Slideshows For 'Math 21a, Spring 2008' http://www.slideshare.net/group/math-21a-spring-2008 http://www.slideshare.net/images/logo.gif Slideshows For 'Math 21a, Spring 2008' http://www.slideshare.net/group/math-21a-spring-2008 Fri, 09 May 2008 19:06:34 GMT SlideShare feed for Slideshows For 'Math 21a, Spring 2008' Final Review II http://www.slideshare.net/leingang/final-review-ii

from: leingang 5 months ago

Review of partial differentiation and multiple integrals

Tags: math math21a multivariable calculus function

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from: leingang 5 months ago

Review of partial differentiation and multiple integrals

Tags: math math21a multivariable calculus function

]]> Fri, 09 May 2008 19:06:34 GMT http://www.slideshare.net/leingang/final-review-ii leingang@slideshare.net(leingang) Final Review II leingang Review of partial differentiation and multiple integrals <div class='snap_preview'><img src="http://cdn.slideshare.net/2007spring21afinalreviewiislides-1210359752386728-8-thumbnail-2?1210359999" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 5 months ago</p><p>Review of partial differentiation and multiple integrals</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/multivariable">multivariable</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/calculus">calculus</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> </p></div> math,math21a,multivariable,calculus,function, Final Review II
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]]> 923 0 http://cdn.slideshare.net/2007spring21afinalreviewiislides-1210359752386728-8-thumbnail-2?1210359999 Lesson 22: Triple Integrals http://www.slideshare.net/leingang/lesson-22-triple-integrals

from: leingang 6 months ago

You knew this was coming. From double integrals over plane regions we move onward to triple integrals over solid regions. The visualization is a little harder, but the calculus not that much.

Tags: math math21a function integrations triple

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from: leingang 6 months ago

You knew this was coming. From double integrals over plane regions we move onward to triple integrals over solid regions. The visualization is a little harder, but the calculus not that much.

Tags: math math21a function integrations triple

]]> Fri, 04 Apr 2008 18:52:18 GMT http://www.slideshare.net/leingang/lesson-22-triple-integrals leingang@slideshare.net(leingang) Lesson 22: Triple Integrals leingang You knew this was coming. From double integrals over plane regions we move onward to triple integrals over solid regions. The visualization is a little harder, but the calculus not that much. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson22tripleintegralsslides-1207335056955112-9-thumbnail-2?1207335138" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 6 months ago</p><p>You knew this was coming. From double integrals over plane regions we move onward to triple integrals over solid regions. The visualization is a little harder, but the calculus not that much.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/integrations">integrations</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/triple">triple</a> </p></div> math,math21a,function,integrations,triple, Lesson 22: Triple Integrals
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]]> 532 0 http://cdn.slideshare.net/lesson22tripleintegralsslides-1207335056955112-9-thumbnail-2?1207335138 Lesson 21: Surface Area http://www.slideshare.net/leingang/lesson-21-surface-area-336169

from: leingang 6 months ago

Tags: math21a math integration double calculus

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from: leingang 6 months ago

Tags: math21a math integration double calculus

]]> Fri, 04 Apr 2008 10:02:07 GMT http://www.slideshare.net/leingang/lesson-21-surface-area-336169 leingang@slideshare.net(leingang) Lesson 21: Surface Area leingang <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson21surfaceareaslides-1207306901222605-8-thumbnail-2?1207303327" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 6 months ago</p><p></p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/integration">integration</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/double">double</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/calculus">calculus</a> </p></div> math21a,math,integration,double,calculus, Lesson 21: Surface Area
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]]> 597 0 http://cdn.slideshare.net/lesson21surfaceareaslides-1207306901222605-8-thumbnail-2?1207303327 Lesson 20: Integration in Polar Coordinates http://www.slideshare.net/leingang/lesson-20-integration-in-polar-coordinates

from: leingang 6 months ago

sometimes a region (or a function) is more concisely described in polar coordinates. This can make integrating it a much easier task.

Tags: math math21a mulivariable calculus integration

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from: leingang 6 months ago

sometimes a region (or a function) is more concisely described in polar coordinates. This can make integrating it a much easier task.

