Barrow, Leibniz and the Geometrical Proof of the Fundamental Theorem of the Calculus

2013 ◽  
Vol 71 (3) ◽  
pp. 335-354 ◽  
Author(s):  
Michael Nauenberg
Keyword(s):  
Fundamental Theorem ◽  
Geometrical Proof

On some definite integrals and a new method of reducing a function of spherical co-ordinates to a series of spherical harmonics

1903 ◽  
Vol 71 (467-476) ◽  
pp. 97-101 ◽  
Keyword(s):  
Spherical Harmonics ◽  
Fundamental Theorem ◽  
New Method ◽  
Definite Integrals

The expansion of a function f(θ) of an angle θ varying between 0 and π in terms of a series proceeding by the sines of the multiples of θ depends on the fundamental theorem, ∫ π 0 sin pθ sin qθ dθ = 0, where p and q are integer numbers not equal to each other.

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