| 1 |
Introduction to numerical methods in engineering
MATLAB® proficiency evaluation
First day of classes
|
(PDF) |
(ZIP) (The ZIP file contains: dudt.m, piv.m, and sph_drag_2.m.) |
| 2 |
Number representations
Errors of numerical operations
Recursion
|
(PDF) |
(ZIP) (The ZIP file contains: heron.m, horner.m, radd.m, recur.m, sbfj.m, sbfj_3.m, sbfj_f.m, sbfy.m, and tsbfj.m.) |
| 3 |
Error analysis
Error propagation
Condition numbers
|
(PDF) |
|
| 4 |
Roots of non-linear equations
General/Bisection/Secant/Newton-Raphson methods
|
(PDF) |
(ZIP) (The ZIP file contains: bisect.m, cube.m, div.m, heron.m, and sqr.m.) |
| 5 |
Linear systems
Gaussian elimination
|
(PDF) |
(ZIP) (The ZIP file contains: tbt.m, tbt2.m,tbt3.m, and tbt4.m.) |
| 6 |
Linear systems
Multiple right-hand-sides
LU factorization
|
(PDF) |
(ZIP) (The ZIP file contains: tbt6.m, tbt7.m, and tbt8.m.) |
| 7 |
Special matrices
Examples
|
(PDF) |
(ZIP) (The ZIP file contains: vib_string.m.) |
| 8 |
Linear systems
Iterative techniques
Gauss-Seidel
|
(PDF - 1.0 MB) (Courtesy of Reza Karimi. Used with permission.) |
|
| 9 |
Root finding and linear systems
Examples and applications
|
(PDF) (Courtesy of Dr. Yuming Liu. Used with permission.) |
|
| 10 |
Optimization
Curve fitting
|
(PDF) |
(ZIP) (The ZIP file contains: cost.m, curve.m, lstsq.m, and salesman.m.) |
| 11 |
Interpolation
Polynomial interpolation
Lagrange polynomials
Splines
|
(PDF) |
(ZIP) (The ZIP file contains: interp_test.m, lagrange.m, newton.m, and newton_coef.m.) |
| 12 |
Fourier interpolation
Fourier transforms
|
(PDF) |
(ZIP) (The ZIP file contains: tpcoef.m, tpeval.m, tptest.m, trig_poly.m, and ts.m.) |
| 13 |
Quiz 1 |
|
|
| 14 |
Numerical integration
Newton-Cotes
Gaussian quadratutre
|
(PDF) |
|
| 15 |
Numerical differentiation
Finite differences
Ordinary differential equations
Initial value problems
Euler's method
|
(PDF) |
(ZIP) (The ZIP file contains: dudt.m, sph_drag_2.m, and sph_param.m.) |
| 16 |
ODE-IVP
Runge-Kutta methods
|
(PDF) |
(ZIP) (The ZIP file contains: pcm.m, stiff.m, and stiff_imp.m.) |
| 17 |
Higher order ODEs
Boundary value problems
|
(PDF) |
(ZIP) (The ZIP file contains: back_tri.m, dudy.m, forw_tri.m, lu_fact.m, lu_tri.m, plate_flow.m, and sou_flow.m.) |
| 18 |
Partial differential equations
Introduction
Examples
|
(PDF) |
(ZIP) (The ZIP file contains: waveeq.m and wavei.m.) |
| 19 |
PDE review |
|
|
| 20 |
PDEs
Parabolic equations
|
(PDF) |
(ZIP) (The ZIP file contains: back_tri.m, forw_tri.m, heat_cn.m, heat_cn_sin.m, heat_fw.m, heat_fw_2.m, and lu_tri.m.) |
| 21 |
PDEs
Elliptic equations
|
(PDF) |
(ZIP) (The ZIP file contains: duct.m, duct_fs.m, duct_oil.m, and heat_plate.m.) |
| 22 |
Finite element methods |
(PDF) |
(ZIP) (The ZIP file contains: duct_galerkin.m, and exp_eq.m.) |
| 23 |
Boundary element methods
Panel methods (1)
|
(PDF)# (Courtesy of Dr. Yuming Liu. Used with permission.) |
(ZIP) (The ZIP file contains: cpm_main.m, cylinder_geom.m, gxy.m, inflcoef.m, localize.m, matrices.m, setbcs.m, and setpanels.m.) |
| 24 |
Boundary element methods
Panel methods (2)
|
|
|
| 25 |
Review |
(PDF - 1.0 MB) |
|
| 26 |
Quiz 2 |
|
|