Download Math 2020 Midterm Review

Numerical Computation Final Review
Calculus Review
Taylor Series, Taylor’s Formula (with remainder term)
Big O notation
Matlab Programming
Basic Operations, Functions, Plotting
Vectors, Matrices, Looping
Algorithm Convergence
Error Analysis: Round-off vs Truncation error
Rate of convergence, Linear, Quadratic, Super-linear
Finding Roots (Zeroes) of Functions
Bisection method, Newton’s method, Secant method
Newton’s method for calculating complex values (e.g. sqrt(z), etc)
Linear Systems
Singular matrices, Inverses
Final Exam: Friday, June 4, 9:30-12:00 (2.5 hrs)
Gaussian Elimination
Room D305
Lower, Upper Triangular Matrices
Notes: You will be allowed to bring a piece of A4 paper
Pivoting: Partial and Scaled
Calculators: You will need a calculator (you cannot use
LU Factorization
your cell phone)
Interpolation
Definition
Lagrange Interpolating Polynomial
Newton Interpolating Method – Newton’s Nested Formula
Divided Differences
Spline Functions
Definition, Partition, Knots
Linear and Quadratic Splines
Cubic Spline – Natural Spline
Bezier Curves (Not Bezier Surfaces)
Parametric Curve and Control Points
de Casteljau Algorithm
Bernstein Polynomial
Matrix Form
Approximating Derivatives and Integrals
Forward, Backward, Centered Divided Difference Formulas
Richardson Extrapolation
Quadrature – Numerical Integration
Trapezoid, Midpoint, Simpson’s Rules
Romberg Integration Method
Least Squares
Approximation vs Interpolation
Normal Equation
Linear Least Squares
Polynomial Least Squares
Ordinary Differential Equation
Definition
Euler method
Runge-Kutta method (2nd order)