Tags: math math21a mulivariable calculus integration

]]> Tue, 01 Apr 2008 17:57:25 GMT http://www.slideshare.net/leingang/lesson-20-integration-in-polar-coordinates leingang@slideshare.net(leingang) Lesson 20: Integration in Polar Coordinates leingang sometimes a region (or a function) is more concisely described in polar coordinates. This can make integrating it a much easier task. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-20-integration-in-polar-coordinates-120707264429558-4-thumbnail-2?1207072645" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 6 months ago</p><p>sometimes a region (or a function) is more concisely described in polar coordinates. This can make integrating it a much easier task.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/mulivariable">mulivariable</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/calculus">calculus</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/integration">integration</a> </p></div> math,math21a,mulivariable,calculus,integration, Lesson 20: Integration in Polar Coordinates
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]]> 774 0 http://cdn.slideshare.net/lesson-20-integration-in-polar-coordinates-120707264429558-4-thumbnail-2?1207072645 Lesson 19: Double Integrals over General Regions http://www.slideshare.net/leingang/lesson-19-double-integrals-over-general-regions

from: leingang 6 months ago

Tags: math integration calculus mulivariable math21a

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from: leingang 6 months ago

Tags: math integration calculus mulivariable math21a

]]> Thu, 20 Mar 2008 16:50:42 GMT http://www.slideshare.net/leingang/lesson-19-double-integrals-over-general-regions leingang@slideshare.net(leingang) Lesson 19: Double Integrals over General Regions leingang <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-19-double-integrals-over-general-regions-1206031841913031-4-thumbnail-2?1206031842" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 6 months ago</p><p></p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/integration">integration</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/calculus">calculus</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/mulivariable">mulivariable</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> </p></div> math,integration,calculus,mulivariable,math21a, Lesson 19: Double Integrals over General Regions
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]]> 388 0 http://cdn.slideshare.net/lesson-19-double-integrals-over-general-regions-1206031841913031-4-thumbnail-2?1206031842 Lesson18 Double Integrals Over Rectangles Slides http://www.slideshare.net/leingang/lesson18-double-integrals-over-rectangles-slides

from: leingang 6 months ago

We develop double integrals for measuring volume and iterated integrals for calculating double integrals.

Tags: math math21a multivariable calculus integral

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from: leingang 6 months ago

We develop double integrals for measuring volume and iterated integrals for calculating double integrals.

Tags: math math21a multivariable calculus integral

]]> Mon, 17 Mar 2008 18:05:57 GMT http://www.slideshare.net/leingang/lesson18-double-integrals-over-rectangles-slides leingang@slideshare.net(leingang) Lesson18 Double Integrals Over Rectangles Slides leingang We develop double integrals for measuring volume and iterated integrals for calculating double integrals. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson18-double-integrals-over-rectangles-slides-12057771568837-2-thumbnail-2?1205777157" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 6 months ago</p><p>We develop double integrals for measuring volume and iterated integrals for calculating double integrals.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/multivariable">multivariable</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/calculus">calculus</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/integral">integral</a> </p></div> math,math21a,multivariable,calculus,integral, Lesson18 Double Integrals Over Rectangles Slides
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]]> 693 0 http://cdn.slideshare.net/lesson18-double-integrals-over-rectangles-slides-12057771568837-2-thumbnail-2?1205777157 Lesson 17: The Method of Lagrange Multipliers http://www.slideshare.net/leingang/lesson-17-the-method-of-lagrange-multipliers

from: leingang 7 months ago

The Method of Lagrange multipliers allows us to find constrained extrema. It's more equations, more variables, but less algebra.

Tags: mulivariable calculus gradient constrained optimization

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from: leingang 7 months ago

The Method of Lagrange multipliers allows us to find constrained extrema. It's more equations, more variables, but less algebra.

Tags: mulivariable calculus gradient constrained optimization

]]> Fri, 14 Mar 2008 18:52:11 GMT http://www.slideshare.net/leingang/lesson-17-the-method-of-lagrange-multipliers leingang@slideshare.net(leingang) Lesson 17: The Method of Lagrange Multipliers leingang The Method of Lagrange multipliers allows us to find constrained extrema. It's more equations, more variables, but less algebra. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-17-the-method-of-lagrange-multipliers-1205520730452706-2-thumbnail-2?1205520731" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 7 months ago</p><p>The Method of Lagrange multipliers allows us to find constrained extrema. It's more equations, more variables, but less algebra.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/mulivariable">mulivariable</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/calculus">calculus</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/gradient">gradient</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/constrained">constrained</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/optimization">optimization</a> </p></div> mulivariable,calculus,gradient,constrained,optimization, Lesson 17: The Method of Lagrange Multipliers
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]]> 1185 0 http://cdn.slideshare.net/lesson-17-the-method-of-lagrange-multipliers-1205520730452706-2-thumbnail-2?1205520731 Lesson 15: Gradients and level curves http://www.slideshare.net/leingang/lesson-15-gradients-and-level-curves

from: leingang 5 months ago

The gradient of a function is the collection of its partial derivatives, and is a vector field always perpendicular to the level curves of the function.

