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Welcome to the website for a Numerical Methods course for engineering undergraduates. It is dedicated to reaching a large audience of undergraduate students through its holistic but customized approach.

Holistically, the resources review background information; present numerical methods through notes, presentations, simulations and assessments; show how what they learned is applied in real life; tell stories to illustrate special topics and pitfalls; and give historical perspectives.

From a customized perspective, the user can choose a major of choice - Chemical, Civil, Computer, Electrical, General, Industrial or Mechanical Engineering. You can choose Maple, Mathcad, Mathematica or Matlab as one of the packages used to illustrate algorithms, convergence and pitfalls of the numerical methods.

NUMERICAL METHODS BY TOPIC, MAJOR & LANGUAGE

MAPLE	Chemical	Civil	Computer	Electrical	General	Industrial	Mechanical

Intro to Sci Comp
Differentiation
Nonlinear Equations
Interpolation
Regression
Integration
Simult Linear Eqns
Ordinary Diff Eqns


MATHCAD

Intro to Sci Comp
Differentiation
Nonlinear Equations
Interpolation
Regression
Integration
Simult Linear Eqns
Ordinary Diff Eqns


MATHEMATICA

Intro to Sci Comp
Differentiation
Nonlinear Equations
Interpolation
Regression
Integration
Simult Linear Eqns
Ordinary Diff Eqns

MATLAB

Intro to Sci Comp
Differentiation
Nonlinear Equations
Interpolation
Regression
Integration
Simult Linear Eqns
Ordinary Diff Eqns

