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] [TRANSCRIPT]

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

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

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

MEASURING ERRORS (CHAPTER 01.02)

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

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

Approximate Error Definition & Example  [YOUTUBE 6:39]  [TRANSCRIPT]

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

SOURCES OF ERROR (CHAPTER 01.03)

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

Effect of Carrying Significant Digits [YOUTUBE 7:48] [TRANSCRIPT]

Truncation Error: Definition [YOUTUBE 8:34] [TRANSCRIPT]

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

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

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

BINARY REPRESENTATION (CHAPTER 01.04)

Introduction to Binary Representation [YOUTUBE 6:41] [TRANSCRIPT]

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

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

FLOATING POINT REPRESENTATION (CHAPTER 01.05)

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

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

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

Floating Point Representation: Example:   [YOUTUBE 6:35]

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

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

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

TAYLOR'S THEOREM REVISITED (CHAPTER 01.06)

Introduction to Taylor Series [YOUTUBE 7:28] [TRANSCRIPT]

Taylor Series: Example [YOUTUBE 6:31] [TRANSCRIPT]

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

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

DIFFERENTIATION

BACKGROUND (CHAPTER 02.01)

Background of Differentiation [YOUTUBE 7:17] [TRANSCRIPT]

Differentiation of Continuous Functions (CHAPTER 02.02)

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

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

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

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

Central Divided Difference [YOUTUBE 9:53] [TRANSCRIPT]

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

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

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

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

Differentiation of Discrete Functions (CHAPTER 02.03)

Divided Difference Approach [YOUTUBE 10:07] [TRANSCRIPT]

Polynomial Interpolation Method [YOUTUBE 8:09] [TRANSCRIPT]

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

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

NONLINEAR EQUATIONS

QUADRATIC EQUATIONS (CHAPTER 03.01)

The Quadratic Equation Formula [YOUTUBE 4:22] [TRANSCRIPT]

Derivation of the Quadratic Formula [YOUTUBE  5:41] [TRANSCRIPT]

Example of Quadratic Equation [YOUTUBE  7:48] [TRANSCRIPT]

BISECTION METHOD (CHAPTER 03.03)

Background of Bisection Method [YOUTUBE  9:04] [TRANSCRIPT]

Algorithm  of Bisection Method [YOUTUBE  9:47] [TRANSCRIPT]

Example of Bisection Method [YOUTUBE  9:53] [TRANSCRIPT]

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

Newton-Raphson Method (CHAPTER 03.04)

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

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

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

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

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

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

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

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

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

SECANT METHOD (CHAPTER 03.05)

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

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

Algorithm  of Secant Method  [YOUTUBE  5:16] [TRANSCRIPT]

Example of Secant Method [YOUTUBE  8:16] [TRANSCRIPT]

FALSE-POSITION METHOD (CHAPTER 03.06)

False-Position Method: Part 1 of 3 [YOUTUBE  15:08] 

False-Position Method: Part 2 of 3 [YOUTUBE  15:01] 

False-Position Method: Part 3 of 3 [YOUTUBE  11:09] 

REGRESSION

Linear Regression (CHAPTER 06.03)

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

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

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

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

Linear Regression: Example [YOUTUBE 10:24] [TRANSCRIPT]

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

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

Nonlinear Regression (CHAPTER 06.04)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Adequacy of regression models (CHAPTER 06.05)

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

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

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

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

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

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

INTEGRATION

primer ON INTEGRAL CALCULUS (CHAPTER 07.01)

Accumulation Function: Example [YOUTUBE 10:51] [TRANSCRIPT]

Trapezoidal Rule (CHAPTER 07.02)

Trapezoidal Rule Derivation [YOUTUBE 10:51] [TRANSCRIPT]

Trapezoidal Rule: Example [YOUTUBE  7:18] [TRANSCRIPT] 

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

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

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

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

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

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

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

SIMPSON'S 1/3 RULE (CHAPTER 07.03)

Simpson's One Third Rule Derivation [YOUTUBE 10:44] [TRANSCRIPT]