Tags: gradient vectorfield function math21a math

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from: leingang 5 months ago

The gradient of a function is the collection of its partial derivatives, and is a vector field always perpendicular to the level curves of the function.

Tags: gradient vectorfield function math21a math

]]> Tue, 15 Apr 2008 17:20:14 GMT http://www.slideshare.net/leingang/lesson-15-gradients-and-level-curves leingang@slideshare.net(leingang) Lesson 15: Gradients and level curves leingang The gradient of a function is the collection of its partial derivatives, and is a vector field always perpendicular to the level curves of the function. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson15gradientslevelcurvesslides-1208280012216101-9-thumbnail-2?1208280014" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 5 months ago</p><p>The gradient of a function is the collection of its partial derivatives, and is a vector field always perpendicular to the level curves of the function.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/gradient">gradient</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/vectorfield">vectorfield</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> gradient,vectorfield,function,math21a,math, Lesson 15: Gradients and level curves
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]]> 599 0 http://cdn.slideshare.net/lesson15gradientslevelcurvesslides-1208280012216101-9-thumbnail-2?1208280014 Math 21a Midterm I Review http://www.slideshare.net/leingang/math-21a-midterm-i-review

from: leingang 7 months ago

Review of the first five weeks of Math 21a

Tags: surface quadric approximation linear derivative

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from: leingang 7 months ago

Review of the first five weeks of Math 21a

Tags: surface quadric approximation linear derivative

]]> Mon, 10 Mar 2008 01:31:01 GMT http://www.slideshare.net/leingang/math-21a-midterm-i-review leingang@slideshare.net(leingang) Math 21a Midterm I Review leingang Review of the first five weeks of Math 21a <div class='snap_preview'><img src="http://cdn.slideshare.net/math-21a-midterm-i-review-1205112660646395-2-thumbnail-2?1205112661" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 7 months ago</p><p>Review of the first five weeks of Math 21a</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/surface">surface</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/quadric">quadric</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/approximation">approximation</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/linear">linear</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/derivative">derivative</a> </p></div> surface,quadric,approximation,linear,derivative, Math 21a Midterm I Review
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]]> 867 1 http://cdn.slideshare.net/math-21a-midterm-i-review-1205112660646395-2-thumbnail-2?1205112661 Lesson 11: Limits and Continuity http://www.slideshare.net/leingang/lesson-11-limits-and-continuity

from: leingang 7 months ago

The concept of limit is a lot harder for functions of several variables than for just one. We show the more dramatric ways that a limit can fail.

Tags: function math21a math continuous limit

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from: leingang 7 months ago

The concept of limit is a lot harder for functions of several variables than for just one. We show the more dramatric ways that a limit can fail.

Tags: function math21a math continuous limit

]]> Fri, 29 Feb 2008 19:44:05 GMT http://www.slideshare.net/leingang/lesson-11-limits-and-continuity leingang@slideshare.net(leingang) Lesson 11: Limits and Continuity leingang The concept of limit is a lot harder for functions of several variables than for just one. We show the more dramatric ways that a limit can fail. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-11-limits-and-continuity-1204314244516703-4-thumbnail-2?1204314245" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 7 months ago</p><p>The concept of limit is a lot harder for functions of several variables than for just one. We show the more dramatric ways that a limit can fail. </p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/continuous">continuous</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/limit">limit</a> </p></div> function,math21a,math,continuous,limit, Lesson 11: Limits and Continuity
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]]> 1067 0 http://cdn.slideshare.net/lesson-11-limits-and-continuity-1204314244516703-4-thumbnail-2?1204314245 Lesson 10: Functions and Level Sets http://www.slideshare.net/leingang/lesson-10-functions-and-level-sets

from: leingang 7 months ago

A contour plot is a nice way to visualize the graph of a function of two variables. If the function is a utility function, this is nothing more than the set of indifference curves. More generally, it's like a topographical map of the surface

