Download Numerics - interactive by Risse T. PDF

By Risse T.

The target of this rfile is to supply an oportunity to discover varied easy numerical algorithms interactively. themes lined contain precision of computation, vector calculus in 2nd and 3D, platforms of linear equations, a few numerical constants, overview of person precise capabilities and of the easy features with their inverse capabilities (exponential, logarithm, trigonometric and hyperbolic), approximation of zeroes and of integrals, and numerical suggestions of first order traditional differential equations.

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E. e. get y(x) = xo = yo = xn = n= exact test y= Heun y = Euler-Cauchy y = Runge-Kutta y = )= repeat Euler y(x) = y( step reset Ex. Experiment with y = cos x and y(0) = 0 or y = xy and y(0) = 1 or the like. Ex. Compare the different methods by their complexity in terms of number of evaluations of f (x, y). 6 Systems of Ordinary First Order Differential Equations The methods of the previous sections can be applied to systems of ordinary first order differential equations also. The default example is the development of predator and prey populations in time.

3 Tangent and Arc Tangent . . . . . . . . . . 4 Cotangent and Arc Cotangent . . . . . . . . 14 Hyperbolic Functions with their Inverse Functions . . . . . . . . . . . 1 Hyperbolic Sine . . . . . . . . . . . . . 2 Hyperbolic Cosine . . . . . . . . . . . . 3 Hyperbolic Tangent . . . . . . . . . . . 4 Hyperbolic Cotangent . . . . . . . . . . . 1 Evaluating Trigonometric Functions . . . . . . . . . 2 Evaluating Inverse Trigonometric Functions .

3 Euler-Cauchy-Method . . . . . . . . . . . . . 4 Runge-Kutta-Method . . . . . . . . . . . . . 5 Interactive Synopsis of these Methods . . . . . . . . 6 Systems of Ordinary First Order Differential Equations . . . 1 Exponential Function and Logarithm . . . . . . . . . 2 Sine and Cosine . . . . . . . . . . . . . . . 3 Tangent and Cotangent . . . . . . . . . . . . 4 Hyperbolic Sine and Hyperbolic Cosine . . .

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