| SES # | TOPICS | LECTURE NOTES | MATLAB® SCRIPTS |
|---|---|---|---|
| 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 |