MATLAB - Suranaree University of Technology

MATLAB - Suranaree University of Technology

MATLA B Week 7 Numerical Integration and Differentiation x h f x1 dy f lim 1 dx h 0

h y=f(x) dy f(x1) h=dx x1 x1+h x

MATLAB diff(x) element x [x(2)-x(1), x(3)-x(2),x(2)-x(1), x(3)-x(2), ,x(n)-x(n-1)] diff(x,n) element x n A

A MATLAB 1 x d cos x + sinsin(x) cos(x) dx x

x y d f x, y MATLAB 2x y 2 dx 2

x y MATLAB polyder(A) A

a Q f x dx b f(x) a

b x (Trapezoidal rule) h Q f x f x 2 f x 2

k1 0 n k k 1 f(x) b

a x0 x1 xi xn b a h n x

(Trapezoidal rule) trapz(x,y) y cumtrapz(x,y) y

(Trapezoidal rule) trapezodalc (Symsons rule) n n 1 n 2 h Q f x0 f xn 4 f xk 2 f xk 3 b a

h n k 1, 3, 5 k 2 , 4 , 6 (Symsons rule) Q=quad(F,a,b) F

a b Symsons rule (Symsons rule) -

Q=quad8(F,a,b) F a b Newton-Cotes error = 10-3 () Q=quadl(F,a,b) F a b Newton-Cotes error = 10-6 -

- int symbolic int(E) E int(E,v) E

v int(E,a,b) E a b int(E,v,a,b) E v a b

A t 3 t 1. 2. A(t) t=1.85 A(t) 1 pi

2 0.8-1.2 2t x 1 x e 0 cos 3t 3

0 1. 2. 2t 2

e cos 3t x 1 x 1. 2. sin xt 3.

Recently Viewed Presentations

  • Solving MRF using SOCP Relaxations

    Solving MRF using SOCP Relaxations

    Solving Markov Random Fields using Second Order Cone Programming Relaxations M. Pawan Kumar Philip Torr Andrew Zisserman Aim Aim Aim Aim Aim Aim Aim Aim Aim Aim Motivation Motivation Motivation Motivation Motivation Motivation Motivation Outline Integer Programming Formulation Previous Work...
  • TMC Overweight and Obesity (O2) ChallengeDiet and food ...

    TMC Overweight and Obesity (O2) ChallengeDiet and food ...

    *Sharma SV, Upadhyaya M*, Karhade M*, Baun B, Perkison WB, Feltovich M, Pompeii L, Brown HS, Hoelscher DM. Are hospital workers healthy? A study of cardiometabolic, behavioral and psychosocial factors associated with obesity among hospital workers. Journal of Occupational and...
  • CS 414 Review

    CS 414 Review

    CS 414 Review Operating System: Definition What is in an OS? Crossing Protection Boundaries User calls OS procedure for "privileged" operations Calling a kernel mode service from user mode program: Using System Calls System Calls switches execution to kernel mode...
  • "Theses on Feuerbach" Karl Marx - Adam Gómez

    "Theses on Feuerbach" Karl Marx - Adam Gómez

    Theory & practice * Historical Materialism "Reality" is the product of activity, the relationships and practices of people and things Rejection of idealism (the position that ideas precede things) Materialism new and old Old (Feuerbach): things are meaningful as objects...
  • Electrophilic Aromatic Substitution (Aromatic compounds) Ar-H = aromatic

    Electrophilic Aromatic Substitution (Aromatic compounds) Ar-H = aromatic

    Common substituent groups and their effect on EAS: -NH2, -NHR, -NR2 -OH -OR -NHCOCH3 -C6H5 -R -H -X -CHO, -COR -SO3H -COOH, -COOR -CN -NR3+ -NO2 increasing reactivity ortho/para directors meta directors Friedel-Crafts alkylation (variations) Ar-H + R-X, AlCl3 Ar-R...
  • Baywind Energy Co-op AGM 2006

    Baywind Energy Co-op AGM 2006

    Accounts : Sue Shields, Steph Tyson, Claire "Milly" Beattie, Qef Bogiqi and Cassie Bell. Tammy Calvert . Office Manager. Marketing & Membership. Lorraine Bilton, Holly McCreanor-Smith. Welcome and thanks to our staff - no change since last year. Rare photo...
  • TEST YOUR KNOWLEDGE Drug and Alcohol IQ Challenge

    TEST YOUR KNOWLEDGE Drug and Alcohol IQ Challenge

    D. Alcohol overdose occurs when there is so much alcohol in the bloodstream that areas of the brain controlling basic life-support functions, such as breathing, heart rate, and temperature control, begin to shut down.
  • PHONICS IN RECEPTION ENGLISH ALPHABETIC CODE 44 sounds

    PHONICS IN RECEPTION ENGLISH ALPHABETIC CODE 44 sounds

    Daily handwriting activities- practicing letter formation. Weekly mark making activity . Supporting activities around the classroom. How does it progress over the year? This half term - Taught as a whole class, learn roughly four sounds per week.