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Diffstat (limited to 'usth/MATH2.2/hw')
| -rw-r--r-- | usth/MATH2.2/hw/README.md | 22 | ||||
| -rwxr-xr-x | usth/MATH2.2/hw/cubic | 25 | ||||
| -rw-r--r-- | usth/MATH2.2/hw/fibonacci.m | 7 | ||||
| -rw-r--r-- | usth/MATH2.2/hw/homework.pdf | bin | 0 -> 122465 bytes | |||
| -rwxr-xr-x | usth/MATH2.2/hw/linear | 11 | ||||
| -rwxr-xr-x | usth/MATH2.2/hw/quadratic | 14 |
6 files changed, 79 insertions, 0 deletions
diff --git a/usth/MATH2.2/hw/README.md b/usth/MATH2.2/hw/README.md new file mode 100644 index 0000000..fbb5730 --- /dev/null +++ b/usth/MATH2.2/hw/README.md @@ -0,0 +1,22 @@ +# Numerical Methods: Homework 1 + +My name is Nguyễn Gia Phong, my student ID is BI9-184. + +The homework were written in Octave and saved as + +* `linear`: interactive script to solve linear equation +* `quadratic`: interactive script to solve quadratic equation +* `cubic`: interactive script to solve cubic equation +* `fibonacci.m`: function `fibonacci (n)` returning a vector containing + Fibonacci numbers from F<sub>1</sub> to F<sub>n</sub> + +The scripts are named without any file extension following the \*nix traditions. +The homework can be downloaded as a whole in a ZIP package using the button +near the top-left corner, or alternatively cloned using `git`: + + git clone https://gist.github.com/McSinyx/1d9ff91d1ecfd60254c188bddb7926d5 + +If this causes any inconvenience, please let me know. + +[](http://creativecommons.org/licenses/by-sa/4.0/) +This work is licensed under a [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/). diff --git a/usth/MATH2.2/hw/cubic b/usth/MATH2.2/hw/cubic new file mode 100755 index 0000000..ca24739 --- /dev/null +++ b/usth/MATH2.2/hw/cubic @@ -0,0 +1,25 @@ +#!/usr/bin/env octave +disp ("Solve quadratic equation a*x^3 + b*x^2 + c*x + d = 0"); +a = input ("a = "); +while (a == 0) + disp ("a must be nonzero"); + a = input ("a = "); +end +b = input ("b = "); +c = input ("c = "); +d = input ("d = "); + +% Using the trigonometric and hyperbolic solutions on Wikipedia: +% https://en.wikipedia.org/wiki/Cubic_function +p = (3*a*c - b^2) / (3*a^2); +q = (2*b^3 - 9*a*b*c + 27*a^2*d) / (27*a^3); +if (p == 0) + disp ("The given cubic equation has only one distinct solution:"); + x = cbrt(-q) - b/a/3 +else + r = 2 * sqrt(-p/3); + disp ("The three solutions of the given quadratic equation are:"); + for k = 0 : 2 + x = r * cos((acos(3*q/p/r) - 2*pi*k) / 3) - b/a/3 + end +end diff --git a/usth/MATH2.2/hw/fibonacci.m b/usth/MATH2.2/hw/fibonacci.m new file mode 100644 index 0000000..340c108 --- /dev/null +++ b/usth/MATH2.2/hw/fibonacci.m @@ -0,0 +1,7 @@ +function fib = fibonacci (n) + fib = 0 : n; + for i = 2 : n + fib(i + 1) = fib(i) + fib(i - 1); + end + fib = fib(2:end); +end diff --git a/usth/MATH2.2/hw/homework.pdf b/usth/MATH2.2/hw/homework.pdf new file mode 100644 index 0000000..9d3f2e9 --- /dev/null +++ b/usth/MATH2.2/hw/homework.pdf Binary files differdiff --git a/usth/MATH2.2/hw/linear b/usth/MATH2.2/hw/linear new file mode 100755 index 0000000..fad7e67 --- /dev/null +++ b/usth/MATH2.2/hw/linear @@ -0,0 +1,11 @@ +#!/usr/bin/env octave +disp ("Solve quadratic equation ax + b = 0"); +a = input ("a = "); +while (a == 0) + disp ("a must be nonzero"); + a = input ("a = "); +end +b = input ("b = "); + +disp ("The two solutions of the given linear equation is:"); +x = -b / a diff --git a/usth/MATH2.2/hw/quadratic b/usth/MATH2.2/hw/quadratic new file mode 100755 index 0000000..b6ea91a --- /dev/null +++ b/usth/MATH2.2/hw/quadratic @@ -0,0 +1,14 @@ +#!/usr/bin/env octave +disp ("Solve quadratic equation a*x^2 + b*x + c = 0"); +a = input ("a = "); +while (a == 0) + disp ("a must be nonzero"); + a = input ("a = "); +end +b = input ("b = "); +c = input ("c = "); + +sd = sqrt(b*b - a*c*4); +disp ("The two solutions of the given quadratic equation are:"); +x0 = (-b - sd) / a / 2 +x1 = (-b + sd) / a / 2 |