![]() Here are a few exercises to test the Plot command. To integrate x*Sqrt between x = 0 and x = 1, use the command The last x in the command Integrate, x] indicates the variable of integration.ĭefinite integrals are done similarly. For example, to integrate x*Sqrt use the command We can obtain the same result from the single commandįinally, we can integrate functions symbolically. Īfter evaluating the cell defining f, the derivative can be found be evaluating The definition statement is indicated by :=, the variable in the function is indicated by an underscore x_, and the variable is enclosed by square brackets f. ![]() Note some features of defining functions. For example, to differentiate sin(x 2), first define a function FunctionRange f, x, y, dom considers f to be a function with arguments and values in the domain dom. In addition to graphics, Mathematica can perform symbolic computations, including differentiation and integration. Here is an animation of the resulting pictures. We can plot more than one function on the same graph, and use different colors, with commands of this form. Is it clear how to plot a domain other than 0 ≤ x ≤ 5? The original idea for such formulas seems to be due to C. Note the first letter of Sin is capitalized, and the argument is enclosed in square brackets: Sin. Runge-Kutta of order 4 The fourth-order formula, known as the Runge-Kutta formula, has been used extensively to obtain approximate solutions of differential equations of first, second, and higher orders. To plot the graph of sin(x 2), for x bewteen 0 and 5, use this command In addition to the obvious arithmetic operations, Mathematica can do graphics and symbolic computations. If you begin to get badly wrong answers or strange error messages, try quitting Mathematica and restarting it. Someone may have been using Mathematica on this machine before you. For instance, the x-axis should range from -0.3 to 1.3 and similarly for the y-axis. Mathematica remembers values assigned to symbols, even if the notebook in which the symbol was defined has been closed, so long as Mathematica has not been shut down. I am puzzled how I can modify the Axes Range. Introduction to Mathematica Basic Mathematica CommandsĪ note on Mathematica's memory.
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