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Gradient & Mathematical Modeling and Simulation Using MATLAB Prof. Muhammad Saeed
Gradient I: x =-2:0.2:2; y = x.* exp(-x.^2); px = gradient(y,.2); quiver(x,px)
Gradient II: [x,y] = meshgrid(-2:0.2:2); z = x.* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(x,y,z), hold on, quiver(x,y,px,py), hold off
Gradient II: [x,y] = meshgrid(-2:0.2:2); u = x.* exp(-x.^2 - y.^2); [gx,gy] = gradient(u,.2,.2); contour(x,y,u), hold on, quiver(x,y,gx,gy), hold off
[x,y] = meshgrid(-4:4,-3:3); u = x.*x+y.*y; v = 4*del2(u) V =
[x,y,z] = meshgrid(-3:3,-3:3,-3:3); u = x.*x + y.*y + z.*z; v = 6*del2(u)
v(:,:,1) = v(:,:,2) = v(:,:,3) = v(:,:,4) = v(:,:,5) = v(:,:,6) = v(:,:,7) =
September 24, 2009Theory of Computation Lecture 6: Primitive Recursive Functions II 1 Homework Questions Question 1: Write a program P that computes
S i m u l i n k Prof. Muhammad Saeed Mathematical Modeling and Simulation UsingMATLAB 1.
基 督 再 來 （一）. 經文： 1 你們心裡不要憂愁；你們信神，也當信我。 2 在我父的家裡有許多住處；若是沒有，我就早 已告訴你們了。我去原是為你們預備地去 。 3 我 若去為你們預備了地方，就必再來接你們到我那 裡去，我在 那裡，叫你們也在那裡， ] ( 約 14 ： 1-3)
Start of Presentation Mathematical Modeling of Physical Systems © Prof. Dr. François E. Cellier September 20, st Homework Problem We wish to analyze.
1 Solve each: 1. 5x – 7 > 8x |x – 5| < 2 3. x 2 – 9 > 0 :
[FX,FY,FZ,...] = GRADIENT(F,...) [FX,FY,FZ,…] is numerical gradient of matrix F Distance between grid points in X,Y,Z,… direction FX corresponds to dF/dx,
C O N I C S E C T I O N S 1.2 CIRCLES. (a) Find the equation of a tangent and normal to a circle. (b) Find the length of a tangent from a fixed point.
Part 5 Chapter 19 Numerical Differentiation PowerPoints organized by Dr. Michael R. Gustafson II, Duke University All images copyright © The McGraw-Hill.
7-3 NOTES Algebra II. Starter Given that f(x) = 3x – 2, and g(x) = 2x 2, f(x) – g(x) = f(x) *g(x) g(f(x)) =
Piecewise Graphs A piecewise function is defined by at least two equations, each of which applies to a different part of the function’s domain. One example.
1. 3x + 2 = ½ x – 5 2. |3x + 2| > x – 5 < -3x |x + 2| < 15 Algebra II 1.
Lecture 14 Prof. Dr. M. Junaid Mughal Mathematical Statistics 1.
Binomial test (a) p = 0.07 n = 17 X ~ B(17, 0.07) (i) P(X = 2) = = using Bpd on calculator Or 17 C 2 x x (ii) n = 50 X ~ B(50,
Национальная процедура одобрения и регистрации проектов (программ) международной технической помощи (исключая представление информации об организации и.
The gradient as a normal vector. Consider z=f(x,y) and let F(x,y,z) = f(x,y)-z Let P=(x 0,y 0,z 0 ) be a point on the surface of F(x,y,z) Let C be any.
7.6 Rational Zero Theorem Algebra II w/ trig. RATIONAL ZERO THEOREM: If a polynomial has integer coefficients, then the possible rational zeros must be.
Mathematics Roots, Differentiation and Integration Prof. Muhammad Saeed.
1. (a) (b) The random variables X 1 and X 2 are independent, and each has p.m.f.f(x) = (x + 2) / 6 if x = –1, 0, 1. Find E(X 1 + X 2 ). E(X 1 ) = E(X 2.
Jeopardy Factoring Functions Laws of Exponents Polynomial Equations Q $100 Q $200 Q $300 Q $400 Q $100 Q $200 Q $300 Q $400 Final Jeopardy Q $500.
1. Overview 2. plot in 2D 3. Plot in 3D 4. Other possible charts 5. Engineers: label your plots! 6. Plots & Polynomial Plotting 11.
1 Financial Mathematics Clicker review session, Final.
Computer Graphics Prof. Muhammad Saeed. Introduction & Hardware 1 August 1, Hardware I Computer Graphics.
Proof Methods & strategies Section 1.7. Proof by Cases We use the rule of inference P 1 P 2 ... P n q (P 1 q) (P 2 q) .. (P n q)
Stress Matrix Visualization Wednesday, 9/4/2002. Stress Vector.
Moody Mathematics $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400.
CSE 123 Plots in MATLAB. Easiest way to plot Syntax: ezplot(fun) ezplot(fun,[min,max]) ezplot(fun2) ezplot(fun2,[xmin,xmax,ymin,ymax]) ezplot(fun) plots.
Bell Assignment 1.Graph the equation y = x 3 + 3x 2 – 1 on your GUT. Then use the graph to describe the increasing or decreasing behavior of the function.
1 Mathematics for Business (Finance) Instructor: Prof. Ken Tsang Room E409-R11
Computer Graphics Prof. Muhammad Saeed Dept. of Computer Science & IT Federal Urdu University of Arts, Sciences and Technology.
Step 1 Create a new Photoshop documents with the size 200 x 600px. Open up the image you wish to use as your reflection and copy and paste the image.
Differential Equations Prof. Muhammad Saeed Mathematical Modeling and Simulation UsingMATLAB (Plus Symbolic Mathematics) 1.
1 Financial Mathematics Clicker review session, Midterm 01.
Prof. Muhammad Saeed ( Differentiation and Integration )
Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.
Section 8.3 Suppose X 1, X 2,..., X n are a random sample from a distribution defined by the p.d.f. f(x)for a < x < b and corresponding distribution function.
1 Edge Operators a kind of filtering that leads to useful features.
Estimating Car Demand Demand Function for Car Industry Q = a 1 P + a 2 P x + a 3 I + a 4 Pop + a 5 i + a 6 A Demand Equation for Car Industry Q = -500P.
Last Answer LETTER I h(x) = 3x 4 – 8x Last Answer LETTER R Without graphing, solve this polynomial: y = x 3 – 12x x.
Program design and algorithm development We will consider the design of your own toolbox to be included among the toolboxes already available with your.
Interpolation and Curve Fitting Prof. Muhammad Saeed Mathematical Modeling and Simulation UsingMATLAB.
ADC Calculations Joshua Kim. I. Objective and Goals II. Current ADC Results III. Current Progress on MatLab Program Outline.
Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.
EXAMPLES: Example 1: Consider the system Calculate the equilibrium points for the system. Plot the phase portrait of the system. Solution: The equilibrium.
Quiz #1 30/30 congratulations 1)AL-AMER, AHMAD ADNAN MOHA 2)AL-AGEELI, AHMAD IBRAHIM 3)AL-GARNI, BANDAR HASSAN S 4)AL-ARJANI, ALI SAEED ABDU 5)AL-BUGMI,
Prof. Muhammad Saeed ( Ordinary Differential Equations )
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