By Stephan Kaufmann

"A Crash path in Mathematica" is a compact advent to this system Mathematica, that is regularly occurring in arithmetic, in addition to within the average and engineering sciences.

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**Extra resources for A Crash Course in Mathematica**

**Example text**

In[86]:= Qul[86]= Solve [a x + b == ~_-la+b}} {{X ~ 1, xl 52 Part 1 In[87):= Out[87)= Solve [myEquation, x] { {x --) - -1a+ b }} Let us give the solution a name: In[88):= Out[88)= result = % {{x --) _ -1a+ b }} The result of So 1 ve is written as a list of transformation rules, which may be irritating at first. In addition, it is a nested list, because we can also solve sets of equations with several solutions and several unknowns. We get the first (and in this case only) solution by accessing the first (and only) element of the list: In[89):= Out[89)= first Solution = result [[1]] { x--) -1+b} ---- a This is a transformation rule which we can apply to expressions.

In addition, Mathematica recognizes many definite integrals which can be written as hypergeometric or other special functions. The function NIn tegra te returns numerical approximations of definite integrals. 22919 • Differential Equations Analogous to algebraic equations, differential equations are also written using ==. The functional dependence of variables must be indicated explicitly. Derivatives are usually written using the form x' [t] instead of D [x [ t] , t] . In[136]:= Out[136]= x" [t] + x[t] == 0 x[t] +x" [t] == 0 We get the solution with DSol ve, where the unknown function and the independent variable are given as second and third argument.

X2 + Y == 1, 3 Y - x == a} • Elimination of Variables Eliminate x and y from the following set of simultaneous equations: {x2 +y+z==l, 3y-x==a, x+2z==0} • Inequalities Determine where the inequalities Ix 2 neously). 6 Calculus • Limits Limits are determined with the function Limi t as follows: In[117):= Out[117)= In[118):= Limit[(x-1)A21 (xA2-1), x->l] 0 Limit [ (x _ 1) 2 x2 - , x-+ -1] 1 Out[118)= We see that the symbol Inf ini ty or grals, among other things. In[119):= Out[119)= 00 is predefined.