Instructional Videos for Numerical Methods

DIGITAL AUDIOVISUAL LECTURES

In Spring 2009, we recorded 200 instructional videos for the topics of a typical course in Numerical Methods at University of South Florida and Arizona State University. These videos have been annotated, and also available at the YouTube channel named numericalmethodsguy.

Additions to the video lectures will be made in Spring 2010 to cover a few more topics (such as Simpson's 1/3 rule, Gauss Seidel Method, Lagrange Interpolation, etc) that may be taught at other universities.

INTRODUCTION TO SCIENTIFIC COMPUTING

INTRODUCTION TO NUMERICAL METHODS

On Steps of Solving an Engineering Problem: Part 1 of 2 [YOUTUBE 8:54]

On Steps of Solving an Engineering Problem: Part 2 of 2 [YOUTUBE 7:35]

Enumerating Use of Numerical Methods for Mathematical Procedures: Part 1 of 2 [YOUTUBE 10:42]

Enumerating Use of Numerical Methods for Mathematical Procedures: Part 2 of 2 [YOUTUBE 7:13]

MEASURING ERRORS

True Error: Definition & Example [YOUTUBE 8:10]

Relative True Error: Definition & Example [YOUTUBE 7:39]

Approximate Error Definition & Example [YOUTUBE 6:39]

Relative Approximate Error: Definition & Example [YOUTUBE 8:45]

SOURCES OF ERROR

Round-off Error: Definition and Examples [YOUTUBE 3:47]

Effect of Carrying Significant Digits [YOUTUBE 7:48]

Truncation Error: Definition [YOUTUBE 8:34]

Truncation Error: Example: Series [YOUTUBE 6:44]

Truncation Error: Example: Integration [YOUTUBE 6:12]

Truncation Error: Example: Differentiation [YOUTUBE 10:14]

BINARY REPRESENTATION

Introduction to Binary Representation [YOUTUBE 6:41]

Base-10 to Base-2 Conversion Method [YOUTUBE 9:14]

Base-10 to Base-2 Conversion Another Method [YOUTUBE 9:14]

FLOATING POINT REPRESENTATION

Floating Point Representation Background: Part 1 of 3 [ YOUTUBE 7:37]

Floating Point Representation Background: Part 2 of 3 [ YOUTUBE 10:43]

Floating Point Representation Background: Part 3 of 3[ YOUTUBE 1:58]

Floating Point Representation: Example [YOUTUBE 10:10]

Floating Point Representation - Biased Exponent: Example [YOUTUBE 8:51]

IEEE-754 Single Precision Representation: Part 1 of 2 [YOUTUBE 4:57]

IEEE-754 Single Precision Representation: Part 2 of 2 [YOUTUBE 8:38]

TAYLOR'S THEOREM REVISITED

Introduction to Taylor Series [YOUTUBE 7:28]

Taylor Series: Example [YOUTUBE 6:31]

Taylor Series: Deriving the Series for exp(x) [YOUTUBE 5:30]

Taylor Series: Example: Finding sin(2.0) [YOUTUBE 10:32]

DIFFERENTIATION

BACKGROUND

Background of Differentiation [YOUTUBE 7:17]

Differentiation of Continuous Functions

Forward Divided Difference: Part 1 of 2 [YOUTUBE 9:28]

Forward Divided Difference: Part 2 of 2 [YOUTUBE 4:41]

Backward Divided Difference: Part 1 of 2 [YOUTUBE 9:08]

Backward Divided Difference: Part 2 of 2[YOUTUBE 5:32]

Central Divided Difference [YOUTUBE 9:53]

Higher Order Derivative Divided Difference: Theory [YOUTUBE 8:37] |

Higher Order Derivative Divided Difference: Example [YOUTUBE 6:04]

Accuracy of Divided Difference Formulas: Part 1 of 2 [YOUTUBE 8:16]

Accuracy of Divided Difference Formulas Part 2 of 2 [YOUTUBE 3:51]

Differentiation of Discrete Functions

Divided Difference Approach [YOUTUBE 10:07]

Polynomial Interpolation Method [YOUTUBE 8:09]

Newton's Divided Difference Polynomial Method: Theory [YOUTUBE 7:45]

Newton's Divided Difference Polynomial Method: Example [YOUTUBE 8:28]

NONLINEAR EQUATIONS

QUADRATIC EQUATIONS

The Quadratic Equation Formula [YOUTUBE 4:22]

