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- randy patton

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Also an Expert in Oceanography

Mathematics enables us to apply abstract principals to provide solutions to everyday problems as well as extend our understanding of the Universe. Being able to provide a mathematical solution that bridges the gap between intuition and a solid appication is very fulfilling.

I hope to acquire more thorough understanding of the many aspects of math and their relation to real world problems. I enjoy helping people understand the often deep results of mathematics and how they can reveal underlying relationships.

Integrating functions of real numbers (basically summing the values of a process to reveal its behaviour), uses several techniques taught in calculus. For complex numbers, combining real and imaginary numbers (square root of -1), the approach relies on powerful, elegant theorems to transform the function and its domain to obtain the value of the integral in a completely different way.

Humor: The famous mathematician Erdos once quipped that a mathematician is a machine that turns coffe into theorems.

User | Date | K | C | P | Comments |
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Nick | 02/16/17 | 10 | 10 | 10 | |

Nick | 02/07/17 | 10 | 10 | 10 | Thank you for this I learned a ..... |

Snehal | 01/15/17 | 10 | 10 | 10 | Great help |

Snehal | 01/04/17 | 10 | 10 | 10 | |

Carol | 12/20/16 | 5 | 5 | 5 | Hi Randy, Thanks for the help. These ..... |

I can see that you recognize that velocity and position are related by a derivative of time, namely, u(t) = dx(t)/dt, and that the solution as a function of time requires must require an integration in

Aishwarya, I am not sure what knowledge you are asking for specifically but it looks like you are anxious about your upcoming exams. Here is some advice I got from my abstract algebra professor at Berkeley

Hi Nick. The answer requires a math editor and so I need to attach figures. I'm assuming you know the basics of suffix notation and summation convention (at least the notation). Good luck. Let me know

I think the trace of X should be zero. Here's my derivation: Traces have some simple and useful properties, such as (for a matrices A and B) 1. Tr(A +B) = Tr(A) + Tr(B) 2. Tr(A) = Tr(A^t) 3

For A and B are in Mnxn, the form S = AB - BA, is called a commutator, made famous by the Heisenberg Principal (just FYI). As you probably know, the dimension of the vector space of matrices

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