﻿ Prof. Dr. Serkan Dag

MAPLE WORKSHEETS FOR NUMERICAL METHODS

Following list includes MAPLE worksheet PDF files for numerical methods
For actual MAPLE files you can contact me at the email address sdag@metu.edu.tr

ERROR ANALYSIS
Maclaurin series of the exponential function: File_1_1
Round-off error in the solution of the quadratic equation: File_1_2
Taylor series expansion of cos(x): File_2_1

ROOTS OF EQUATIONS
Graphical method: File_3_1
Bisection method: File_3_2
Root of sin(x) = x^2: File_3_3
Fixed-point iteration: File_4_1
Root of sin(sqrt(x)) - x = 0: File_4_2
Newton-Raphson method for a single equation: File_4_3
Newton-Raphson method for a system of two equations: File_4_4
Roots of the system: (x=y+x^2-0.5; y=x^2-5xy): File_4_5

LINEAR ALGEBRAIC EQUATIONS
Naive Gauss elimination: File_5_1
Gauss-Seidel iterative solver: File_6_1

OPTIMIZATION
Golden-section search for maximum of a function: File_7_1

CURVE FITTING
Linear regression: File_8_1
Polynomial regression: File_8_2
Newton's interpolating polynomials: File_9_1
Lagrange's interpolating polynomials: File_9_2
Cubic splines: File_9_3

NUMERICAL DIFFERENTIATION AND INTEGRATION
Integration commands in MAPLE: File_10_1
Trapezoidal rule: File_10_2
Simpson's 1/3 rule: File_10_3
Derivation of two-point Gauss-Legendre points and weights: File_11_1
Multiple application of three-point Gauss-Legendre quadrature: File_11_2

ORDINARY DIFFERENTIAL EQUATIONS
Euler's method: File_13_1
Numerical results by Euler's method: Euler.pdf
Heun's method: File_13_2
Numerical results by Heun's method: Heun.pdf