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# Joseph-Louis Lagrange (1736 - 1813)

This Prezi is about a man who proved the mean value theorem to be true and work, so that we can do calculations more easily in calculus today :D

by

Tweet## Kaitie Walker

on 24 February 2011#### Transcript of Joseph-Louis Lagrange (1736 - 1813)

The Early Years... Lagrange was born in Turnin Piedmont... His father, was of good social position and wealthy, but before his son grew up he lost the majority of his property. He was educated at the college of Turin, but it was not until he was seventeen that he showed any interest in mathematics. His interest began with a memoir by Edmund Halley which he came across by accident. Alone and unaided he threw himself into mathematical studies. WIthin a year he was an acomplished mathematician, and became a lecturer in the artillery school. Joseph-Louis Lagrange Studies... Mathematics Calculus

Algebra Types of Mathematics... Mathematical Physics Astronomy Types of Mathematical Physics... Lagrange's treatise on analytical mechanics written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century.

Astronomy Lagrange wrote several important papers based on Astronomy... Of all the papers he wrote, Some of the most well known ones are... On the attraction of ellipsoids, 1773

On the secular equation of the Moon, 1773

On the motion of the nodes of a planet's orbit, 1774.

On the stability of the planetary orbits, 1776.

What is Analytical

Mechanics??? Analytical mechanics is a form of classical mechanics, which is a branch of mechanics based on Newton's laws of motion. What is an Ellipsis??? An ellipsis is a planet's revolutionary path. This is stated as Keplar's first law of planetary motion... The Mean Value Theorem The Mean Value Theorem Formula... For a More in Depth Explanation of the Mean Value Theorem Click on this Video... It states that if f(x) is continuous and differentiable on the interval (a,b) then there is at least one point on the interval (a,b) that makes the derivative of c equal to the function of b minus the function of a divided by the b value minus the a value.

So...

The value of the derivative is equal to the slope between the two endpoints of the function. The Requirements...

1) The function must be continuous

2) The function must be differentiable For Further Help on the Mean Value Theorem Click on the Link Below... Examples of the Mean Value Theorem... f(x)=3x+2 [-1,3] f'(c)=f(b)-f(a)/b-a f'(c)=((3*3)+2)-((-1*3)+2)

_______________ 3+1 f'(c)=11+1 ______ 4 f'(c)=3 Step 1 Step 2 Step 3 Step 4 Step 5 Example 1 Example 2 f(x)=3sin2x [2,6] f'(c)=f(b)-f(a)/b-a f'(c)=3sin(2*6)-3sin(2*2) ___________________ 6-2 f'(c)=.1675 Step 1 Step 2 Step 3 Step 4 Did You Know??? Joseph-Louis Lagrange was the first person to ever prove the mean value theorem!!! Extra Practice... f(x)=7x+3 [6,9] Practice Problem Solutions f'(c)=66-45 _______ 3 f'(c)=7 f(x)=7x+9 [1,5] f'(c)=44-16 _______ 3 f'(c)=9.3 - f(x)=17sin2x [-3,2] f'(c)=15.5+2.4 ________ 5 f'(c)=3.58 Quiz... f(x)=4x+1 [-3,4] f(x)=3(-6x) [2,5] f(x)=4cos2x [3,8] f(x)=2/3x [.5,8.5] f(x)=2-3x [2,3] 2 Quiz Solutions... .86 -18 -1.534 -.1525 -15 Works Cited... http://www.sosmath.com/calculus/diff/der11/der11.html http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange http://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.html

Full transcriptAlgebra Types of Mathematics... Mathematical Physics Astronomy Types of Mathematical Physics... Lagrange's treatise on analytical mechanics written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century.

Astronomy Lagrange wrote several important papers based on Astronomy... Of all the papers he wrote, Some of the most well known ones are... On the attraction of ellipsoids, 1773

On the secular equation of the Moon, 1773

On the motion of the nodes of a planet's orbit, 1774.

On the stability of the planetary orbits, 1776.

What is Analytical

Mechanics??? Analytical mechanics is a form of classical mechanics, which is a branch of mechanics based on Newton's laws of motion. What is an Ellipsis??? An ellipsis is a planet's revolutionary path. This is stated as Keplar's first law of planetary motion... The Mean Value Theorem The Mean Value Theorem Formula... For a More in Depth Explanation of the Mean Value Theorem Click on this Video... It states that if f(x) is continuous and differentiable on the interval (a,b) then there is at least one point on the interval (a,b) that makes the derivative of c equal to the function of b minus the function of a divided by the b value minus the a value.

So...

The value of the derivative is equal to the slope between the two endpoints of the function. The Requirements...

1) The function must be continuous

2) The function must be differentiable For Further Help on the Mean Value Theorem Click on the Link Below... Examples of the Mean Value Theorem... f(x)=3x+2 [-1,3] f'(c)=f(b)-f(a)/b-a f'(c)=((3*3)+2)-((-1*3)+2)

_______________ 3+1 f'(c)=11+1 ______ 4 f'(c)=3 Step 1 Step 2 Step 3 Step 4 Step 5 Example 1 Example 2 f(x)=3sin2x [2,6] f'(c)=f(b)-f(a)/b-a f'(c)=3sin(2*6)-3sin(2*2) ___________________ 6-2 f'(c)=.1675 Step 1 Step 2 Step 3 Step 4 Did You Know??? Joseph-Louis Lagrange was the first person to ever prove the mean value theorem!!! Extra Practice... f(x)=7x+3 [6,9] Practice Problem Solutions f'(c)=66-45 _______ 3 f'(c)=7 f(x)=7x+9 [1,5] f'(c)=44-16 _______ 3 f'(c)=9.3 - f(x)=17sin2x [-3,2] f'(c)=15.5+2.4 ________ 5 f'(c)=3.58 Quiz... f(x)=4x+1 [-3,4] f(x)=3(-6x) [2,5] f(x)=4cos2x [3,8] f(x)=2/3x [.5,8.5] f(x)=2-3x [2,3] 2 Quiz Solutions... .86 -18 -1.534 -.1525 -15 Works Cited... http://www.sosmath.com/calculus/diff/der11/der11.html http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange http://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.html