Stochastic calculus

Here, we extend the weak KAM and Aubry-Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton-Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit

1. ht= -4.9t2+ 450, where t is the time elapsed in seconds and h is the height in metres. a) Table of Values t(s) | h(t) (m) | 0 | ht= -4.9(0)2+ 450= 450 | 1 | ht= -4.9(1)2+ 450= 445.1 | 2 | ht= -4.9(2)2+ 450= 430.4 | 3 | ht= -4.9(3)2+ 450= 405.9 | 4 | ht= -4.9(4)2+ 450=371.6 | 5 | ht= -4.9(5)2+ 450=327.5 | 6 | ht= -4.9(6)2+ 450= 273.6 | 7 | ht= -4.9(7)2+ 450= 209.9 | 8 | ht= -4.9(8)2+ 450= 136.4 | 9 | ht= -4.9(9)2+ 450=53.1 | 10 | ht= -4.9(10)2+ 450= -40 |

Derivative is a complex subject of calculus. In calculus, derivative is a key term developed by both Newton and Leibniz. With function f (t), the first derivative is defined asf^ ' (t)= df/dt= lim┬(h→0)⁡〖(f(t)-f(t-h))/h〗. There is also a second derivative known as second-order derivative. The second-order derivative is defined: f^ ' ' (t)= (d^2 f)/(dt^2 )= lim┬(h→0)⁡〖(f^ ' (t)-f^ ' (t-h))/h〗 =lim┬(h→0)⁡〖1/h {(f(t)-f(t-h))/h- (f(t-h)-f(t-2h))/h}〗 =lim┬(h→0)⁡〖(f(t)-2f(t-h)+f(t-2h))/h^2 〗 (Podlubny

Throughout the paper, we will compare a novice and expert responses to certain mathematical concepts in order to recognize the different techniques they practice. We will interpret the procedures they use to make connections and to check their level of comprehension on a specific mathematical concept. An expert typically has a broad interpretation and connects their ideas to more concepts, in this case introducing graphs, definitions, formulas and physics whereas the novice will have useful knowledge

PI (π) One of the oldest and most commonly known and used concepts in mathematics is that of Pi (π). In the earliest of know human civilizations, people realized the importance of finding the exact value of π for practical reasons. Even by todays standards, we still only need to know the exact value of π to a few decimal place values, although that hasn’t stopped mathematicians from pursuing a more accurate representation for its value throughout time. The earliest know approximations for the

Why is math required in college? Most students in my algebra II class, in high school, disliked math substantially. Math was only required to be taken for two years and if you were going to attend college, Algebra II was a requirement. When their two years were up, I could say that about half the students did not continue math. Many students in my Pre-Cal class always had a thing about asking the teacher when they were ever going to solve a problem like that in the “real world”. I noticed that the

Integrated Cirriculum Research Paper Integrated curriculums are constantly becoming more popular with educators each and every day. It seems that with this increased enthusiasm there should also be an increased activity of integration taking place within the classroom. This, however, does not seem to be the case. Math and Science integration has been widely talked about and supported by educators young and old, but critics state that there is little evidence to show the effectiveness of integration

Mathematics is considered a science that manipulates symbols according to given rules or instructions which can also be considered the science of numbers. My belief is that being literate in mathematics is crucial in this world because I consider math to be the base to explain various quantitative disciplines in fields such as finance, physics, biology, economics and chemistry. Moreover, I have always had a positive attitude while solving mathematical problems because there are so many different

above average student, receiving A’s and B’s on my report card. However, sophomore year hit me like a bolt of lightning. I failed two semesters of AP Calculus AB class. In order to bounce back from this fiasco, I retook the class to prove to myself that I could have done better. Through hard work, late nights, and dedication, I was able to pass Calculus the second time. If only I tried harder, I could have passed on the first try. My teacher that year was known as one of the “hardest” math teachers

Introduction: Pi has been used for the past 250 years. The first zero in pi comes after the first 31 digits. Archimides was the first person to study pi in the ancient times. Objective: The objective for this lab was to determine an experimental value for pi by measuring sixteen different round objects, and calculate the percent error between the experimental value and the accepted value. Hypothesis: If the circumference and diameter are measured on a round object then the relationship of the graph