Derivation of the Quadratic Formula [YOUTUBE 5:41]

Example of Quadratic Equation [YOUTUBE 7:48]

BISECTION METHOD

Background of Bisection Method [YOUTUBE 9:04]

Algorithm of Bisection Method [YOUTUBE 9:47]

Example of Bisection Method [YOUTUBE 9:53]

Advantages & Drawbacks of Bisection Method [YOUTUBE 8:31]

Newton-Raphson Method

Derivation of Newton-Raphson Method [YOUTUBE 8:24]

Example for Newton-Raphson Method [YOUTUBE 10:06]

Advantages & Drawbacks for Newton-Raphson Method: Part 1 of 2 [YOUTUBE 7:09]

Advantages & Drawbacks for Newton-Raphson Method: Part 2 of 2 [YOUTUBE 4:43]

Derivation from Taylor Series of Newton-Raphson Method [YOUTUBE 7:56]

Supercomputers have No Divide Unit - A Newton-Raphson Method Approach [YOUTUBE 10:14]

Supercomputers have No Divide Unit - Example [YOUTUBE 5:23]

Finding Square Root of a Number - A Newton-Raphson Method Approach [YOUTUBE 6:34]

Finding Square Root of a Number - Example [YOUTUBE 7:03]

SECANT METHOD

Derivation of Secant Method: Approach 1 of 2 [YOUTUBE 5:58]

Derivation of Secant Method: Approach 2 of 2 [YOUTUBE 6:59]

Algorithm of Secant Method [YOUTUBE 5:16]

Example of Secant Method [YOUTUBE 8:16]

SIMULTANEOUS LINEAR EQUATIONS
BACKGROUND
	Diagonal and Identity Matrices [YOUTUBE 5:21] What is a Diagonally Dominant Matrix [YOUTUBE 10:49] Upper and Lower Triangular Matrices [YOUTUBE 5:21] Adding Two Matrices [YOUTUBE 4:53] Subtracting Two Matrices [YOUTUBE 5:34] Multiplying Two Matrices [YOUTUBE 10:06] Inverse of a Matrix [YOUTUBE 4:53] Setting up Equations in a Matrix Form [YOUTUBE 7:07]
GAUSSIAN ELIMINATION
	Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27] Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22] Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49] Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40] Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20] Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20] Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40] Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07] Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39] Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15] Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08] Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18] Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58] Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17] Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48] Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17] Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07]
LU DECOMPOSITION
	LU Decomposition: Basis [YOUTUBE 9:02] LU Decomposition Method: Example [YOUTUBE 10:29] Why LU Decomposition: Part 1 [YOUTUBE 4:58] Why LU Decomposition: Part 2 [YOUTUBE 8:05] Decomposing a Square Matrix: Part 1 of 2 [YOUTUBE 6:56] Decomposing a Square Matrix: Part 2 of 2 [YOUTUBE 4:37] Finding Inverse of a Matrix Using LU Decomposition: Background [YOUTUBE 6:03] Finding Inverse of a Matrix Using LU Decomposition: Example [YOUTUBE 10:20]

INTERPOLATION

BACKGROUND

Uniqueness of Polynomial Interpolant: Part 1 of 2 [YOUTUBE 8:26]

Uniqueness of Polynomial Interpolant: Part 2 of 2 [YOUTUBE 9:50]

Direct Method

Linear Interpolation [YOUTUBE 8:53]

Quadratic Interpolation [YOUTUBE 8:17]

Cubic Interpolation - Part 1 of 2 [YOUTUBE 9:37]

Cubic Interpolation - Part 2 of 2 [YOUTUBE 7:51]

SPLINE Interpolation

Linear Spline Interpolation: Theory [YOUTUBE 7:56]

Linear Spline Interpolation: Example [YOUTUBE 5:27]

Quadratic Spline Theory: Part 1 of 2 [YOUTUBE 9:49]

Quadratic Spline Theory: Part 2 of 2 [YOUTUBE 5:27]

Quadratic Spline Interpolation: Example: Part 1 of 2 [YOUTUBE 10:48]

Quadratic Spline Interpolation: Example: Part 2 of 2 [YOUTUBE 7:05]

SPECIAL TOPICS OF INTERPOLATION

The Lurking Dangers of Extrapolation [YOUTUBE 5:58]

