MY-ASSIGNMENTEXPERT™可以为您提供sydney MATH3078 Partial Differential Equations偏微分方程的代写代考和辅导服务！
这是悉尼大学 偏微分方程的代写成功案例。
MATH3078课程简介
The aim of this unit is to introduce some fundamental concepts of the theory of partial differential equations (PDEs) arising in Physics, Chemistry, Biology and Mathematical Finance. The focus is mainly on linear equations but some important examples of nonlinear equations and related phenomena re introduced as well. After an introductory lecture, we proceed with first-order PDEs and the method of characteristics. Here, we also nonlinear transport equations and shock waves are discussed. Then the theory of the elliptic equations is presented with an emphasis on eigenvalue problems and their application to solve parabolic and hyperbolic initial boundary-value problems. The Maximum principle and Harnack’s inequality will be discussed and the theory of Green’s functions.
Prerequisites
At the completion of this unit, you should be able to:
- LO1. demonstrating the ability to recognize different types of partial differential equations: “linear” or “nonlinear”, “order of the given equation”, “homogeneous” or “inhomogeneous”, and if it concerns 2nd-order equations, whether they are of “elliptic”, “parabolic”, or “hyperbolic” type
- LO2. demonstrating the conceptional understanding of how to apply different methods for solving different types of partial differential equations. Those methods include the use of classical ODE-concepts to solve PDEs
- LO3. understanding the definitions, main theorem, and corollaries of Green’s functions and Poisson kernel
- LO4. be fluent with “change of variable” into polar, cylindrical and spherically coordinates and to be able to compute partial derivatives in these coordinates
- LO5. develop an appreciation and strong working knowledge of the theory and application of elementary partial differential equations
- LO6. be fluent in using generalized Fourier transforms to solve parabolic and hyperbolic initial boundary value problems where the spatial variable might be of more than one variable
MATH3078 Partial Differential Equations HELP（EXAM HELP， ONLINE TUTOR）
Given $A=\left[\begin{array}{ccccc}2 & 3 & 4 & 5 & 6 \ 3 & 4 & 5 & 6 & 7 \ 4 & 5 & 6 & 7 & 8 \ 5 & 6 & 7 & 8 & 9 \ 6 & 7 & 8 & 9 & 10\end{array}\right]$. In each of the vectors $\vec{b}$ given, determine whether the system $A \vec{x}=\vec{b}$ has 0,1 or $\infty$ many solutions.
a) $\vec{b}=\left[\begin{array}{c}1 \ 1 \ 1 \ 1 \ 1\end{array}\right]$
b) $\vec{b}=\left[\begin{array}{l}1 \ 2 \ 3 \ 2 \ 1\end{array}\right]$
c) $\vec{b}=\left[\begin{array}{l}5 \ 6 \ 7 \ 8 \ 9\end{array}\right]$
d) $\vec{b}=\left[\begin{array}{l}0 \ 0 \ 0 \ 0 \ 0\end{array}\right]$
e) $\vec{b}=\left[\begin{array}{l}0 \ 0 \ 0 \ 0 \ 1\end{array}\right]$
Consider the set $X$ of all $2 \times 2$ matrices with matrix entries 0 or
The probability of a set of matrices $Y$ with some property is the number of matrices in $Y$ divided by the number of matrices in $X$.
a) What is the probability that the rank of the matrix is 1 ?
b) What is the probability that the rank of the matrix is 0 ?
c) What is the probability that the rank of the matrix is 2 ?
As in the previous problem, now also the 2 -vector $b$ take randomly the values 0,1 , we can look at all the possible equations $A x=b$, where $A, b$ are obtained with 0 or 1 entries. The probability space has now 64 elements.
a) What is the probability that the system has a unique solution?
b) What is the probability that the system has no solution?
c) What is the probability that the system has infinitely many solutions?
Build your own system of equations for three variables:
a) An example with exactly one solution.
b) An example with no solutions.
c) An example where the solution is a plane.
d) An example where the solution is a line.
e) An example where the solution space is three dimensional.
In a herb garden, the soil has the property that at any given point the humidity is the sum of the neighboring humidities. Samples are taken on a hexagonal grid on 14 spots. The humidity at the four locations $x, y, z, w$ is unknown. Solve the equations $\left|\begin{array}{rr}\mathrm{x}= & \mathrm{y}+\mathrm{z}+\mathrm{w}+2 \ \mathrm{y}= & \mathrm{x}+\mathrm{w}-3 \ \mathrm{z}= & \mathrm{x}+\mathrm{w}-1 \ \mathrm{w}= & \mathrm{x}+\mathrm{y}+\mathrm{z}-2\end{array}\right|$ using row reduction.
MY-ASSIGNMENTEXPERT™可以为您提供SYDNEY MATH3078 PARTIAL DIFFERENTIAL EQUATIONS偏微分方程的代写代考和辅导服务！