Simpsons 1/3 Rule of Integration: Example [YOUTUBE 7:03] [TRANSCRIPT]

Multiple Segment Simpson 1/3 Rule Derivation Part 1 of 2  [YOUTUBE 8:14] [TRANSCRIPT]

Multiple Segment Simpson 1/3 Rule Derivation Part 2 of 2 [YOUTUBE 6:41] [TRANSCRIPT]

Multiple Segment Simpson 1/3 Rule Example: Part 1 of 2 [YOUTUBE 8:26] [TRANSCRIPT]

Multiple Segment Simpson 1/3 Rule Derivation Part 2 of 2 [YOUTUBE 8:47] [TRANSCRIPT]

rOMBERG INTEGRATION (CHAPTER 07.04)

Multiple Segment Trapezoidal Rule Error: Derivation [YOUTUBE 8:45] [TRANSCRIPT]

Multiple Segment Trapezoidal Rule Error: Example [YOUTUBE 8:51] [TRANSCRIPT]

Richardsons Extrapolation of Trapezoidal Rule: Theory [YOUTUBE 9:45] [TRANSCRIPT]

Richardsons Extrapolation of Trapezoidal Rule: Example [YOUTUBE 9:23] [TRANSCRIPT]

Romberg Integration: Theory: Part 1 of 2[YOUTUBE 9:17] [TRANSCRIPT]

Romberg Integration: Theory: Part 2 of 2 [YOUTUBE 6:35] [TRANSCRIPT]

Gauss Quadrature Rule (CHAPTER 07.05)

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

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

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

Converting Limits of Integration [YOUTUBE 7:13] [TRANSCRIPT]

Gaussian Quadrature Rule: Example [ YOUTUBE 8:55] [TRANSCRIPT]

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

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

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

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

Discrete Data Integration (CHAPTER 07.06)

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

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

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

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

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

improper Integration (CHAPTER 07.07)

Improper Integration: Background  [YOUTUBE 4:56] [TRANSCRIPT]

Improper Integration: Singular Integrand: Example  [YOUTUBE 9:16] [TRANSCRIPT]

Multiple Segment Gauss Quadrature Rule for Singular Integrands: Part 1 of 2  [YOUTUBE 5:24] [TRANSCRIPT]

Multiple Segment Gauss Quadrature Rule for Singular Integrands: Part 2 of 2  [YOUTUBE 7:41] [TRANSCRIPT]

simpson's 3/8 rule of integration (CHAPTER 07.08)

Simpsons 3/8 Rule of Integration: Part 1 of 7 [YOUTUBE 15:09]

Simpsons 3/8 Rule of Integration: Part 2 of 7 [YOUTUBE 14:48]

Simpsons 3/8 Rule of Integration: Part 3 of 7 [YOUTUBE 15:13]

Simpsons 3/8 Rule of Integration: Part 4 of 7 [YOUTUBE 12:39]

Simpsons 3/8 Rule of Integration: Part 5 of 7 [YOUTUBE 13:37]

Simpsons 3/8 Rule of Integration: Part 6 of 7 [YOUTUBE 11:59]

Simpsons 3/8 Rule of Integration: Part 7 of 7 [YOUTUBE 05:09]

ORDINARY DIFFERENTIAL EQUATIONS

Primer on ODE (CHAPTER 08.01)

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

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

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

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

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

EuLER's METHOD (CHAPTER 08.02)

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

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

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

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

RuNGE-KUTTA 2ND ORDER METHOD (CHAPTER 08.03)

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

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

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

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

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

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

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

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

RuNGE-KUTTA 4th ORDER METHOD (CHAPTER 08.04)

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

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

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

HIGHER ORDER/COUPLED DIFFERENTIAL EQUATIONS (CHAPTER 08.05)

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

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

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

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

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

Higher Order Differential Equations: Heun's Method: Part 1 of 3  [YOUTUBE 7:48] [TRANSCRIPT]

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

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

shooting meTHOD (CHAPTER 08.06)