Higher Order Interpolation is a Bad Idea [YOUTUBE 8:36]

Interpolating a Short and Smooth Path for a Robot [YOUTUBE 4:18]

REGRESSION

Linear Regression

Linear Regression Background: Part 1 of 2 [YOUTUBE 8:10]

Linear Regression Background: Part 2 of 2 [YOUTUBE 3:55]

Linear Regression Derivation: Part 1 of 2 [YOUTUBE 6:22]

Linear Regression Derivation: Part 2 of 2 [YOUTUBE 8:44]

Linear Regression: Example [YOUTUBE 10:24]

Linear Regression With Zero Intercept: Derivation [YOUTUBE 9:32]

Linear Regression With Zero Intercept: Example [YOUTUBE 8:48]

Nonlinear Regression

Power Model: Derivation: Part 1 of 2 [YOUTUBE 4:07]

Power Model: Derivation: Part 2 of 2 [YOUTUBE 8:11]

Power Model : Transformed Data: Derivation [YOUTUBE 8:52]

Power Model : Transformed Data: Example Part 1 of 2 [YOUTUBE 5:49]

Power Model : Transformed Data: Example Part 2 of 2 [YOUTUBE 9:12]

Exponential Model Regression: Derivation: Part 1 of 2 [YOUTUBE 5:50]

Exponential Model Regression: Derivation: Part 2 of 2 [YOUTUBE 9:50]

Exponential Model : Example Part 1 of 2 [YOUTUBE 10:07]

Exponential Model : Example Part 2 of 2 [YOUTUBE 1:44]

Exponential Model : Transformed Data: Derivation [YOUTUBE 9:37]

Exponential Model : Transformed Data: Example Part 1 of 2 [YOUTUBE 7:11]

Exponential Model : Transformed Data: Example Part 2 of 2 [YOUTUBE 9:14]

Saturation Growth Model: Transformed Data: Derivation [YOUTUBE 8:27]

Harmonic Decline Curve: Transformed Data: Derivation [YOUTUBE 9:16]

Harmonic Decline Curve : Transformed Data: Example Part 1 of 2 [YOUTUBE 6:18]

Harmonic Decline Curve : Transformed Data: Example Part 2 of 2 [YOUTUBE 8:47]

Polynomial Model : Derivation: Part 1 of 2 [YOUTUBE 7:47]

Polynomial Model : Derivation: Part 2 of 2 [YOUTUBE 9:40]

Polynomial Model : Example Part 1 of 2 [YOUTUBE 6:42]

Polynomial Model : Example Part 2 of 2 [YOUTUBE 6:16]

INTEGRATION

Trapezoidal Rule

Trapezoidal Rule Derivation [YOUTUBE 10:51]

Trapezoidal Rule: Example [YOUTUBE 7:18]

Trapezoidal Rule Multiple Segment Rule: Motivation [YOUTUBE 4:53]

Trapezoidal Rule Multiple Segment Rule: Derivation [YOUTUBE 7:48]

Trapezoidal Rule Multiple Segment Rule: Example: Part 1 of 2 [YOUTUBE 8:17]

Trapezoidal Rule Multiple Segment Rule: Example: Part 2 of 2 [YOUTUBE 3:41]

Trapezoidal Rule Multiple Segment Rule: Error Derivation [YOUTUBE 8:46]

Trapezoidal Rule Multiple Segment Rule: Error Example [YOUTUBE 8:52]

Method of Undetermined Coefficients: Trapezoidal Rule Derivation [YOUTUBE 10:00]

Gauss Quadrature Rule

Method of Undetermined Coefficients: Trapezoidal Rule Derivation [YOUTUBE 10:00]

2-pt Gaussian Quadrature Rule: Derivation [YOUTUBE 8:43]

n-pt Gaussian Quadrature Rule: Discussion [YOUTUBE 8:52]

Converting Limits of Integration [YOUTUBE 7:13]

Gaussian Quadrature Rule: Example [ YOUTUBE 8:55]

1-pt Gaussian Quadrature Rule: Derivation [YOUTUBE 8:36]

Complete Derivation of Two Point Gaussian Quadrature Rule: Part 1 of 3 [ YOUTUBE 9:46]

Complete Derivation of Two Point Gaussian Quadrature Rule: Part 2 of 3 [ YOUTUBE 3:31]

Complete Derivation of Two Point Gaussian Quadrature Rule: Part 3 of 3 [ YOUTUBE 9:58]