Tags: math math21a function graph contour

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from: leingang 7 months ago

A contour plot is a nice way to visualize the graph of a function of two variables. If the function is a utility function, this is nothing more than the set of indifference curves. More generally, it's like a topographical map of the surface

Tags: math math21a function graph contour

]]> Wed, 27 Feb 2008 19:53:15 GMT http://www.slideshare.net/leingang/lesson-10-functions-and-level-sets leingang@slideshare.net(leingang) Lesson 10: Functions and Level Sets leingang A contour plot is a nice way to visualize the graph of a function of two variables. If the function is a utility function, this is nothing more than the set of indifference curves. More generally, it's like a topographical map of the surface <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-10-functions-and-level-sets-1204141994818033-4-thumbnail-2?1204141995" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 7 months ago</p><p>A contour plot is a nice way to visualize the graph of a function of two variables. If the function is a utility function, this is nothing more than the set of indifference curves. More generally, it's like a topographical map of the surface</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/graph">graph</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/contour">contour</a> </p></div> math,math21a,function,graph,contour, Lesson 10: Functions and Level Sets
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]]> 428 0 http://cdn.slideshare.net/lesson-10-functions-and-level-sets-1204141994818033-4-thumbnail-2?1204141995 Lesson 9: Parametric Surfaces http://www.slideshare.net/leingang/lesson-9-parametric-surfaces

from: leingang 7 months ago

A parametric surface is function from a subset of the plane into space.

Tags: math math21a math math21a

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from: leingang 7 months ago

A parametric surface is function from a subset of the plane into space.

Tags: math math21a math math21a

]]> Wed, 27 Feb 2008 01:32:00 GMT http://www.slideshare.net/leingang/lesson-9-parametric-surfaces leingang@slideshare.net(leingang) Lesson 9: Parametric Surfaces leingang A parametric surface is function from a subset of the plane into space. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-9-parametric-surfaces-1204075919696414-4-thumbnail-2?1204075920" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 7 months ago</p><p>A parametric surface is function from a subset of the plane into space.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> </p></div> math,math21a,math,math21a, Lesson 9: Parametric Surfaces
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]]> 347 0 http://cdn.slideshare.net/lesson-9-parametric-surfaces-1204075919696414-4-thumbnail-2?1204075920 Lesson 31: The Divergence Theorem http://www.slideshare.net/leingang/lesson-31-the-divergence-theorem

from: leingang 5 months ago

Gauss's divergence theorem, the last of the big three theorems in multivariable calculus, links the integral of the divergence of a vector field over a region with the flux integral of the vector field over the boundary surface.

Tags: integral function math21a math integral

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from: leingang 5 months ago

Gauss's divergence theorem, the last of the big three theorems in multivariable calculus, links the integral of the divergence of a vector field over a region with the flux integral of the vector field over the boundary surface.

Tags: integral function math21a math integral

]]> Thu, 01 May 2008 14:55:34 GMT http://www.slideshare.net/leingang/lesson-31-the-divergence-theorem leingang@slideshare.net(leingang) Lesson 31: The Divergence Theorem leingang Gauss's divergence theorem, the last of the big three theorems in multivariable calculus, links the integral of the divergence of a vector field over a region with the flux integral of the vector field over the boundary surface. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson31divergencetheoremslides-1209653696964461-9-thumbnail-2?1209653734" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 5 months ago</p><p>Gauss's divergence theorem, the last of the big three theorems in multivariable calculus, links the integral of the divergence of a vector field over a region with the flux integral of the vector field over the boundary surface.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/integral">integral</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/integral">integral</a> </p></div> integral,function,math21a,math,integral, Lesson 31: The Divergence Theorem
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]]> 447 0 http://cdn.slideshare.net/lesson31divergencetheoremslides-1209653696964461-9-thumbnail-2?1209653734 Lesson 6: Polar, Cylindrical, and Spherical coordinates http://www.slideshare.net/leingang/lesson-6-polar-cylindrical-and-spherical-coordinates

from: leingang 7 months ago

"The fact that space is three-dimensional is due to nature. The way we measure it is due to us." Cartesian coordinates are one familiar way to do that, but other coordinate systems exist which are more useful in other situations.

Tags: math math21a geometry coordinates math

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from: leingang 7 months ago

"The fact that space is three-dimensional is due to nature. The way we measure it is due to us." Cartesian coordinates are one familiar way to do that, but other coordinate systems exist which are more useful in other situations.

