Term Project Applications of Computer Programming in Earth Sciences Instructor: Dr. Cheng-Chien LiuCheng-Chien Liu Department of Earth Sciences National Cheng Kung University Last updated: 12 December 2015Chapter

Project description  Solution of Linear Algebraic Equations Gauss-Jordan matrix inversion and linear equation solution (2.1) Linear equation solution, backsubstitution (2.3) （駱守凡） Singular value decomposition of a matrix (2.6)  Interpolation and Extrapolation Two-dimensional polynomial interpolation (3.6) （張家鳳） Two-dimensional bicubic interpolation (3.6) （劉益廷） Two-dimensional spline interpolation (3.6)

Project description (cont.)  Integration of Functions Integrate a function over a three-dimensional space (4.6) （林維芝）  Evaluation of Functions Evaluate a polynomial and its derivatives (5.3) （李涵瑜）  Random Numbers Random deviates from DES-like hashing (7.5) （蘇鴻林） Adaptive multidimensional Monte Carlo integration (7.8) （王博賢）

Project description (cont.)  Sorting Sort an array by quicksort method (8.2) （王若梅） Find the Nth largest, without altering an array (8.5) （盧旭宇） Find M largest values, without altering an array (8.5) （黃姿勳）  Root Finding and Nonlinear Sets of Equations Find root of a function by Ridders‘ method (9.2) （劉晃丞） Find root of a function by Brent's method (9.3) （歐兆強） Find root of a function by Newton-Raphson and bisection (9.4) （陳治宇） roots of a polynomial by Laguerre's method with deflation (9.5) （蕭雅竹）

Project description (cont.)  Eigensystems Eigenvalues and eigenvectors of a symmetric matrix (11.1) ( 李奇峰 )  Fast Fourier Transform Fast Fourier transform in multidimensions (12.4) ( 江彥廷 )  Fourier and Spectral Applications Correlation or autocorrelation of data using FFT (13.2) ( 唐健庭 )  Modeling of Data Fit a polynomial using LFIT or SVDFIT (15.4)