Untitled Document

INTRODUCTION TO SCIENTIFIC COMPUTING
INTRODUCTION TO NUMERICAL METHODS (CHAPTER 01.01)
	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 (CHAPTER 01.02)
	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 (CHAPTER 01.03)
	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 (CHAPTER 01.04)
	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 (CHAPTER 01.05)
	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: Part 1 of 1 [YOUTUBE 7:50] Floating Point Representation: Example: Part 2 of 2 [YOUTUBE 6:48] Floating Point Representation - Biased Exponent: Example [YOUTUBE 8:51]
TAYLOR'S THEOREM REVISITED (CHAPTER 01.06)
	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 (CHAPTER 02.01)
	Background of Differentiation [YOUTUBE 7:17]
DIFFERENTIATION OF CONTINUOUS FUNCTIONS (CHAPTER 02.02)
	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 (CHAPTER 02.03)
	Divided Difference Approach [YOUTUBE 10:07] Polynomial Interpolation Method [YOUTUBE 8:09]
NONLINEAR EQUATIONS
QUADRATIC EQUATIONS (CHAPTER 03.01)
	The Quadratic Equation Formula [YOUTUBE 4:22] Derivation of the Quadratic Formula [YOUTUBE 5:41] Example of Quadratic Equation [YOUTUBE 7:48]
BISECTION METHOD (CHAPTER 03.03)
	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 (CHAPTER 03.04)
	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]

SIMULTANEOUS LINEAR EQUATIONS
BACKGROUND (CHAPTER 04.01)
	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 (CHAPTER 04.06)
	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] 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] 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 (CHAPTER 04.08)
	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 ((CHAPTER 05.01)

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

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

DIRECT METHOD ((CHAPTER 05.02)

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 (CHAPTER 05.05)

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 (CHAPTER 05.06)

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 (CHAPTER 06.03)

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 (CHAPTER 06.04)

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]

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]

ADEQUACY OF REGRESSION MODELS (CHAPTER 06.05)

Adequacy of Regression Models: Introduction [YOUTUBE 6:04]

Adequacy of Regression Models : Check One: Plot the Data [YOUTUBE 2:06]

Adequacy of Regression Models : Check Two: Standard Error of Estimate [YOUTUBE 10:00]

Adequacy of Regression Models : Check Three: Coefficient of Determination: Part 1 of 2 [YOUTUBE 7:54]

Adequacy of Regression Models : Check Three: Coefficient of Determination: Part 2 of 2 [YOUTUBE 6:47]

Adequacy of Regression Models : Check Four: Assumption of Random Errors [YOUTUBE 6:32]

INTEGRATION

PRIMER ON INTEGRAL CALCULUS (CHAPTER 07.01)

Accumulation Function: Example [YOUTUBE 10:51]

TRAPEZOIDAL RULE (CHAPTER 07.02)

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 (CHAPTER 07.05)

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 (CHAPTER 07.06)

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 (CHAPTER 08.01)

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 (CHAPTER 08.02)

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 (CHAPTER 08.03)

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]

HIGHER ORDER/COUPLED DIFFERENTIAL EQUATIONS (CHAPTER 08.05)

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 7:48]

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]