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  1. M

    B Optimisation problem

    Firstly, I'm not even sure how to frame this mathematically, but I'd be curious to know what kind of problem it is and what kind of subjects within maths it requires to be able to solve it. Here's my problem-- I've set it up in excel to help you visualise it. There is a different amount of...
  2. M

    Parameterising a line given by two points

    I'm working on a green's theorem integral and I'm given a line (0,0) to (1,2) which i parameterise as (t,2t) but the answer is actually (1-t, 2(1-t)) and if I use my parameterisation on the integral I get a different answer!
  3. M

    Line integrals in physics

    Wasn't sure which section to put this q in. Just reading now that f(x,y) can represent the density of a semicircular wire and so if you take a line integral of some curve C and f(x,y) you can find the mass of the wire... makes sense. What I don't get is that if I then move the wire around the...
  4. M

    Line integrals

    When I think line integral - I understand when I'm taking a line integral for a function f(x,y) which is in 3D space above a curve that the integral is this curtain type space, just like if you had a 2D function and you find the area under the curve, except now it's turned on its side and it's...
  5. M

    Spherical coordinates

    Homework Statement Find VR_{z}^{2} = \int \!\!\! \int \!\!\! \int_{E} (x^{2} + y^{2})dV given a constant density lying above upper half of x^{2}+y^{2} = 3z^{2} and below x^{2}+y^{2}+z^{2} = 4z. Homework Equations The Attempt at a Solution Why does it say upper half of x^{2}+y^{2} =...
  6. M

    Improving problem solving skills

    I've often been plagued by the thought of being unintelligent and slow compared to others. I seem to take much longer to understand concepts and work out problems. With that said, I do really well at school (but also put in much more time than others). I'm also quite obsessive when it comes to...
  7. M

    Python Trouble understanding recursion (Python)

    I'm trying to understand a function which draws a koch curve using a library which draws (lt = left turn, fd = move forward, t represents an object class). def koch(t, n): if n<3: fd(t, n) return m = n/3.0 koch(t, m) lt(t, 60) koch(t, m) rt(t, 120)...
  8. M

    Algorithm for drawing an arc

    Hi, I'm working through thinkpython and there is an exercise which requires drawing flowers and arcs. I'm having some trouble understanding the arc function. def arc(t, r, angle): """Draws an arc with the given radius and angle. t: Turtle r: radius angle: angle subtended by the...
  9. M

    Center of mass of a lamina

    Homework Statement The boundary of a lamina consists of the semicircles y=\sqrt{1-x^{2}} and y=\sqrt{4-x^{2}} together with the portions of the x-axis that join them. Find the centre of mass of the lamina if the density at any point is proportion to its distance from the origin. Homework...
  10. M

    LaTeX Latex is frustrating

    Latex produces some really good looking documents and because of this I tried to pick it up. I was hoping it would make typing up my maths assignment a much quicker process. What I find insanely frustrating is that because of all the marks up in a .tex file it becomes impossible to navigate...
  11. M

    Using chain rule to derive 2nd derivative

    Homework Statement Use \frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y} and \frac{\partial z}{\partial\theta}=-r\sin\theta\frac{\partial z}{\partial x}+r\cos\theta\frac{\partial z}{\partial y} to show that...
  12. M

    The region within circles r=cosθ and r=sinθ

    Homework Statement Use a double integral to find the area of the region enclosed within both circles of r=cosθ and r=sinθ Homework Equations The Attempt at a Solution I begin by finding the region in polar co-ordinates. For r=\cos\theta 0\leq r \leq\cos\theta...
  13. M

    Trouble taking 2nd deriv of multi variable

    Homework Statement Use * to show --> Homework Equations The Attempt at a Solution So I've begun by trying to take the 2nd derivative of \frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y} Which gives me this...
  14. M

    Double integral for loop of rose r=cos2θ

    Homework Statement Homework Equations The Attempt at a Solution Solution is given. I don't understand how +-∏/4 is found as a range for θ Also why is 0 <= r <= cos2θ r is always r which is defined as cos2θ
  15. M

    Z=f(x,y), x=function, y=function. dz/dx=

    Homework Statement Consider z=f(x,y), where x=rcosθ and y=rsinθ Show that \frac{\partial z}{\partial x}=\cos\theta\frac{\partial z}{\partial r}-\frac{1}{r}\sin\theta\frac{\partial z}{\partial\theta} Homework Equations The Attempt at a Solution Z Connects to X and Y X...
  16. M

