You can write the submission in word or using latex and export it as a file. You can take a screenshot of the codes you modify and enter in the file and everything should be a single file document.
\nTask 1
\nExplain what the program below performs line by line:<\/p>\n
Task 2
\nGiven system of differential equations:<\/p>\n
Set up the system in matrix form (x\u00b4=Ax there x= ).
\nSketch the direction vector for the solution curve at the point (-2, 1).
\nDetermine eigenvalues and eigenvectors of A
\nSolve the system given x(0)=0,y(0)=10 (the solution curve passes the point
\n(0,10) at t = 0).
\nSolve the differential equation system:<\/p>\n
Write briefly what the following program performs and adapt the program by writing appropriate syntax \/ mathematical expressions or numbers to sketch the solution curve in part c)<\/p>\n
Given the 2nd order differential equation
\nmx\u2019\u2019+ ax\u2019 + kx = cos x
\nthere m = 1[kg],a = 0.4 [kg\/s],k = 0.5 [kg\/s^2 ],x(0) = 2,x\u2019 (0) = 1.5.<\/p>\n
Write about the given differential equation of a differential equation system. (Hint: Let \u2019= y). Then customize the code below to this system as must outline the solution curve of the system over the interval [0,6].
\nTask 3
\nLet f (x,y)= x y^2 be a function with the definition set the (x,y) so that
\n2x^2+y^2=6
\nExplain how we can know that f has the definition set of maximum point and minimum point. Explain why f does not have stationary points.
\nDetermine the largest and smallest value of f using the Lagranges method.
\nWhat is the answer to parts a) and b) if the definition set is 2x^2 + y^2= 6?
\nLet h: R^2 ? R be a function given by h(x,y)=4-x^2-y^2
\nFind the level curve of f in the point P(1,-1). Determine ?h(1 ,-1).
\nDraw the point P, as well as the level curve and the gradient to h at this point.
\nCalculate how fast h changes at point P in the direction
\nIn which direction from point P is this change greatest? (Hint: the direction can be given as a vector).<\/p>\n","protected":false},"excerpt":{"rendered":"
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