Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

MOOC | MOBILE | VIDEOS | BLOG | YOUTUBE | TWITTER | COMMENTS | ANALYTICS | ABOUT | CONTACT | COURSE WEBSITES | BOOKS | MATH FOR COLLEGE


 

TEXTBOOK: NUMERICAL METHODS WITH APPLICATIONS

Abridged Print Version Available

Dedicated Website for book

 

Authors: Autar K Kaw | Co-Author: Egwu E Kalu, Duc Nguyen

Contributors: Glen Besterfield, Sudeep Sarkar, Henry Welch, Ali Yalcin, 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] [MORE]

       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]

          Chapter 03.06 False Position Method [PDF] [DOC] [MORE]

 

 

4: Simultaneous Linear Equations

 

       Chapter 04.01   Introduction [PDF] [DOC] [MORE]

       Chapter 04.02   Vectors [PDF] [DOC] [MORE]

       Chapter 04.03   Binary Matrix Operations [PDF] [DOC] [MORE]

       Chapter 04.04   Unary Matrix Operations [PDF] [DOC] [MORE]

       Chapter 04.05   System of Equations [PDF] [DOC] [MORE]

       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]

       Chapter 04.11   Cholesky and LDLT Method [PDF] [DOC] [MORE]

 

 

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] [MORE]

      Chapter 06.02 Introduction to Regression [PDF] [DOC [MORE]

      Chapter 06.03 Linear Regression [PDF] [DOC] [MORE]

         Chapter 06.04 Nonlinear Regression [PDF] [DOC] [MORE]

         Chapter 06.05 Adequacy of Regression Models [PDF] [DOC] [MORE]

                      

 

7: Integration         

 

       Chapter 07.01 Primer on Integral Calculus [PDF] [DOC] [MORE]

      Chapter 07.02 Trapezoidal Rule [PDF] [DOC] [MORE] [MORE]
       Chapter 07.03 Simpson's 1/3 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] [MORE]

          Chapter 07.08  Simpson's 3/8 rule [PDF]  [DOC] [MORE]

 

 

8: Ordinary Differential Equations     

 

       Chapter 08.01 Primer on Ordinary Differential Equations [PDF] [DOC] [MORE]

       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] [MORE]

       Chapter 08.06 Shooting Method [PDF] [DOC] [MORE]

       Chapter 08.07 Finite Difference Method [PDF] [DOC] [MORE]

      

 

9: OPTIMIZATION

 

       Chapter 09.01 Golden Section Search Method [PDF] [DOC] [MORE]

       Chapter 09.02 Newton's Method [PDF] [DOC] [MORE]

       Chapter 09.03 Multidimensional Direct Search Method [PDF] [DOC] [MORE]

       Chapter 09.04 Multidimensional Gradient Method [PDF] [DOC] [MORE]

          Chapter 09.05 Simplex Method [PDF] [DOC]

   
 

10: PARTIAL DIFFERENTIAL EQUATIONS

 

       Chapter 10.01 Introduction to Partial Differential Equations [PDF] [DOC] [MORE]

       Chapter 10.02 Parabolic Partial Differential Equations [PDF] [DOC] [MORE]

       Chapter 10.03 Elliptic Partial Differential Equations [PDF] [DOC] [MORE]

       Chapter 10.04 Finite Element Methods [PDF] [DOC]

   
 

11: Fast Fourier Transforms      

 

        Chapter 11.01  Introduction to Fourier Series [PDF] [DOC] [MORE]

            Chapter 11.02 Continuous Fourier Series [PDF] [DOC] [MORE]

        Chapter 11.03 Fourier Transform Pair [PDF] [DOC] [MORE]

        Chapter 11.04 Discrete Fourier Transform [PDF] [DOC] [MORE]

        Chapter 11.05 Informal Development of Fast Fourier Transform [PDF] [DOC] [MORE]      

   

Companion Tools for the Textbook

Video Lectures |PowerPoint Presentations | Worksheets | Multiple-Choice Tests | Anecdotes

 

   

 

 

 

 

 


AUDIENCE |  AWARDS  |  PEOPLE  |  TRACKS  |  DISSEMINATION  |  PUBLICATIONS


Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

ANALYTICS