MY-ASSIGNMENTEXPERT™可以为您提供stanford Math220 Ordinary Differential Equations常微分方程的代写代考和辅导服务！
这是斯坦福大学 常微分方程课程的代写成功案例。
Math220课程简介
Grading policy: The grade will be based on the weekly homework (25%), on the in-class midterm exam (30%) and on the in-class (i.e. not take-home, to take place during finals week, as designated by the registrar) final exam (45%).
The homework will be due in class or in the instructor’s mailbox by 9am on the designated day, which will usually (but not always) be Fridays. You are allowed to discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution, and be able to reproduce it yourself. This ensures that, apart from satisfying a requirement for this class, you can solve the similar problems that are likely to arise on the exams.
Prerequisites
Course Description : We will cover most of the textbook. This includes formulating physical systems as differential equations, learning various methods to solve them, basics of infinite series and how to use them to solve differential equations, studying linear and nonlinear systems of differential equations, and topological methods.
Learning Outcomes:: The broad learning goals of the course are:
Model various physical phenomena with differential equations
Understand that solutions to differential equations can be addressed with both exact methods and qualitative methods
Math220 Ordinary Differential Equations HELP（EXAM HELP， ONLINE TUTOR）
Roughly sketch the slope field associated to the first-order ODE
$$
\frac{d y}{d x}=\frac{x}{y} .
$$
(Note that along the line $y=0$ the slope is infinite, so you should draw a vertical line there.) Sket ch the int egral curve for each of the following initial conditions: $y(0)=2$, $y(2)=0$, and $y(-1)=-1$
Solve the general non-homogeneous first-order linear ODE with constant coefficients
$$
\frac{d y}{d x}+a y=b
$$
using the same method we used in class to solve the homogeneous version $y^{\prime}+a y=0$.
Solve the IV P
$$
\frac{d y}{d x}=-3 x^2 y^2, \quad y(0)=1 .
$$
If we wanted $y(0)=0$ instead, what would be the solution?
Consider the ODE
$$
\frac{d y}{d x}=\frac{\sin (x)^2 x y}{2-e^x}
$$
Is it linear? Does there exist a solution with $y(0)=0$ ? What is the interval of validity for the solution?
Consider the partial differ ential equation
$$
\frac{\partial f}{\partial x}+y \frac{\partial f}{\partial y}=f
$$
for the two-variable function $f(x, y)$. Check that both
$$
f(x, y)=e^x, \quad f(x, y)=e^x+y
$$
are solutions satisfying the initial condition that $f(x, 0)=e^x$ for all $x$. So we see that IVPs for PDEs do not have unique solutions, and that something special happens for ODEs to guarantee uniqueness.
MY-ASSIGNMENTEXPERT™可以为您提供STANFORD MATH220 ORDINARY DIFFERENTIAL EQUATIONS常微分方程的代写代考和辅导服务！