	TEXTBOOK: NUMERICAL METHODS WITH APPLICATIONS Abridged Print Version Available Dedicated Website for book Authors: Autar K Kaw \| Co-Author: Egwu E Kalu \| Future Co-Author: Duc Nguyen Contributors: Glen Besterfield, Sudeep Sarkar, Henry Welch, Ali Yalcin \| Future Contributor: Venkat Bhethanabotla
	1: Introduction, Approximation and Errors
	Chapter 01.01 Introduction to Scientific Computing [PDF] [DOC] [MORE] Chapter 01.02 Measuring Errors [PDF] [DOC] [MORE] Chapter 01.03 Sources of Error [PDF] [DOC] [MORE] Chapter 01.04 Binary Representation of Numbers [PDF] [DOC] [MORE] Chapter 01.05 Floating Point Representation [PDF] [DOC] [MORE] Chapter 01.06 Propagation of Errors [PDF] [DOC] [MORE] Chapter 01.07 Taylor Series Revisited [PDF] [DOC] [MORE]
	2: Differentiation
	Chapter 02.01 Primer on Differential Calculus [PDF] [DOC] Chapter 02.02 Differentiation of Continuous Functions [PDF] [DOC] [MORE] Chapter 02.03 Differentiation of Discrete Functions [PDF] [DOC] [MORE]
	3: Nonlinear Equations
	Chapter 03.01 Solving Quadratic Equations Exactly [PDF] [DOC] [MORE] Chapter 03.02 Solving Cubic equations Exactly [PDF] [DOC] Chapter 03.03 Bisection Method [PDF] [DOC] [MORE] Chapter 03.04 Newton-Raphson Method [PDF] [DOC] [MORE] Chapter 03.05 Secant Method [PDF] [DOC] [MORE]
	4: Simultaneous Linear Equations
	Chapter 04.01 Introduction [PDF] [DOC] Chapter 04.02 Vectors [PDF] [DOC] Chapter 04.03 Binary Matrix Operations [PDF] [DOC] Chapter 04.04 Unary Matrix Operations [PDF] [DOC] Chapter 04.05 System of Equations [PDF] [DOC] Chapter 04.06 Gaussian Elimination Method [PDF] [DOC] [MORE] Chapter 04.07 LU Decomposition Method [PDF] [DOC] [MORE] Chapter 04.08 How does Gauss-Seidel method work? [PDF] [DOC] [MORE] Chapter 04.09 Adequacy of Solutions [PDF] [DOC] Chapter 04.10 Eigenvalues and Eigenvectors [PDF] [DOC]
	5: Interpolation
	Chapter 05.01 History of Interpolation [PDF] [DOC] Chapter 05.02 Direct Method [PDF] [DOC] [MORE] Chapter 05.03 Newton's Divided Difference Method [PDF] [DOC] [MORE] Chapter 05.04 Lagrange Method [PDF] [DOC] [MORE] Chapter 05.05 Spline Method [PDF] [DOC] [MORE] Chapter 05.06 The lurking dangers of extrapolation! [PDF] [DOC] Chapter 05.07 Why is higher order interpolation a bad idea? [PDF] [DOC] Chapter 05.08 Why do we need spline interpolation [PDF] [DOC] Chapter 05.09 How choice of points of interpolation affects approximations! [PDF] [DOC] Chapter 05.10 How splines can help in developing a shorter path for a robot! [PDF] [DOC]
	6: Regression
	Chapter 06.01 Primer on statistical terminology [PDF] [DOC] Chapter 06.02 Introduction to Regression [PDF] [DOC] Chapter 06.03 Linear Regression [PDF] [DOC] [MORE] Chapter 06.04 Nonlinear Regression [PDF] [DOC] [MORE]
	7: Integration
	Chapter 07.01 Primer on Integral Calculus [PDF] [DOC] Chapter 07.02 Trapezoidal Rule [PDF] [DOC] [MORE] Chapter 07.03 Simpson's 1/3rd Rule [PDF] [DOC] [MORE] Chapter 07.04 Romberg Rule [PDF] [DOC] [MORE] Chapter 07.05 Gauss-Quadrature Rule [PDF] [DOC] [MORE] Chapter 07.06 Discrete Data Integration [PDF] [DOC] [MORE] Chapter 07.07 Improper Integration [PDF] [DOC]
	8: Ordinary Differential Equations
	Chapter 08.01 Primer on Ordinary Differential Equations [PDF] [DOC] Chapter 08.02 Euler's method [PDF] [DOC] [MORE] Chapter 08.03 Runge-Kutta 2nd order method [PDF] [DOC] [MORE] Chapter 08.04 Runge-Kutta 4th order method [PDF] [DOC] [MORE] Chapter 08.05 On solving higher order & coupled ordinary differential equations [PDF] [DOC] Chapter 08.06 Shooting Method [PDF] [DOC] [MORE] Chapter 08.07 Finite Difference Method [PDF] [DOC] [MORE]
	9: Fast Fourier Transforms
	2009

	10: PARTIAL DIFFERENTIAL EQUATIONS
	2010

	11: optimization
	2010

Companion Tools for the Textbook

POWER POINT PRESENTATIONS

INTRODUCTION TO SCIENTIFIC COMPUTING

Introduction to numerical methods [PDF] [PPT]

Measuring errors [PDF] [PPT]

Sources of error [PDF] [PPT]

Binary representation of numbers [PDF] [PPT]

Floating point representation of numbers [PDF] [PPT]

Propagation of errors [PDF] [PPT]

Taylor series [PDF] [PPT]

differentiation

Continuous functions [PDF] [PPT]

Discrete functions [PDF] [PPT]

Effect of step size on accuracy of numerical first derivative: Forward Divided Difference [PDF] [PPT]

Effect of step size on accuracy of numerical first derivative: Backward Divided Difference [PDF] [PPT]

Effect of step size on accuracy of numerical first derivative: Central Divided Difference [PDF] [PPT]

Nonlinear Equations

Bisection Method [PDF] [PPT]

Newton-Raphson Method [PDF] [PPT]

Secant Method [PDF] [PPT]

SIMULTANEOUS LINEAR Equations

Gaussian Elimination [PDF] [PPT]

LU Decomposition method [PDF] [PPT]

Gauss-Seidal method [PDF] [PPT]

Interpolation

Direct Method [PDF] [PPT]