Tags: math math21a geometry coordinates math

]]> Sat, 16 Feb 2008 22:43:44 GMT http://www.slideshare.net/leingang/lesson-6-polar-cylindrical-and-spherical-coordinates leingang@slideshare.net(leingang) Lesson 6: Polar, Cylindrical, and Spherical coordinates leingang "The fact that space is three-dimensional is due to nature. The way we measure it is due to us." Cartesian coordinates are one familiar way to do that, but other coordinate systems exist which are more useful in other situations. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-6-polar-cylindrical-and-spherical-coordinates-1203201823198492-4-thumbnail-2?1203201824" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 7 months ago</p><p>"The fact that space is three-dimensional is due to nature. The way we measure it is due to us." Cartesian coordinates are one familiar way to do that, but other coordinate systems exist which are more useful in other situations.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/geometry">geometry</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/coordinates">coordinates</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> math,math21a,geometry,coordinates,math, Lesson 6: Polar, Cylindrical, and Spherical coordinates
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]]> 1326 0 http://cdn.slideshare.net/lesson-6-polar-cylindrical-and-spherical-coordinates-1203201823198492-4-thumbnail-2?1203201824 Lesson 5: Functions and surfaces http://www.slideshare.net/leingang/lesson-5-functions-and-surfaces

from: leingang 8 months ago

A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.

Tags: function graph math math21a math

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from: leingang 8 months ago

A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.

Tags: function graph math math21a math

]]> Wed, 13 Feb 2008 20:22:32 GMT http://www.slideshare.net/leingang/lesson-5-functions-and-surfaces leingang@slideshare.net(leingang) Lesson 5: Functions and surfaces leingang A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-5-functions-and-surfaces-1202934151623899-3-thumbnail-2?1202934152" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 8 months ago</p><p>A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/function">function</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/graph">graph</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> function,graph,math,math21a,math, Lesson 5: Functions and surfaces
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]]> 445 0 http://cdn.slideshare.net/lesson-5-functions-and-surfaces-1202934151623899-3-thumbnail-2?1202934152 Lesson 4: Lines, Planes, and the Distance Formula http://www.slideshare.net/leingang/lesson-4-lines-planes-and-the-distance-formula

from: leingang 8 months ago

Using vectors and the various operations defined on them we can get equations for lines and planes based on descriptive data. We can also find distances between linear objects, such as point to line, point to plane, plane to plane, and line to line.

Tags: math math21a vector geometry math

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from: leingang 8 months ago

Using vectors and the various operations defined on them we can get equations for lines and planes based on descriptive data. We can also find distances between linear objects, such as point to line, point to plane, plane to plane, and line to line.

Tags: math math21a vector geometry math

]]> Tue, 12 Feb 2008 16:00:31 GMT http://www.slideshare.net/leingang/lesson-4-lines-planes-and-the-distance-formula leingang@slideshare.net(leingang) Lesson 4: Lines, Planes, and the Distance Formula leingang Using vectors and the various operations defined on them we can get equations for lines and planes based on descriptive data. We can also find distances between linear objects, such as point to line, point to plane, plane to plane, and line to line. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-4-lines-planes-and-the-distance-formula-1202832030465602-3-thumbnail-2?1202832031" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 8 months ago</p><p>Using vectors and the various operations defined on them we can get equations for lines and planes based on descriptive data. We can also find distances between linear objects, such as point to line, point to plane, plane to plane, and line to line.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/vector">vector</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/geometry">geometry</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> math,math21a,vector,geometry,math, Lesson 4: Lines, Planes, and the Distance Formula
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]]> 1361 0 http://cdn.slideshare.net/lesson-4-lines-planes-and-the-distance-formula-1202832030465602-3-thumbnail-2?1202832031 Lesson 3: The Cross Product http://www.slideshare.net/leingang/lesson-3-the-cross-product

from: leingang 8 months ago

The cross product is an important operation, taking two three-dimensional vectors and producing a three-dimensional vector. It's not a product in the commutative, associative, sense, but it does produce a vector which is perpendicular to the two crossed vectors and whose length is the area of the parallelogram spanned by the them. The direction is chosen again to follow the right-hand rule.

Tags: math math21a vector geometry math

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from: leingang 8 months ago

The cross product is an important operation, taking two three-dimensional vectors and producing a three-dimensional vector. It's not a product in the commutative, associative, sense, but it does produce a vector which is perpendicular to the two crossed vectors and whose length is the area of the parallelogram spanned by the them. The direction is chosen again to follow the right-hand rule.