Shooting Method: Background [YOUTUBE 6:32]

Shooting Method: The Method [YOUTUBE 6:53]

Shooting Method: Example: Part 1 of 4 [YOUTUBE 7:31]

Shooting Method: Example: Part 2 of 4 [YOUTUBE 9:40]

Shooting Method: Example: Part 3 of 4 [YOUTUBE 4:48]

Shooting Method: Example: Part 4 of 4 [YOUTUBE 8:18]

FINITE DIFFERENCE METHOD (CHAPTER 08.07)

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]

OPTIMIZATION

golden search method (CHAPTER 09.01)

Golden Section Search Method: Theory: Part 1 of 6 [YOUTUBE 14:17]

Golden Section Search Method: Theory: Part 2 of 6 [YOUTUBE 14:11]

Golden Section Search Method: Theory: Part 3 of 6 [YOUTUBE 15:24]

Golden Section Search Method: Theory: Part 4 of 6 [YOUTUBE 15:48]

Golden Section Search Method: Theory: Part 5 of 6 [YOUTUBE 13:46]

Golden Section Search Method: Theory: Part 6 of 6 [YOUTUBE 11:48]

Golden Section Search Method: Example: Part 1 of 2 [YOUTUBE 13:51]

Golden Section Search Method: Example: Part 2 of 2 [YOUTUBE 13:26]

NEWTON's METHOD (CHAPTER 09.02)

Newton's Method for One Dimensional Optimization: Theory: Part 1 of 2 [YOUTUBE 12:04]

Newton's Method for One Dimensional Optimization: Theory: Part 2 of 2 [YOUTUBE 15:07]

Newton's Method for One Dimensional Optimization: Example [YOUTUBE 14:16]

MULTIDIRECTIONAL DIRECT SEARCH METHOD (CHAPTER 09.03)

Multi Dimensional Direct Search Method of Optimization: Theory [YOUTUBE 13:37]

Multi Dimensional Direct Search Method of Optimization: Example: Part 1 of 2 [YOUTUBE 13:55]

Multi Dimensional Direct Search Method of Optimization: Example: Part 2 of 2 [YOUTUBE 08:41]

MULTIDIRECTIONAL gradient SEARCH METHOD (CHAPTER 09.04)

Multi Dimensional Gradient Method of Optimization: Theory: Part 1 of 2 [YOUTUBE 11:34]

Multi Dimensional Gradient Method of Optimization: Theory: Part 2 of 2 [YOUTUBE 14:33]

Multi Dimensional Gradient Method of Optimization: Example: Part 1 of 2 [YOUTUBE 13:50]

Multi Dimensional Gradient Method of Optimization: Example: Part 2 of 2 [YOUTUBE 04:44]

PARTIAL DIFFERENTIAL EQUATIONS

INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (CHAPTER 09.01)

Introduction to Partial Differential Equations [YOUTUBE 9:41]

elliptic partial differential equations (CHAPTER 09.02)

Introduction to Partial Differential Equations [YOUTUBE 9:41]

Introduction to Numerical Solution of 2nd Order Linear Elliptic PDEs  [YOUTUBE 8:59]

Direct method: Numerical Solution of Elliptic PDEs [YOUTUBE 9:17]

Elliptic PDEs: Gauss-Seidel Method [YOUTUBE 13:42]

Elliptic PDEs: Lieberman Method: Part 1 of 2 [YOUTUBE 5:18]

Elliptic PDEs: Lieberman Method: Part 2 of 2 [YOUTUBE 12:11]

FAST FOURIER TRANSFORMS

INTRODUCTION TO FOURIER SERIES (CHAPTER 11.01)

Introduction to Fourier Series: Part 1 of 2 [YOUTUBE 10:36]

Introduction to Fourier Series: Part 2 of 2 [YOUTUBE 8:32]

continuous FOURIER SERIES (CHAPTER 11.02)

Continuous Fourier Series: Part 1 of 2 [YOUTUBE 9:41]