Newton's Divided Difference Method [PDF] [PPT]

Lagrange Method [PDF] [PPT]

Spline Method [PDF] [PPT]

REGRESSION

Linear Regression [PDF] [PPT]

Nonlinear regression [PDF] [PPT]

Integration

Trapezoidal Rule [PDF] [PPT]
Simpson's 1/3rd Rule [PDF] [PPT]

Romberg Rule [PDF] [PPT]
Gauss-Quadrature Rule [PDF] [PPT]

ordinary differential equations

Euler's Method [PDF] [PPT]

Runge-Kutta 2nd order Method [PDF] [PPT]

Runge-Kutta 4th order Method [PDF] [PPT]
Shooting Method [PDF] [PPT]

Finite Difference Method [PDF] [PPT]

WORKSHEETS
INTRODUCTION TO SCIENTIFIC COMPUTING
	Measuring Errors
		True Error [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Approximate Error [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB
	Binary Representation
		Decimal to binary representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Binary to decimal representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Measuring Errors
		Decimal to floating point representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Binary to floating point representation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Propagation of Errors
		Propagation of Errors [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Differentiation
	Continuous Functions
		Forward Divided Difference [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Backward Divided Difference [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Central Divided Difference [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Continuous functions Second Order Derivative [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Discrete Data
		Discrete functions [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Nonlinear Equations
	Bisection Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Slow convergence of bisection method simulation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Newton-Raphson Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Division by zero [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Slow Convergence at Inflection Points [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Root jumps over several roots [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Roots oscillates around local maxima and minima [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Secant Method
		Simulation of secant method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence Simulation of secant method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Division by zero in secant method simulation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Pitfall: Root jumps over several roots in secant method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

SIMULTANEOUS LINEAR EQUATIONS
	Gaussian Elimination
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Gauss-Seidel Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
		Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	LU Decomposition
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Interpolation
	Direct Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Newton's Divided Difference Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Lagrange Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Spline Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

REGRESSION
	Linear Regression
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Nonlinear Regression
		Without Data Linearization [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] With Data Linearization [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Polynomial Regression [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Comparing with and without Data Linearization [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Adequacy of a Regression Model
		Adequacy [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Integration
	Trapezoidal Rule
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Simpson's 1/3rd Rule
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Romberg Rule
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Gauss-Quadrature Rule
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Integrating Discrete Functions
		Integrating discrete functions [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

ORDINARY DIFFERENTIAL EQUATIONS
	Euler's Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Runge-Kutta 2nd order Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Runge-Kutta 4th order Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB] Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Shooting Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]
	Finite Difference Method
		Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

ANECDOTES

DIFFERENTIATION

Effect of step size on accuracy of numerical first derivative: Forward Divided Difference [PDF] [PPT] Effect of step size on accuracy of numerical first derivative: Backward Divided Difference[PDF][PPT]

Effect of step size on accuracy of numerical first derivative: Central Divided Difference [PDF] [PPT]

Comparing the Forward Divided Difference, Backward Divided Difference

Central Divided Difference [PDF] [MWS] | [PDF] [MCD] | [PDF] [NB]|[PDF] [MFILE]

Effect of Significant Digits on the Value of the

Numerical Derivative [PDF] [MWS] | [PDF] [MCD]|[PDF] [NB]|[PDF] [MFILE]

NONLINEAR EQUATIONS

Quest for cubic equation solution [PDF] [DOC]

Newton [HTML] [PDF] [DOC]

Raphson [HTML] [PDF] [DOC]

Galois [HTML] [PDF] [DOC]

SIMULTANEOUS LINEAR EQUATIONS

Effect of significant digits on solution of equations

Simulation [MWS] [MCD] [NB] [MFILE] | Textbook notes (pages 5-16 of) [PDF] [DOC]

Saving of computational time for finding inverse of a matrix using LU decomposition

Simulation [MWS] [MCD] [NB] [MFILE] | Textbook notes (pages 2-4 of) [PDF] [DOC]

