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Unformatted text preview: Lecture 7 Symbolic Computations The focus of this course is on numerical computations, i.e. calculations, usually approximations, with floating point numbers. However, Matlab can also do symbolic computations which means exact calculations using symbols as in Algebra or Calculus. You should have done some symbolic Matlab computations in your Calculus courses and in this chapter we review what you should already know. Defining functions and basic operations Before doing any symbolic computation, one must declare the variables used to be symbolic: > syms x y A function is defined by simply typing the formula: > f = cos(x) + 3*x^2 Note that coefficients must be multiplied using * . To find specific values, you must use the command subs : > subs(f,pi) This command stands for substitute , it substitutes π for x in the formula for f . If we define another function: > g = exp(-y^2) then we can compose the functions: > h = compose(g,f) i.e. h ( x ) = g ( f ( x )). Since f and g are functions of different variables, their product must be a function of two variables: > k = f*g > subs(k,[x,y],[0,1]) We can do simple calculus operations, like differentiation: > f1 = diff(f) indefinite integrals (antiderivatives): > F = int(f) and definite integrals: > int(f,0,2*pi) To change a symbolic answer into a numerical answer, use the double command which stands for double precision , (not times 2): > double(ans) Note that some antiderivatives cannot be found in terms of elementary functions, for some of these it can be expressed in terms of special functions: > G = int(g) and for others Matlab does the best it can: 20 21-6-4-2 2 4 6-1-0.5 0.5 1 x cos(x 5 ) Figure 7.1: Graph of cos( x 5 ) produced by the ezplot command. It is wrong because cos u should oscillate smoothly between...
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