Tags: math math21a vector geometry math

]]> Tue, 12 Feb 2008 15:59:30 GMT http://www.slideshare.net/leingang/lesson-3-the-cross-product leingang@slideshare.net(leingang) Lesson 3: The Cross Product leingang The cross product is an important operation, taking two three-dimensional vectors and producing a three-dimensional vector. It's not a product in the commutative, associative, sense, but it does produce a vector which is perpendicular to the two crossed vectors and whose length is the area of the parallelogram spanned by the them. The direction is chosen again to follow the right-hand rule. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-3-the-cross-product-1202831969830854-3-thumbnail-2?1202831970" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 8 months ago</p><p>The cross product is an important operation, taking two three-dimensional vectors and producing a three-dimensional vector. It's not a product in the commutative, associative, sense, but it does produce a vector which is perpendicular to the two crossed vectors and whose length is the area of the parallelogram spanned by the them. The direction is chosen again to follow the right-hand rule.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/vector">vector</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/geometry">geometry</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> math,math21a,vector,geometry,math, Lesson 3: The Cross Product
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]]> 1212 0 http://cdn.slideshare.net/lesson-3-the-cross-product-1202831969830854-3-thumbnail-2?1202831970 Lesson 2: Vectors and the Dot Product http://www.slideshare.net/leingang/lesson-2-vectors-and-the-dot-product

from: leingang 8 months ago

A vector has magnitude and direction. There is an algebra and geometry of vectors which makes addition, subtraction, and scaling well-defined. The scalar or dot product of vectors measures the angle between them, in a way. It's useful to show if two vectors are perpendicular or parallel.

Tags: math math21a vectors dotproduct math

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from: leingang 8 months ago

A vector has magnitude and direction. There is an algebra and geometry of vectors which makes addition, subtraction, and scaling well-defined. The scalar or dot product of vectors measures the angle between them, in a way. It's useful to show if two vectors are perpendicular or parallel.

Tags: math math21a vectors dotproduct math

]]> Wed, 06 Feb 2008 19:56:54 GMT http://www.slideshare.net/leingang/lesson-2-vectors-and-the-dot-product leingang@slideshare.net(leingang) Lesson 2: Vectors and the Dot Product leingang A vector has magnitude and direction. There is an algebra and geometry of vectors which makes addition, subtraction, and scaling well-defined. The scalar or dot product of vectors measures the angle between them, in a way. It's useful to show if two vectors are perpendicular or parallel. <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-2-vectors-and-the-dot-product-1202327813713073-4-thumbnail-2?1202327814" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 8 months ago</p><p>A vector has magnitude and direction. There is an algebra and geometry of vectors which makes addition, subtraction, and scaling well-defined. The scalar or dot product of vectors measures the angle between them, in a way. It's useful to show if two vectors are perpendicular or parallel.</p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/vectors">vectors</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/dotproduct">dotproduct</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> math,math21a,vectors,dotproduct,math, Lesson 2: Vectors and the Dot Product
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]]> 1808 1 http://cdn.slideshare.net/lesson-2-vectors-and-the-dot-product-1202327813713073-4-thumbnail-2?1202327814 Lesson 1: Coordinates and Distance http://www.slideshare.net/leingang/lesson-1-coordinates-and-distance

from: leingang 8 months ago

Tags: distance coordinates axes math21a math

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from: leingang 8 months ago

Tags: distance coordinates axes math21a math

]]> Mon, 04 Feb 2008 23:51:51 GMT http://www.slideshare.net/leingang/lesson-1-coordinates-and-distance leingang@slideshare.net(leingang) Lesson 1: Coordinates and Distance leingang <div class='snap_preview'><img src="http://cdn.slideshare.net/lesson-1-coordinates-and-distance-1202169110558773-5-thumbnail-2?1202169111" alt ="" style="border:1px solid #C3E6D8;float:right;" /> <p>from: <a href="http://www.slideshare.net/leingang">leingang</a> 8 months ago</p><p></p><p>Tags: <a style="text-decoration:underline;" href="http://slideshare.net/tag/distance">distance</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/coordinates">coordinates</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/axes">axes</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math21a">math21a</a> <a style="text-decoration:underline;" href="http://slideshare.net/tag/math">math</a> </p></div> distance,coordinates,axes,math21a,math, Lesson 1: Coordinates and Distance
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