nm.mathforcollege.comHolistic Numerical Methods – Committed to Bringing Numerical Methods to the STEM Undergraduate

Holistic Numerical Methods Committed to Bringing Numerical Methods to the STEM Undergraduate Menu Home Topics of Numerical Methods Audiovisual Digital Lectures Prerequisite Resources Multiple Choice Tests Simulations Worksheets PowerPoint Presentations Anecdotes Blog Entries Physical Problems Experiments Biographies Dissemination Journal Articles Conference Publications Educational Institution Adoptions Books Awards Workshops Social Media Digital Libraries Presentations Computational Package Repositories Contact Numerical Methods 11 Topics 1 million visits per year 1.6 million YouTube views per year Top 10 in Search Engines for numerical methods About the Course Numerical methods are techniques to approximate mathematical procedures (e.g., integrals). Approximations are needed because we either cannot solve the procedure analytically (e.g., the standard normal cumulative distribution function) or because the analytical method is intractable (e.g., solving a set of a thousand simultaneous linear equations for a thousand unknowns). By end of this course, participants will be able to apply the numerical methods for the following mathematical procedures and topics: differentiation, nonlinear equations, and simultaneous linear equations, interpolation, regression, integration, and ordinary differential equations. Additionally, they will be able to calculate errors and implement their relationship to the accuracy of the numerical solutions. To be prepared for this course, students should have a passing grade in introductory physics, integral calculus, differential calculus, and ordinary differential equations. Course Materials Simply click on topics to access the courseware which includes the following: textbook content , lecture videos , PowerPoint presentations , multiple-choice questions , blog , simulations , related physical problems to engineering majors, and worksheets . We have social media presence through a blog , a YouTube channel, Instagram , Twitter , and a Facebook page . We also have a MOOC that you can access to take the course in an organized manner. History of This Open Education Resource (OER) After successfully extending an interactive educational software package on an Apple IIe in 1985 and developing it from scratch for MS-DOS in 1989 with an Independent Study student for a course in Mechanics of Composite Materials, the idea of this open courseware in Numerical Methods was first formed in 1990. Suffering through three failed attempts (1990, 1991, 2000) of soliciting funding from several foundations, the concept was shelved till 2001. Development restarted in 2001 w hen MIT OCW was released and the open courseware concept gained immediate acceptance. It took three consecutive grants from NSF (2002-2012) and a village of colleagues and students around the nation to develop the courseware. Read or hear the history behind the courseware. The development of the courseware is ongoing but was completed mostly by 2012. Since then, the courseware has been used to conduct educational research on the cognitive and affective efficacy of flipped classrooms, and the use of adaptive learning in such settings. Course Structure This University of South Florida course is taught on campus twice per week for 75 minutes. The printed textbook for the course is available for purchase online . while the individual textbook chapters (fewer problem sets) can be accessed online. Topics Introduction Introduction Measuring Errors Sources of Error Binary Representation Floating Pt Representation Propagation of Errors Taylor Theorem Revisit Differentiation Primer on Differentiation Continuous Function Discrete Function Nonlinear Equations Quadratic Equations Cubic Equations Bisection Method Newton-Raphson Method Secant Method False-Position Method Simultaneous Linear Equations Intro to Matrix Algebra Gaussian Elimination Gauss-Seidel Method LU Decomposition Cholesky and LDL Decomposition Interpolation Background of Interpolation Direct Method Newton’s Dif Method Lagrange Method Spline Method Regression Primer on Regression Linear Regression Nonlinear Regression Adequacy of Regression Integration Primer on Integral Calculus Trapezoidal Rule Simpson’s 1/3rd Rule Romberg Integration Gauss-Quad Rule Discrete Data Integration Improper Integration Simpson’s 3/8 Rule Ordinary Differential Equations Primer on Ordinary Differential Equations Euler’s Method Runge-Kutta 2nd Runge-Kutta 4th Finite Diff Method Shooting Method Higher Order/Coupled Optimization Golden Section Search Method Newton’s Method Multidimensional Direct Search Method Multidimensional Gradient Method Simplex Method Partial Differential Equations Introduction to Partial Differential Equations Parabolic Partial Differential Equations Elliptic Partial Differential Equations Finite Element Methods Fast Fourier Transforms Introduction to Fourier Series Continuous Fourier Series Fast Transform Pair Informal Development of Fast Transform Pair Based on work at Holistic Numerical Methods licensed under an Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Questions, suggestions or comments, contact kaw@eng.usf.edu This material is based upon work partially supported by the National Science Foundation under Grant# 0126793 , 0341468 , 0717624 , 0836981, 0836916 , 0836805 , 1322586 , 1609637 , 2013271 . 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 in-kind and financial funders include USF College of Engineering, USF STEER Program, Maple, MathCAD, MATLAB, USF, FAMU, ASU, AAMU, and MSOE. Search for: Search Tweets by @numericalguy Home Topics of Numerical Methods Audiovisual Digital Lectures Prerequisite Resources Multiple Choice Tests Simulations Worksheets PowerPoint Presentations Anecdotes Blog Entries Physical Problems Experiments Biographies Dissemination Journal Articles Conference Publications Educational Institution Adoptions Books Awards Workshops Social Media Digital Libraries Presentations Computational Package Repositories Contact Holistic Numerical Methods Proudly powered by...