MAT 421: Applied Computational Methods

MAT 421 Homework and Projects Repository

Instructor: Professor Haiyan Wang

Section: 18212 (Spring 2022)

Contents

Module A: Representation of Numbers

• Base-N and Binary
• Floating Point Numbers
• IEEE 754
• Round-off Errors

Module B: Interpolation

Part 1

• Linear Interpolation
• Cubic Spline Interpolation

Part 2

• Lagrange Polynomial Interpolation
• Newton's Polynomial Interpolation

Module C: Root Finding

• Bisection Method
• Newton Raphson Method

Module D: Linear Algebra

• Matrix Operations
• Eigenvalues and Eigenvectors
• Linear and Least Squares Regression

Module E and F: Numerical Differentiation

• Forward, Central and Backward Differentiation
• Numerical Differentiation with Noise

Module G: Numerical Integration

• Reimanns Integral
• Trapezoidal Rule
• Simpson's Rule
• Polynomial Integration
• Fourier Approximation

Module H: Ordinary Differential Equations

• Initial Value Problems
• Boundary Value Problems
• Python ODE Solvers