Mechanical Engineering



EML3041: Computational Methods: Spring 2016

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1: Introduction, Approximation and Errors


       Chapter 01.01      Introduction to Scientific Computing [MORE]

       Chapter 01.02     Measuring Errors [MORE]

       Chapter 01.03     Sources of Error [MORE]

       Chapter 01.04     Binary Representation of Numbers [MORE]

       Chapter 01.05     Floating Point Representation [MORE]

       Chapter 01.07     Taylor Series Revisited [MORE]



2: Differentiation


       Chapter 02.01     Primer on Differential Calculus (optional) [MORE]

       Chapter 02.02    Differentiation of Continuous Functions  [MORE]

       Chapter 02.03    Differentiation of Discrete Functions  [MORE]



3: Nonlinear Equations


       Chapter 03.01      Solving Quadratic Equations Exactly  [MORE]

       Chapter 03.03     Bisection Method  [MORE]

       Chapter 03.04     Newton-Raphson Method  [MORE]



4: Simultaneous Linear Equations


       Chapter 04.01     Introduction to Matrix Algebra [MORE]

       Chapter 04.06    Gaussian Elimination Method  [MORE]

       Chapter 04.07     LU Decomposition Method  [MORE]



5: Interpolation


      Chapter 05.02      Direct Method  [MORE]

      Chapter 05.05      Spline Method  [MORE]

      Chapter 05.06      The lurking dangers of extrapolation!  [MORE]

      Chapter 05.07      Why is higher order interpolation is a bad idea? [MORE]

      Chapter 05.08      Why do we need spline interpolation  [MORE]

      Chapter 05.10       How splines can help in developing a shorter path for a robot!  [MORE]



6: Regression          


      Chapter 06.01       Primer on statistical terminology (optional) [PDF]

      Chapter 06.02       Introduction to Regression [MORE]

      Chapter 06.03       Linear Regression  [MORE]

        Chapter 06.04       Nonlinear Regression  [MORE]

        Chapter 06.05       Adequacy of Regression Models [MORE]



7: Integration         


       Chapter 07.01       Primer on Integral Calculus (optional) [MORE]

      Chapter 07.02       Trapezoidal Rule  [MORE]
       Chapter 07.05       Gauss-Quadrature Rule
       Chapter 07.06       Discrete Data Integration
       Chapter 07.07       Improper Integration



8: Ordinary Differential Equations     


       Chapter 08.01       Primer on Ordinary Differential Equations (optional) [MORE]

       Chapter 08.02       Euler's Method  [MORE]

       Chapter 08.03       Runge-Kutta 2nd order method  [MORE]

       Chapter 08.05       On Solving Higher Order & Coupled Ordinary Differential Eqns [MORE

       Chapter 08.07       Finite Difference Method  [MORE]      

Copyrights: UnCreative Commons Licenseiversity of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact  This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981.  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.  Numerical Methods for Undergraduates by  is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.  Based on a work at