### MATH 373 NUMERICAL ANALYSIS I

SUMMER 2018

640:373, Index: 00279, Section H1

###

Instructor: Surya Teja Gavva

Email: suryateja@math.rutgers.edu

Lectures: MTWH 10:10 am - 12:10 pm, SEC 211, Busch Campus

Course Site: Sakai- NUMERICAL ANALYSIS H1 Summer 2018

Course Objectives: The main objective of the courses is to introduce techniques and concepts of numerical analysis. We study various numerical algorithms to compute "good" approximations to various quantities of interest. The focus will both on the theoretical analysis and the computational aspects of these numerical methods. We study the implementation, efficiency, reliability, stability of these numerical algorithms.

Topics :
- Introduction
- Bisection Method and Fixed Point Iteration
- Newton's Method and Convergence
- Accelerating convergence and roots of polynomials
- Interpolating polynomials and divided differences
- Hermite interpolation
- Cubic Splines
- Bezier curves
- Numerical Differentiation
- Richardson extrapolation
- Numerical Integration
- Composite Integration
- Romberg Integration
- Adaptive and Gaussian Quadrature
- Differential equations
- Euler's method
- Higher order Taylor and Runge-Kutta methods
- Multistep methods, variable step-sizes and extrapolation
- Systems of equations
- Stability and Stiff systems

NOTES

Class Introduction

Root Finding

Weierstrass Approximation using Bernstein Polynomials

Polynomial Interpolation

Polynomial Interpolation1

HOMEWORK

HW1

HW2

HW3

HW4

**MATLAB Resources**

Students can download, install, and use Matlab on on their personally owned computers. The software can be accessed on the Rutgers University Software Portal

Guide to Available Mathematical Software
Netlib: a collection of mathematical software, papers, and databases
Math Forum Internet Mathematics Library

General Matlab Resources on the Web

Matlab Tutorial by Mark Gockenbach
Matlab at the University of Indiana
Matlab introduction from the University of Utah
Matlab at MIT
Matlab at Northwestern University
The MathWorks
Symbolic Math toolbox
Experiments with MATLAB

Numerical Computing with MATLAB

Solving ODE with MATLAB
Octave

GNU Octave is a high-level language, primarily intended for numerical computations. It is freely redistributable software.

**Latex Resources**

ShareLatex Videos

Latex Tutorial

Latex for Beginners

The Not So Short Introduction to LATEX 2ε

LATEX Project

Latex Wikibook

Numerical errors and Disasters

**Solutions to Equations**

John H. Mathews Animations

Bisection Method app

False Position app

False Position app

Secant Method app

Newton Method app

**Interpolation**

Cubic Spline Interpolation

Bezier Curves

**Numerical Integration**

PlanetCalc

suryatejagavva