Numerical Methods
for Calculus & DE
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MA3457/CS4033 Projects MATLAB Procedures |
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Sections B01/B01
Mon, Tue, Thu, Fri - 2:00 pm| Basics: |
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During the course, a number of MATLAB scripts implementing corresponding numerical algorithms will come into use - some of them will be introduced in classes, others will be adapted/composed by the students themselves working on the HW assignments.
The set of these scripts will create a Library of MATLAB Procedures which each students will work with on Part II of the Final Exam when solving problems in the MATLAB environment. The Table below contains the list of those scripts along with their basic descriptions.
| Procedure: | Function: | Source: | Download: | |||
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| Lagrange_coef | Computation of coefficients of the Lagrange interpolation polynomial | Class: Thur, Oct 30 | Lagrange_coef.txt | |||
| Lagrange_Eval | Evaluation of the Lagrange polynomial at point x = t | Class: Thur, Oct 30 | Lagrange_Eval.txt | |||
| Newton_coef | Evaluation of the Newton interpolation polynomial | Class: Fri, Oct 31 | Newton_coef.txt | |||
| Newton_Eval | Evaluation of the Newton polynomial at point x = t | Class: Fri, Oct 31 | Newton_Eval.txt | |||
| [Poly-Graph] | Visualization of the resulting interpolation polynomials | HW [C5]: Mon, Nov 3 | - | |||
| [Chebyshev-Nodes] | Computation of abscissas of Chebyshev points | HW [C6]: Mon, Nov 3 | - | |||
| interp1 | MATLAB built-in interpolation function | HW [C7]: Mon, Nov 3 | - | |||
| Spline_test | Script calling MATLAB "spline" function and plotting the result | Class: Thur, Nov 6 | Spline_test.txt | |||
| FBC_Diff | Numerical differentiation with forward, backward, and central differences | HW [C10]: Fri, Nov 7 | - | |||
| Lin_LS | Linear least squares approximation | Class: Tue, Nov 11 | Lin_LS.txt | |||
| Quad_LS | Quadratic least squares approximation | Class: Thur, Nov 13 | Quad_LS.txt | |||
| Cubic_LS | Cubic least squares approximation | HW [C15]: Thur, Nov 13 | - | |||
| polyfit | MATLAB built-in approximation function | HW [C17]: Thur, Nov 13 | - | |||
| [Legendre-Poly] | Visualization of the Legendre polynomials | HW [C18]: Fri, Nov 14 | - | |||
| [Chebyshev-Poly] | Visualization of the Chebyshev polynomials | HW [C19]: Fri, Nov 14 | - | |||
| Trap | Composite Trapezoid Rule | Class: Thur, Nov 20 | Trap.txt | |||
| Simp | Composite Simpson's Rule | HW [C22]: Fri, Nov 21 | - | |||
| Romb | Romberg integration | Class: Mon, Nov 24 | Romb.txt | |||
| Gauss_quad | Integration using Gaussian Quadratures | Class: Tue, Nov 26 | Gauss_quad.txt | |||
| Euler | Solution of IVP using Euler's method | Class: Thur, Dec 4 | Euler.txt | |||
| Taylor_2 | Solution of IVP using the 2nd order Taylor method | HW [C33]: Thur, Dec 4 | - | |||
| RK2 | Solution of IVP using the Runge-Kutta method of order 2 | Class: Fri, Dec 5 | RK2.txt | |||
| RK4 | Solution of IVP using the Runge-Kutta method of order 4 | Class: Fri, Dec 5 | RK4.txt | |||
| RK4_sys | Solution of ODE-IVP system using the Runge-Kutta method of order 4 | Class: Tue, Dec 9 | RK4_sys.txt | |||
| fivp_sys | Definition of the right-hand sides in ODE-IVP systems | Class: Tue, Dec 9 | fivp_sys.txt | |||
| BVP_shooting | Solution of BVP with the shooting method | Class: Tue, Dec 9 | BVP_shooting.txt | |||
| BVP_shooting_b | Version of BVP_shooting for general boundary conditions at x = b | HW [C43]: Fri, Dec 14 | - | |||
| BVP_FD | Solution of BVP with the finite-difference method | Class: Fri, Dec 14 | BVP_FD.txt | |||
| Trid_Thomas | Solution of system of linear equations with tridiagoanl matrix | Class: Fri, Dec 14 | Trid_Thomas.txt |
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