Example_15_Cubic_Spline | STEM Course Prep

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Numerical Analysis for Engineering Students

Root Finding Methods

Download the Outline of Notes Here
1.1 Error Calculations (14:43)
1.2 Bisection Method (10:56)
1.3 Bisection Method Algorithm (5:38)
1.4 Example 1 (12:21)
1.5 MATLAB Bisection Method (9:05)
1.6 Newtons Method (11:17)
1.7 Newtons Algorithm and Example 2 (12:53)
1.8 MATLAB Example 2 (5:26)
1.9 MATLAB Example 3 (7:33)
1.10 Secant Method (8:11)
1.11 Secant Method Algorithm and Example 4 (12:24)
1.12 MATLAB Example 4 Secant Method (4:01)
1.13 MATLAB Example 5 Secant Method (5:51)

Solving Systems of Linear Equations

2.1 Solving Systems of Linear Equations (13:23)
2.2 Gaussian Elimination (16:05)
2.3 Gaussian Elimination Algorithm and MATLAB example (8:35)
2.4 MATLAB Example 6 Gaussian Elimination (9:39)
2.5 Gaussian Elimination with Pivoting (8:58)
2.6 Gauss Jordan Elimination and Example 7 (16:00)
2.7 Gauss Jordan and MATLAB example (5:01)

Curve Fitting and Interpolation

3.1 Least Squares Regression (24:41)
3.2 Example 8 with MATLAB (10:50)
3.3 Polynomial Regression (18:02)
3.4 Example 9 (21:36)
3.5 Example 9 with MATLAB functions (12:39)
3.6 Lagrange Interpolating Polynomials (6:08)
3.7 Example 10 (21:28)
3.8 Example 11 (10:49)
3.9 Lagrange Interpolating Polynoimal Alorithm with MATLAB (8:45)
3.10 Newtons Divided Differences (21:17)
3.11 Example 12 Divided Differences (17:45)
3.12 Divided Differences Algorithm and MATLAB Example 12 (8:03)
3.13 Linear Splines (10:15)
3.14 Example 13 MATLAB Linear Spline (7:39)
3.15 Quadratic Splines (15:28)
3.16 Example 14 Quadratic Spline with MATLAB (28:48)
3.17 Cubic Splines (16:31)
3.18 Example 15 Cubic Spline with MATLAB (15:24)
3.19 Cubic Spline with Lagrange Polynomials (16:45)
3.20 Example 16 Cubic Spline (15:22)
3.21 Cubic Spline Algorithm with MATLAB (10:01)
3.22 Cubic Spline built in MATLB function (6:42)

Numerical Differentiation

4.1 Numerical Differentiation (15:52)
4.2 Example 17 and Example 18 (10:27)
4.3 Finite Difference with Taylor Series Part 1 (19:42)
4.4 Three Point Difference Equations (9:11)
4.5 Example 19 Three Point Difference (6:32)
4.6 2nd Derivative with Finite Difference and Example 20 in MATLAB (11:12)
4.7 Differentiation with Lagrange Polynomials (8:15)
4.8 Example 21 Differentiation with Lagrange Polynomials (6:57)
4.9 MATLAB Differentiation Functions (14:24)

Numerical Integration

5.1 Rectangle and Midpoint Methods (18:31)
5.2 Example 22 Midpoint and Rectangle Methods (10:04)
5.3 Example 22 MATLAB Midpoint and Rectangle Methods (8:12)
5.4 Trapezoidal and Simpsons Methods (27:35)
5.5 Example 23 Trapezoidal and Simpsons Methods (21:30)
5.6 Example 23 MATLAB Simpsons Methods (13:40)
5.7 Examples 24 and 25 Composite Trapezoidal (12:55)

Ordinary Differential Equations - Initial Value Problems

6.1 ODE Euler Method (15:46)
6.2 Example 26 Eulers Method (13:52)
6.3 Modified Eulers Method (6:42)
6.4 Example 27 Modified Eulers (11:06)
6.5 2nd Order Runge Kutta (10:51)
6.6 Example 28 2nd Order RK (12:18)
6.7 3rd and 4th Order RK4 (10:28)
6.8 Example 29 4th Order RK (12:18)
6.9 Example 30 System of ODEs with RK (24:40)
6.10 Example 31 Switching to System of 1st Order ODEs (10:46)
6.11 Example 32 Reduction to System of 1st Order ODEs (8:59)

MATLAB Codes

Example_15_Cubic_Spline

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