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Joseph-Louis Lagrange (1736 - 1813)
Transcript of Joseph-Louis Lagrange (1736 - 1813)
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.
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