    Show that r^2 = x^2 + y^2

    Homework Statement Consider z=f(x,y), where x=rcosθ and y=rsinθ (This is a multi part multi variable calculus assignment question). I've just derived dz/dr and now I'm asked... to show that r^{2}=x^{2}+y^{2}, \theta=a\tan(\frac{y}{x}) Homework Equations The Attempt at a Solution I've...
  17. M

    Rule of thumb for double integral order

    Is there any rule of thumb for which variable should be integrated first?, i.e. to make the whole process of double integration easier.
  18. M

    Direction of the fastest rate of change of a function (Solution inclu)

    Homework Statement Find all the points at which the direction of the fastest rate of change of the function f(x,y)=x^{2}+y^{2}-2x-4y is i+j Homework Equations The Attempt at a Solution The direction of the fastest change is \nabla f(x,y)=(2x-2)i+(2y-4)j, so we need to find all...
  19. M

    Finding the distance from a point to a plane using substitution

    If I want to find the distance from a point to a plane. E.g. (2,1,-1) to the plane x+y+z=1 I know that distance from one point to another is given by: \sqrt{(x-2)^{2}+(y-1)^{2}+(z+1)^{2}} And in this case the solution is to substitute in z=x+y-1 which fits nicely giving us...
  20. M

    Finding a tangent line to a level curve - Don't understand solution

    Homework Statement If f(x,y) = xy, find the gradient vector \nabla f(3,2) and use it to find the tangent line to the level curve f(x,y) = 6 at the point (3,2) Homework Equations The Attempt at a Solution f(x,y)=xy \Rightarrow\nabla f(x,y)=<y,x>,\nabla f(3,2)=<2,3> \nabla...
  21. M

    Drawing a contour map for e^(variable)sine(x-t*variable)

    Homework Statement Draw a contour map for T(x,t)=10e^{-\lambda x}\sin(\omega t-\lambda x) 0\leq\lambda x\leq2\Pi and 0\leq\omega t\leq2\Pi Homework Equations The Attempt at a Solution Because those two variables are within that given range I'm not sure how to do this...
  22. M

    Schools Maths, ROTE and suffering at university

    I picked maths up because I thought it would improve my ability to problem solve - but I found maths at university to be far from what I expected. With all my undergrad subjects like calculus II, multi-variable and even linear algebra everything feels rushed and I have a very hard time getting...
  23. M

    Partial derivatives of f(x,y)

    Homework Statement Where T(x,t)=T_{0}+T_{1}e^{-\lambda x}\sin(\omega t-\lambda x) \omega = \frac{\Pi}{365} and \lambda is a positive constant. Show that T satisfies T_{t}=kT_{xx} and determine \lambda in terms of \omega and k. I'm not to sure what is meant by the latter part of "determine...
  24. M

    The domain on which a function is continuous

    Homework Statement Determine domain on which the following function is continuous f(x,y)= \left\{\begin{array}{cc} \frac{x(x+1)y^{2}}{(x+1)^{2}+y^{2}} & (x,y)\neq(-1,0)\\ 1 & (x,y)=(-1,0) \end{array}\right. Homework Equations The Attempt at a Solution Because the numerator...
  25. M

    Prove the limit exists for xy/(sqrt(x^2+y^2)

    Homework Statement Find the limit, if it exists, or show that the limit does not exist. Stewarts Calculus 7th edition 14.2 Q13. Homework Equations The Attempt at a Solution f(x,y)=\frac{xy}{\sqrt{x^{2}+y^{2}}} The limit along any line through (0,0) is 0, as well as along other paths...
  26. M

    Finding limits in 3D. How do you know on what line to approach?

    So say I have an arbitrary function and I want to know it's limit as x,y approaches 0. I could test what happens when the x axis approaches 0, y axis as it approaches 0 but there are some functions where I'm told that I also need to test what happens when y=mx approaches 0, and then y=x^2 and...
  27. M

    (regression) why would you exclude an explanatory variable

    If someone is interested in modelling data on households to find out whether there is discrimination in the workplace why would they ever leave out variables which are relevant to explaining the dependent variable but not so relevant to the investigation? e.g. lets say they survey age, race...
  28. M

    Testing multiple linear restrictions

    If I have 4 variables in my multiple regression and I'm told to test whether one is significant, and 3 others are not what would I do with the one left over? I thought it would be easy as I could just test whether for H0: variable 1>0, variable 2,3 =0 But what if I'm told to restrict...
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