Augustin Cauchy, French Mathematician 1789-1857

Among his achievements is Cauchy’s Integral Theorem which says the line integral of a complex-valued function holomorphic on and within the non-self-intersecting closed curve C(contour) lying in the complex plane is always 0. Cauchy's Integral Formula is a consequence of this theorem which expresses that a holomorphic function defined on a disk is completely determined by its values on the boundary of that disk.

George Green, British Physicist 1793-1841

Green’s Theorem was a significant achievement in his 1828 essay on electricity and magnetism and is used, along with the Cauchy-Riemann equations, to prove Cauchy’s Integral Theorem. Green's Theorem proves the equivalence of a line integral around a simple closed curve and a double integral over the region that curve encloses.

BUILDING MATHEMATICAL MUSCLE EVERYDAY 

I offer comprehensive in person tutoring to anyone living in the Austin area and online if you live anywhere in the United States. My expertise stretches across all levels and branches of mathematics. I've been a full time tutor for over 12 years and I was a professor at ITT Tech for over 6 years prior. 

GEOMETRY

We can prove the sum of the measures of the exterior angles of any polygon is 360 degreees by first proving the sum of the measures of the interior angles of an n sided polygon is 180(n-2).

CALCULUS 

We can calculate the volume of a parabolic region bounded by either coordinate axis and rotated about any line parallel to either coordinate axis by slicing the region up with each slice making a cylindrical shell upon rotation.

VECTOR CALCULUS 

We can calculate the arc length of any path in three dimensions by describing that path with a parametric function that maps a closed interval into three dimensions and integrating the magnitude of the derivative of that function. 

If we construct squares of any length on the sides of an arbitrary quadrilateral, we can prove the line segments joining the centers of opposite squares are perpendicular and congruent.

COMPLEX ANALYSIS

GRE/GMAT

If we are given that three digit codes for locks use digits 0-9 under the conditions 1)the first digit cannot be 0 or 1, 2)the second digit must be 0 or 1, and 3)the second and third digits cannot both be 0, we can calculate the possible number of codes.

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