MATH 365 Texas A&M

c Dr. Patrice Poage, May 17, 2008 1 365 Lecture Notes for Section 1.1 An Introduction to Problem Solving Denitions: The natural numbers are N = {1, 2, 3, 4, 5, .} The whole numbers are W = {0, 1, 2, 3, 4, 5, .} The integers are Z = {. 3, 2, 1,

NONLINEAR PROPERTIES OF DENSE COHERENT MEDIA A Dissertation by EUGENIY EUGENIEVICH MIKHAILOV Submitted to the Oce of Graduate Studies of Texas A&M University in partial fulllment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 20

1 365 Lecture Notes for Section 1.2 Explorations with Patterns Denitions: inductive reasoning - the method of making gerneralizations based upon observations and patterns. Ex: The sun is in the sky. (because that is the way it has been for millions

Class Activity: Logic Vocabulary 1) Statement: a) p: x + 7 = 18 b) q: A triangle is a three sided polygon. c) r: Texas A&M Universitys mascot is the longhorn. d) s: Ethan is tall. 2) Negation: 3) Quantifier 4) Universal Quantifier 5) Existential Q

c Dr. Patrice Poage, May 17, 2008 1 365 Lecture Notes for Section 1.1 An Introduction to Problem Solving Denitions: The natural numbers are N = {1, 2, 3, 4, 5, .} The whole numbers are W = {0, 1, 2, 3, 4, 5, .} The integers are Z = {. 3, 2, 1,

Class Activity: Logic Vocabulary 1) Statement: a) p: x + 7 = 18 b) q: A triangle is a three sided polygon. c) r: Texas A&M Universitys mascot is the longhorn. d) s: Ethan is tall. 2) Negation: 3) Quantifier 4) Universal Quantifier 5) Existential Q

1 365 Lecture Notes for Section 1.2 Explorations with Patterns Denitions: inductive reasoning - the method of making gerneralizations based upon observations and patterns. Ex: The sun is in the sky. (because that is the way it has been for millions

NONLINEAR PROPERTIES OF DENSE COHERENT MEDIA A Dissertation by EUGENIY EUGENIEVICH MIKHAILOV Submitted to the Oce of Graduate Studies of Texas A&M University in partial fulllment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 20

Fall 2003 Math 308/501502 Numerical Methods 3.6, 3.7, 5.3 Runge-Kutta Methods c 2003, Art Belmonte Mon, 27/Oct Summary Geometrical idea Runge-Kutta methods numerically approximate the solution of y = f (t, y), y(a) = y0 The constant M is different t