Introduction to Maple For Mathematics Students by Mustafa Y.T.

By Mustafa Y.T.

This path is a laboratory within the use of the Maple desktop arithmetic application to domathematics. With the arrival of speedy and inexpensive pcs, courses like Maple will change hand calculators and mathematical handbooks (like imperative tables) for many arithmetic students.Mathematics departments have already visible this occurring in a slightly random and unplanned method, so this path used to be invented to supply scholars with an creation to using this robust software. when you examine it you may be hooked and you'll ask yourself the way you ever acquired alongside with out it. this may particularly be so in case you do not simply have Maple to be had at the division desktops, yet have it additionally by yourself laptop laptop, or maybe higher, in your computer. The time is swiftly coming near near whilst laptops for arithmetic scholars may be as universal as slide principles have been in olden instances. If there's any approach to pull it off, you need to get a computer.

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2); 56 Using this value of λ, make a plot of the solution. 9 ∂ p = −mω 2 x , where p is the 0 ∂t mu ∂ , where u is the particle velocity u = x . (a) Write this relativistic momentum p = ∂t u2 1− c2 The equation of motion of a relativistic harmonic oscillator is equation of motion in the form of two coupled first order differential equations. The first one is easy because it has been given in the first line of this problem. The second one is of the form ∂ x = ?. ∂t Solve for u in terms of p to get this second equation.

Do you end up in the same place? ) Rotation should not change the magnitude of the vector; does this sequence of matrix multiplications preserve the magnitude of the vector? You can get the magnitude of a vector v with the command Norm(v,2). ▬Inverse, determinant, norm, etc. Define some matrices to play with > restart:with(LinearAlgebra): > B:=Matrix([[1,2,3],[4,5,6],[7,8,9]]); > C:=Matrix([[3,2,1],[5,6,4],[9,7,8]]); MatrixInverse: To get the inverse of a matrix, say C, just do this > MatrixInverse(C); To check it does this > Multiply(C , MatrixInverse(C)); Determinant: Get the determinant of a matrix this way > Determinant(B);Determinant(C); Transpose: Get the transpose of a matrix; > Transpose(C); > E:=Matrix([[1,2,3]]); > Transpose(E); Trace: The trace of a square matrix is the sum of the diagonal elements.

2) Since the whole point of doing a numerical calculation is to get a number and since Maple is loath to ever give us numbers, doing useful things with what Maple returns as the numerical solution of a differential equation is a bit awkward. We are likely to become more frustrated in this section of the text than any other so far. (3) We will have much better luck at getting Maple to give us what we want if we define our differential equations as first order sets than if we use 2nd, and higher, order derivatives.

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