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）
Find all solutions of the linear system $\left|\begin{array}{l}x+3 y+3 z=10 \ x+2 y+3 z=8 \ x+y+4 z=9\end{array}\right|$
Jake and Maggie are siblings. Jake has twice as many sisters as brothers and Maggie has just as many brothers as sisters. How many kids are there in this family? (Any resemblance to the Gyllenhaal siblings is purely coincidental).
A $8 \mathrm{~km}$ trip downstream from the Swiss waterfall “Rheinfall” to the village “Rheinau” takes 20 minutes. The return trip takes 40 minutes. How fast is the speed $v$ (in $\mathrm{km} / \mathrm{h}$ ) of the boat traveling relative to the water, and how fast is the speed $s$ (in $\mathrm{km} / \mathrm{h})$ of the river?
On a heating mesh, the temperature at exterior mesh points is 0,100 or $200 \mathrm{~F}$ as given in the picture. In thermal equilibrium, each interior mesh point has the average of the temperatures at the 4 adjacent points. For example $T_2=\left(T_3+T_1+100+0\right) / 4$. Find the temperatures $T_1, T_2, T_3$.A ayurvedic dieter eats rice and yogurt only. Rice contains 3 grams of protein and 30 grams of carbs per serving, while yogurt contains 12 grams of protein and 20 grams carbs. If our healthy friend wants to consume 60 grams of protein and 300 grams of carbohydrates, how many servings of rice and yogurt are needed?
Row reduce the following matrices $A, B$. Try to do it in as few
$$
\text { steps as possible. a) } A=\left[\begin{array}{ccccc}
1 & 2 & 3 & 4 & 5 \
2 & 4 & 6 & 8 & 10 \
3 & 6 & 9 & 12 & 15 \
4 & 8 & 12 & 16 & 20 \
5 & 10 & 15 & 20 & 25
\end{array}\right] \text {, b) } B=\left[\begin{array}{ccccc}
1 & 1 & 0 & 0 & 0 \
1 & 1 & 1 & 0 & 0 \
0 & 1 & 1 & 1 & 0 \
0 & 0 & 1 & 1 & 1 \
0 & 0 & 0 & 1 & 1
\end{array}\right] \text {. }
$$
Solve the system of equations $A \vec{x}=\vec{b}$ for
$$
A=\left[\begin{array}{cccc}
1 & 1 & 1 & 1 \
1 & 2 & 4 & 8 \
1 & 3 & 9 & 27 \
1 & 4 & 16 & 64
\end{array}\right], \vec{b}=\left[\begin{array}{c}
1 \
8 \
27 \
64
\end{array}\right]
$$
by row reducing the augmented $4 \times 5$ matrix $B=[A \mid b]$.
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！
