ECE3040
Lecture Notes
© Prof. Mohamad Hassoun
Lecture 1 Introduction and Overview
(Early Examples of Numerical Methods)
NOTE: Useful references for Lectures 2-6: Matlab Primer, Essentials of Matlab
Lecture 2 Matlab Basics I
Lecture 3 Matlab Basics II
Lecture 4 Matlab Programming I
Lecture 4 Scripts & Functions: Download (.zip)
Lecture 5 Matlab Programming II
Lecture
5 Scripts & Functions: Download (.zip)
Lecture 6 Programming Examples
Lecture 6 Scripts & Functions: Download (.zip)
Lecture 7 Polynomials
Lecture 8 Taylor Series Approximation I
(Movie:
sin(x) approximation
programmed for a vintage calculator)
Lecture 8 Scripts & Functions: Download (.zip)
Lecture
9 Taylor Series Approximation II
(Explorations with function
solve_poly)
Lecture 9 Scripts & Functions: Download (.zip)
Lecture
10 Digital machine Round-off Error
Lecture 10 Scripts & Functions: Download (.zip)
(Floating point numbers: video1 video2) (Binary array to string
conversion)
Lecture 11 Numerical Solution of Nonlinear Equations I
Lecture
11 Scripts & Functions: Download (.zip)
Fixed points, cobwebs, oscillation, chaos and orbit diagrams (read Sections 10.0-10.3)
Lecture
12 Numerical Solution of Nonlinear Equations
II
Lecture 12 Scripts & Functions: Download (.zip)
(Computing the
square-root) (Newton’s Method on a 1971
programmable calculator)
(1969
HP programmable calculator solving f(x)=0) (Suspended Chain Problem)
Lecture 13 Optimization I
Lecture
13 Scripts & Functions Download (.zip)
Lecture 14 Optimization II
Lecture
14 Scripts & Functions Download (.zip)
Lecture
15 Systems of Linear Equations I
Lecture 15 Scripts & Functions: Download
(.zip)
Lecture 16 Systems of Linear Equations II
Lecture
16 Scripts & Functions: Download (.zip)
Lecture
17 Polynomial Interpolation
Lecture 17 Scripts & Functions: Download
(.zip)
Lecture
18 Curve fitting by Least-Square Regression
Lecture
18 Scripts & Functions: Download (.zip)
(Example: Nonlinear LSE
regression with 6 Gaussians and 9 sample points)
Lecture
19 Numerical Integration I
Lecture
19 Scripts & Functions: Download (.zip)
Lecture
20 Numerical Integration II
Lecture
21 Numerical Differentiation
Lecture
22 Numerical Solution of Differential
Equations
Lecture 22 Scripts & Functions: Download (.zip)
MATLAB:
Solving ODEs.
Interactive phase-portrait generation
Symbolic Solution of Linear ODEs
Restricted
Three-Body Gravitation Problem
General Three-Body Gravitation Problem
Calculus of variations based optimization
Deriving the “catenary” (suspended chain) without calculus of variations
Analog
Computer Solution of Differential Equations
· Simple mass-spring system with damping (Linear)
· Coupled oscillators: Hanging mass/spring system (Linear)
Solution using analog electronic circuits
Matlab
generated movie of phase plane: 
vs 
.
·
Lorenz
attractor (Non-linear) [Chaos: Watch movie, Matlab movie]
· Lotka-Volterra (Predator-Prey) Model (Nonlinear)
· Van der Pol Oscillator (Nonlinear)
· Duffing Oscillator (Nonlinear) [Physical system]
· Tunnel Diode Circuit (Nonlinear); Matlab generated movie
· Bifurcation and chaos (scope close up) Watch the movie
Appendices:
Summary of User-Defined and Built-in Matlab
Functions
The 10 Most Important Matlab
Functions for Numerical Methods
Numerical Methods used in Early Electronic Calculators
Graphical input from mouse cursor