# Tagged Questions

67 views

### Two methods of finding a function $f$ such that $Mdx+Ndy=0$ on the curves $f(x,y)=c$

this problem is from my class,i did one way and got one answer,professor did it in another way and got another answer.question is:Find $f(x,y)=constant$ where differential equation is ...
93 views

### Solving a particular system of differential equations

The problem I'm trying to solve is this: $X'(t) \in \mathbb{R}^3 \,, \, \omega = (\omega_1,\omega_2,\omega_3)$ Find the general solution for $$X'(t) = \omega \times X(t)$$ After doing the cross ...
37 views

80 views

### Minimizing the following objective function with matrices

Suppose $A$ and $B$ are known matrices, and we are to find matrix $X$ that minimizes the following function, $$\frac{1}{2}||X||^2+\frac{1}{2}||X^TAX-B||^2$$ Taking the relevant derivative w.r.t $X$ ...
62 views

31 views

### Existence and Uniqueness Theorem--Question Regarding Regions

I have a question. Suppose I have a differential equation for which I want to find the values at which $f(x,y)$ and $âˆ‚f/âˆ‚y$ are discontinuous, that I might know the points at which more than one ...
47 views

### Directional derivatives, linear maps, and uniform convergence

The Exercise Let $f(x,y)=x$ if $|y|>x^2$ and $f(x,y)=0$ otherwise. Show that all the directional derivatives of $f$ exist at the origin but there does not exist a linear map $D$ such that ...
25 views

### Directional Differentiability follows from Multivariate Differentiability

The Exercise: "Suppose that a function $f: R^n \to R^m$ is differentiable at $x \in R^n$. Show that the directional derivative of $f$ in any direction $v\in R^n$ at $x$ exists and $D_vf(x)=Df(x)(v)$" ...
89 views

### Derivative of a Linear Map

I'm devastatingly incompetent at linear algebra and multivariable calculus. I just cannot understand it at all. Here's the easiest problem from my homework, and my attempt at solving it, and where I ...
95 views

### Integrating two equations that equal, what happens to the constant on one of the sides?

In class, we were talking about Newton's 3rd law and how to integrate. $\int(g)dt = \int(y''(t))dt \implies g(t) + C = y'(t)$ I am confused about why the right hand side of the equation doesn't get ...
118 views

68 views

### Help with solving for a flow curve:

So I'm preparing for a final exam in multivariable and our textbook posed the following question: find the flow lines of F(x,y) = (-y, x) Which I can't seem to solve correctly. We are told that a ...
75 views

### Motion in three dimensions with friction.

I am trying to represent the motion of an object in three-dimensional space that is undergoing acceleration, friction, and drag, where: acceleration = $\vec A$ friction = $F$ drag = $D$ The ...
Suppose I have a vector field $\mathbf{A}(x,y,z)$, of which I know: $$\mathbf{A}(x,y,0)=(1+\alpha x)\hat{z}$$ Thus, I know the value of $\mathbf{A}$ in the $xy$-plane. Say, within ...