Computing in Geophysics

Course Description

Prerequisites

References

Course Contents

• Chapter 1: Preliminaries
• 1.1 Numerical Methods and Computing in Geophysics
• 1.2 Mathematical Model, Algorithm, and Error Analysis
• Chapter 2: System of Linear Equations
• 2.1 The Matrices System
• 2.2 Naive Gauss Elimination Method
• 2.3 Gauss-Jordan Elimination Method
• 2.4 Gauss-Seidel Elimination Method
• 2.5 LU Decomposition Method
• Chapter 3: Curve Fitting
• 3.1 Linear Least-Square Regression
• 3.2 Non-linear Least-Square Regression
• 3.3 Interpolation and Linear Approximation
• 3.4 Newton's Polynomial Interpolation
• 3.5 Lagrange's Polynomial Interpolation
• 3.6 Spline Interpolation
• Chapter 4: Numerical Integration and Differentiation
• 4.1 The Trapezoid Rule
• 4.2 The Simpson's Rule
• 4.3 Romberg's Extrapolation
• 4.4 Gauss-Legendre Integration Method
• 4.5 Euler's Method for Differential Equation
• 4.6 Heun's Method for Differential Equation
• 4.7 Runge-Kutta Method for Differential Equation
• Chapter 5: Partial Differential Equation
• 5.1 Elliptic Partial Differential Equation
• 5.2 Finite Difference Method for Elliptic PDE
• 5.3 Parabolic Partial Differential Equations
• 5.4 Von Neumann Stability Analysis
• 5.5 Conservation of Energy Law
• 5.6 Hyperbolic Partial Differential Equations
• Chapter 6: Finite Element Method
• 6.1 Introduction to Finite Element Method
• 6.2 Using Finite Element Method to Solve PDEs
• Chapter 7: Optimizations
• 7.1 Introduction to Optimizations
• 7.2 Random Search Method
• 7.3 Gradient Descent Method
• 7.4 Newton's Optimization Method
• Middle Term Exams
• Middle Term Exams
• Final Term Exams
• Final Term Exams