Simple mathematical programs created in free time.
C programming language (Using 128 bit floating point percission):
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Taylor series calculates the series upon given function and percision.
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SqrtOfPiE calculates the value upon given percision, pi is calculated with Euler's formula and e with Taylor series expansion.
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SumOfNaturalNum calculates partial sums of n given natural numbers and aproximates a parabola using least squares theorem for sequential natural numbers with partial sums of the given natural number. Then it caluculates the difference between the computed value and theorethical value of -1/12.
Numerical methods in Matlab:
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LU decomposition with direct and reverse insertion with tridiagonal version of those.
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Cholesky decomposition for tridiagonal positive definite matrices
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Bisection for finding zeroes of a function
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Secant method for finding zeroes of a function
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Tangent method for finding zeroes of a function
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Newton method for finding function intersections
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Euler method for solving DE y' = f(x, y)
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Modified Euler method for solving DE y' = f(x, y)
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Leapfrog method for solving DE y' = f(x, y)
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Runge-Kutta method of 4-th order for solving DE y' = f(x, y)
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Trapezoidal rule for solving DE y' = f(x, y)
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Methods for numerical integration for numerical calculation of integrals
- Rectangular rule
- Trapezoidal rule
- Simpson 1/3 rule
- Simpson 3/8 rule
- Romberg method