Numerics – interactive

Risse T.

The objective of this document is to provide an oportunity to explore different basic numerical algorithms interactively. Topics covered include precision of computation, vector calculus in 2D and 3D, systems of linear equations, some numerical constants, evaluation of user specified functions and of the elementary functions with their inverse functions (exponential, logarithm, trigonometric and hyperbolic), approximation of zeroes and of integrals, and numerical solutions of first order ordinary differential equations.

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Table of contents :
Conventions and Usage……Page 2
Floating Point Arithmetic……Page 3
Floating Point Arithmetic with Given Precision……Page 4
Length or Modulus a of Vectors in the Plane……Page 5
Vector Product a x b of Vectors in Space……Page 6
Systems of Linear Equations……Page 7
Gauß’ Elimination Method……Page 8
Gauß-Seidel Method……Page 9
Some Constants……Page 11
Evaluation of Functions……Page 12
Logarithm……Page 13
Cotangent and Arc Cotangent……Page 14
Hyperbolic Cotangent……Page 15
CORDIC — Evaluation of Elementary Functions in Hardware……Page 17
Evaluating Trigonometric Functions……Page 18
Evaluating Inverse Trigonometric Functions……Page 20
Transforming Cartesian to Polar Coordinates……Page 21
Computation of Zeroes……Page 22
Computation of Zeroes per Intervall Bisection……Page 23
Computation of Zeroes per regula falsi……Page 24
Computation of Zeroes per Newton Method……Page 25
Integration per Trapezoidal Rule……Page 26
Integration per Simpson Rule……Page 27
Heun-Method……Page 28
Runge-Kutta-Method……Page 29
Interactive Synopsis of these Methods……Page 30
Systems of Ordinary First Order Differential Equations……Page 31
Exponential Function and Logarithm……Page 32
Sine and Cosine……Page 33
Tangent and Cotangent……Page 34
Hyperbolic Sine and Hyperbolic Cosine……Page 35
Hyperbolic Tangent and Hyperbolic Cotangent……Page 36