Discrete Data Integration

Integrating Discrete Functions by Average Method [YOUTUBE 8:29]

Integrating Discrete Functions by Trapezoidal Rule [YOUTUBE 10:52]

Integrating Discrete Functions via Polynomial Interpolation [YOUTUBE 9:32]

Integrating Discrete Functions via Spline Interpolation [YOUTUBE 5:32]

Integrating Discrete Functions via Regression Method [YOUTUBE 8:23]

ORDINARY DIFFERENTIAL EQUATIONS

Primer on ODE

Exact Solution of 1st order ODE [YOUTUBE 6:48]

Exact Solution of 1st order ODE: Another Example [YOUTUBE 7:37]

Exact Solution of 2nd order ODE: Distinct Roots of Characteristic Equation [YOUTUBE 8:50]

Exact Solution of 2nd order ODE: Repeated Roots of Characteristic Equation [YOUTUBE 8:41]

Exact Solution of 2nd order ODE: Complex Roots of Characteristic Equation [YOUTUBE 9:34]

EuLER's METHOD

Euler's Method of Solving ODEs: Derivation [YOUTUBE 9:53]

Euler's Method of Solving ODEs: Example [YOUTUBE 10:57]

Euler's Method of Estimating Integrals: Theory [YOUTUBE 7:11]

Euler's Method of Estimating Integrals: Example [YOUTUBE 8:58]

RuNGE-KUTTA 2ND ORDER METHOD

Runge-Kutta 2nd Order Method: Background [YOUTUBE 9:46]

Runge-Kutta 2nd Order Method: Formulas [YOUTUBE 10:57]

Runge-Kutta 2nd Order Method: Heun's Method [YOUTUBE 9:27]

Runge-Kutta 2nd Order Method: Midpoint Method [YOUTUBE 10:45]

Runge-Kutta 2nd Order Method: Ralston's Method Part 1 of 2 [ YOUTUBE 7:09]

Runge-Kutta 2nd Order Method: Ralston's Method Part 2 of 2 [ YOUTUBE 5:00]

Runge-Kutta 2nd Order Method: Derivation Part 1 of 2 [ YOUTUBE 7:08]|

Runge-Kutta 2nd Order Method: Derivation Part 2 of 2 [ YOUTUBE 5:31]

RuNGE-KUTTA 4th ORDER METHOD

Runge Kutta 4th Order Method: Formulas [YOUTUBE 9:54]

Runge Kutta 4th Order Method: Example: Part 1 of 2 [YOUTUBE 9:29]

Runge Kutta 4th Order Method: Example: Part 2 of 2 [YOUTUBE 8:48]

HIGHER ORDER/COUPLED DIFFERENTIAL EQUATIONS

Higher Order Differential Equations: Background [YOUTUBE 6:47]

Coupled Differential Equations: Background: Part 1 of 2 [YOUTUBE 5:44]

Coupled Differential Equations: Background: Part 2 of 2 [YOUTUBE 6:44]

Higher Order Differential Equations: Euler's Method: Part 1 of 2 [YOUTUBE 9:50]

Higher Order Differential Equations: Euler's Method: Part 2 of 2 [YOUTUBE 4:24]

Higher Order Differential Equations: Heun's Method: Part 1 of 3 [YOUTUBE 4:23]

Higher Order Differential Equations: Heun's Method: Part 2 of 3 [YOUTUBE 7:44]

Higher Order Differential Equations: Heun's Method: Part 3 of 3 [YOUTUBE 10:17]

FINITE DIFFERENCE METHOD

Finite Difference Method of Solving Ordinary Differential Equations: Background Part 1 of 2 [YOUTUBE 3:46]

Finite Difference Method of Solving Ordinary Differential Equations: Background Part 2 of 2 [YOUTUBE 8:40]

Finite Difference Method: Example Beam: Part 1 of 2 [YOUTUBE 6:13]

Finite Difference Method: Example Beam: Part 2 of 2 [YOUTUBE 6:21]

Finite Difference Method: Example Pressure Vessel: Part 1 of 2 [YOUTUBE 9:55]

Finite Difference Method: Example Pressure Vessel: Part 2 of 2 [YOUTUBE 9:50]

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# 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 http://numericalmethods.eng.usf.edu is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. Based on a work at numericalmethods.eng.usf.edu.

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