case of Stokes' Theorem Watch the next lesson: https://www.khanacademy.org/math/mult... Missed the previous lesson? https://www.khanacademy.org/math/mult... Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at thei