Continuous Fourier Series: Part 2 of 2 [YOUTUBE 7:40]

Continuous Fourier Series: Example: Part 1 of 2 [YOUTUBE 9:33]

Continuous Fourier Series: Example: Part 2 of 2 [YOUTUBE 9:06]

Complex Form of Fourier Series: Part 1 of 2 [YOUTUBE 15:05]

Complex Form of Fourier Series: Part 2 of 2 [YOUTUBE 13:42]

FOURIER TRANSFORM PAIR: FREQUENCY & TIME DOMAIN (CHAPTER 11.03)

Fourier Transform Pair: Frequency & Time Domain: Part 1 of 3 [YOUTUBE 8:06]

Fourier Transform Pair: Frequency & Time Domain: Part 2 of 3 [YOUTUBE 13:44]

Fourier Transform Pair: Frequency & Time Domain: Part 3 of 3 [YOUTUBE 11:55]

Fourier Transform Pair: Complex Numbers in Polar Coordinates: Part 1 of 2 [YOUTUBE 09:58]

Fourier Transform Pair: Complex Numbers in Polar Coordinates: Part 2 of 2 [YOUTUBE 09:48]

Fourier Transform Pair: Non-periodic Function: Part 1 of 2 [YOUTUBE 09:10]

Fourier Transform Pair: Non-periodic Function: Part 2 of 2 [YOUTUBE 08:55]

discrete FOURIER TRANSFORM (CHAPTER 11.04)

Discrete Fourier Transform: Part 1 of 3 [YOUTUBE 11:23]

Discrete Fourier Transform: Part 2 of 3 [YOUTUBE 06:37]

Discrete Fourier Transform: Part 3 of 3 [YOUTUBE 12:55]

Discrete Fourier Transform Continued: Part 1 of 2 [YOUTUBE 10:38]

Discrete Fourier Transform Continued: Part 2 of 2 [YOUTUBE 10:32]

Discrete Fourier Transform: Aliasing Phenomenon, Nyquist Sample/Rate: Part 1 of 2 [YOUTUBE 11:46]

Discrete Fourier Transform: Aliasing Phenomenon, Nyquist Sample/Rate: Part 2 of 2 [YOUTUBE 14:38]

INFORMAL DEVELOPMENT OF FAST FOURIER TRANFORM (CHAPTER 11.05)

Informal Development of Fast Fourier Transform: Part 1 of 3 [YOUTUBE 09:59]

Informal Development of Fast Fourier Transform: Part 2 of 3 [YOUTUBE 12:39]

Informal Development of Fast Fourier Transform: Part 3 of 3 [YOUTUBE 09:46]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 1 of 4 [YOUTUBE 14:08]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 2 of 4 [YOUTUBE 14:48]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 3 of 4 [YOUTUBE 13:45]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 4 of 4 [YOUTUBE 11:49]

Fast Fourier Transform: Companion Node Observation: Part 1 of 3 [YOUTUBE 11:22]

Fast Fourier Transform: Companion Node Observation: Part 2 of 3 [YOUTUBE 12:56]

Fast Fourier Transform: Companion Node Observation: Part 3 of 3 [YOUTUBE 09:01]

Fast Fourier Transform: Determination of W^P: Part 1 of 4 [YOUTUBE 13:34]

Fast Fourier Transform: Determination of W^P: Part 2 of 4 [YOUTUBE 09:31]

Fast Fourier Transform: Determination of W^P: Part 3 of 4 [YOUTUBE 07:36]

Fast Fourier Transform: Determination of W^P: Part 4 of 4 [YOUTUBE 09:41]

Fast Fourier Transform: Unscrambling the FFT: Determination of W^P: Part 1 of 3 [YOUTUBE 15:07]

Fast Fourier Transform: Unscrambling the FFT: Determination of W^P: Part 1 of 3 [YOUTUBE 15:14]

Fast Fourier Transform: Unscrambling the FFT: Determination of W^P: Part 1 of 3 [YOUTUBE 14:32]