Adequacy of Solutions [PDF] [MWS] | [PDF] [DOC]

Eigenvalues and Eigenvectors [DOC] [PDF]

Gauss [HTML] [PDF] [DOC]

INTERPOLATION

History of Interpolation [PDF] [DOC]

Dangers of extrapolation through NASDAQ, [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Higher order interpolation is a bad idea [PDF] [DOC]| [MWS] [MCD] [MFILE] [NBM]

Comparison of spline & polynomial interpolation [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Choice of points of interpolation affects approximations [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Splines help in developing a shorter path for a robot [PDF] [DOC]|[MWS] [MCD] [MFILE] [NBM]

Runge [HTML] [PDF] [DOC]

Newton [HTML] [PDF] [DOC]

Lagrange [HTML] [PDF] [DOC]

INTEGRATION

What is integration? [PDF] [DOC]

A Primer on Integral Calculus [PDF] [DOC]

Newton [HTML] [PDF] [DOC]

Cotes [HTML] [PDF] [DOC]

Gauss [HTML] [PDF] [DOC]

Simpson [HTML] [PDF] [DOC]

Romberg [HTML] [PDF] [DOC]

ORDINARY DIFFERENTIAL EQUATIONS

What are ordinary differential equations? [PDF] [DOC]

A primer on ordinary differential equations [PDF] [DOC]

On solving higher order and coupled ordinary differential equations [PDF] [DOC]

Euler [HTML] [PDF] [DOC]

Runge [HTML] [PDF] [DOC]

Kutta [HTML] [PDF] [DOC]

MULTIPLE CHOICE QUESTIONS
INTRODUCTION TO SCIENTIFIC COMPUTING
	Introduction to Numerical Methods [HTML] [FLASH] [PDF] [DOC]
	Measuring Errors [HTML] [FLASH] [PDF] [DOC]
	Sources of Error [HTML] [FLASH] [PDF] [DOC]
	Binary Representation of Numbers [HTML] [FLASH] [PDF] [DOC]
	Floating Point Representation of Numbers [HTML] [FLASH] [PDF] [DOC]
	Propagation of Errors [HTML] [FLASH] [PDF] [DOC]
	Taylor Series Revisited [HTML] [FLASH] [PDF] [DOC]

DIFFERENTIATION
	Background [HTML] [FLASH] [PDF] [DOC]
	Continuous Functions [HTML] [FLASH] [PDF] [DOC]
	Discrete Functions [HTML] [FLASH] [PDF] [DOC]

Nonlinear Equations
	Background [HTML] [FLASH] [PDF] [DOC]
	Bisection Method [HTML] [FLASH] [PDF] [DOC]
	Newton-Raphson Method [HTML] [FLASH] [PDF] [DOC]
	Secant Method [HTML] [FLASH] [PDF] [DOC]
SIMULTANEOUS LINEAR EQUATIONS
	Background [HTML] [FLASH] [PDF] [DOC]
	Gaussian Elimination [HTML] [FLASH] [PDF] [DOC]
	LU Decomposition [HTML] [FLASH] [PDF] [DOC]
	Gauss-Seidel Method [HTML] [FLASH] [PDF] [DOC]

Interpolation
	Background [HTML] [FLASH] [PDF] [DOC]
	Direct Method [HTML] [PDF] [DOC]
	Newton's Divided Difference Method [HTML] [FLASH] [PDF] [DOC]
	Lagrange Method [HTML] [FLASH] [PDF] [DOC]
	Spline Method [HTML] [FLASH] [PDF] [DOC]
REGRESSION
	Background [HTML] [PDF] [DOC]
	Linear Regression [HTML] [FLASH] [PDF] [DOC]
	Nonlinear Regression [HTML] [FLASH] [PDF] [DOC]
Integration
	Background [HTML] [FLASH] [PDF] [DOC]
	Trapezoidal method [HTML] [FLASH] [PDF] [DOC]
	Simpson's 1/3rd Rule method [HTML] [FLASH] [PDF] [DOC]
	Romberg method [HTML] [PDF] [DOC]
	Gauss-Quadrature method [HTML] [FLASH] [PDF] [DOC]
ORDINARY DIFFERENTIAL EQUATIONS
	Background [HTML] [FLASH] [PDF] [DOC]
	Euler's method [HTML] [FLASH] [PDF] [DOC]
	Runge-Kutta 2nd order method [HTML] [PDF] [DOC]
	Runge-Kutta 4th order method [HTML] [FLASH] [PDF] [DOC]
	Shooting Method [HTML] [PDF] [DOC]
	Finite Difference Method [HTML] [FLASH] [PDF] [DOC]

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Resources of Physical Problems
(Do you want to follow one of physical examples given below to learn the numerical methods? Yes)
DIFFERENTIATION
	Chemical Engineering	How quickly does the slick spread?
	Civil Engineering	Stress Concentration Around a Hole (extended version coming soon)
	Computer Engineering	Detecting edges of images
	Electrical Engineering	Avoiding arcing in switches
	General Engineering	Finding the acceleration of a rocket from its velocity.
	Industrial Engineering	Reliability of manufactured parts over time
	Mechanical Engineering	How does the thermal expansion coefficient vary at different temperatures?

Nonlinear Equations
	Chemical Engineering	A scale to measure oil in a tank
	Civil Engineering	Sagging bookshelves!
	Computer Engineering	Divide unit missing in a supercomputer?
	Electrical Engineering	Checking calibration curve of a thermistor
	General Engineering	How much of the float is submerged?
	Industrial Engineering	Mom and Pop shop wants to break even
	Mechanical Engineering	Trunnion cool down for a shrink fit

Simultaneous Linear Equations
	Chemical Engineering	Liquid-Liquid extraction
	Civil Engineering	How much pressure can a compounded cylinder take?
	Computer Engineering	To infer the surface shape from images
	Electrical Engineering	Finding the unbalance in a 3-phase load system
	General Engineering	Finding the velocity profile of a rocket
	Industrial Engineering	Maximizing the production schedule
	Mechanical Engineering	Find model for thermal expansion vs temperature.

Interpolation
	Chemical Engineering	Tea time: time needed to boil the water
	Civil Engineering	Tips on bass fishing
	Computer Engineering	Short and smoothest path for a robot
	Electrical Engineering	Measuring temperature by a thermistor
	General Engineering	Predict velocity of a rocket
	Industrial Engineering	Profiling a cam
	Mechanical Engineering	Calculating the shrinkage of a trunnion correctly

Regression
	Chemical Engineering	Infrared spectroscopy
	Civil Engineering	Finding the longitudinal Young's moduli
	Computer Engineering	Extraction of road networks in images
	Electrical Engineering	Finding the appropriate value for the resistance
	General Engineering	Finding the best mousetrap for a mousetrap car
	Industrial Engineering	When should the machine be stopped?
	Mechanical Engineering	Calculating the contraction of a trunnion


Integration
	Chemical Engineering	Time required for oxygen to be consumed in the fuel cell
	Civil Engineering	Is the toxicity level of benzene dangerous?
	Computer Engineering	To infer the surfaces from vector fields
	Electrical Engineering	Confidence in acceptable circuit behavior
	General Engineering	Distance covered by a rocket
	Industrial Engineering	Are there as many plies of tissue paper in a roll?
	Mechanical Engineering	Finding the shrinkage of a trunnion?


Ordinary Differential Equations
	Chemical Engineering	Controlling sodium chloride waste while making soap.
	Civil Engineering	When is it safe to go back into the lake?
	Computer Engineering	Transient analysis of resistor-capacitor system
	Electrical Engineering	Sizing a rectifier-based power supply
	General Engineering	How much time will it take the ball to cool down?
	Industrial Engineering	Speed Control of DC motors
	Mechanical Engineering	Contracting a cylinder to shrink fit in to a hub