computational physics using matlab

... solution using Euler, Euler Cromer, Runge Kutta and Matlab ODE45 solver 15 Figure The damped pendulum using the Euler-Cromer method 17 Figure Results from Physical pendulum, using ... Runge-Kutta and finally the built in MATLAB solver ODE23 The solution using the built in MATLAB solver ODE23 is somewhat less straightforward than those using the other techniques A discussion ......

Ngày tải lên: 16/05/2015, 12:27

... (x1(n+1) ^2) ); x2(n+1)=b2*y2(n)+a*x2(n) +2* (1-a)*(x2(n)) ^2/ (1+ (x2(n) ^2) ); y2(n+1)=-x2(n)+a*x2(n+1) +2* (1-a)*(x2(n+1) ^2) /(1+ (x2(n+1) ^2) ); end subplot (2, 1,1); plot(x1,y1,'.') title('a =-0 .99 b=1') ... y1(n+1)=b*x1(n)+a*(y1(n )-( x1(n)) ^2) ; x2(n+1)=a*x2(n)-b*(y2(n )-( x2(n)) ^2) ; y2(n+1)=b*x2(n)+a*(y2(n )-( x2(n)) ^2) ; end plot(x1,y1,'ro',x2,y2,'bx') 2. 8 .2. 1 Demon...

Ngày tải lên: 13/08/2014, 02:21

... theory © 2001 by CRC Press LLC FIGURE 3. 4 Profile of the signal of Pb 3. 31 FIGURE 3. 5 Profile of the first input to Pb 3. 32 Pb 3. 33 In DSB-AM (double-sideband amplitude modulation), the amplitude ... following sub-units: mF = 10 3 F (milli-Farad); nF = 10 −9 F (nano-Farad); fF = 10 −15 F (femto-Farad); µF = 10 –6 F (micro-Farad); pF = 10 −12 F (pico-Farad); aF = 10 −18 F (atto-Farad)...

Ngày tải lên: 13/08/2014, 02:21

... +a*D2(k-1)+u(k)); D(k)=(2/dt)*(y(k)-y(k-1))-D(k-1); D2(k)= (4/ dt^2)*(y(k)-y(k-1) )-( 4/ dt)*D(k-1)-D2 (k-1); end plot(t,y,t,u,' ') The dashed curve is the temporal profile of the source term In-Class ... D2(1)=(1/a(1))*(-b(1)*D(1)-c(1)*y(1)+u(1)); for k=2:N y(k)=( (4* a(k)/dt^2+2*b(k)/dt+c(k))^ (-1 ))* (y(k-1)* (4* a(k)/dt^2+2*b(k)/dt)+D(k-1) * (4* a(k)/dt+b(k))+a(k)*D2(k-1)+u(k)); D(k...

Ngày tải lên: 13/08/2014, 02:21

... a(1)) (5. 25) a(2) = c(1) = a(1) + r(b(1) − a(1)) (5. 26) b(2) = b(1) (5. 27) Now, replacing the values of a(2) and b(2) from Eqs (5. 26) and (5. 27) into Eq (5. 25) , we are led to a second-degree ... The command is poly poly(r) In-Class Exercise Pb 5. 14 Find the roots of the polynomial p = [1 pute their sum and product 3], and com- Pb 5. 15 Consider the two polynomials: p1 = [1...

Ngày tải lên: 13/08/2014, 02:21

... LLC (6. 67) and where ˜ ˜ ˜ Vtot = Atot e jφtot = V1 + V2 (6. 68) Preparatory Exercise Pb 6. 35 Write the analytical expression for Atot and φtot in Eq (6. 68) as functions of the amplitudes and phases ... signals? Pb 6. 42 Two- and three-phase power can be extended to N-phase power In such a scheme, the N-110-V /60 -Hz signals are given by: © 2001 by CRC Press LLC πn   Vn = 110...

Ngày tải lên: 13/08/2014, 02:21

... Replacing l by l – in Eq (7. 94) and eliminating Pl′ ( x) from Eq − (7. 95), we find that: (1 − x ) dPl ( x) = lPl−1 ( x) − lxPl ( x) dx (7. 97) Differentiating Eq (7. 97) and using Eq (7. 95), we obtain: ... unique For example, in 4-D space, the canonical four-unit orthonormal basis vectors are given, respectively, by: ê1 = [1 0 0] (7. 15) ê2 = [0 0] (7. 16) ê3 = [0 0] (7. 17) ê4 = [0...

Ngày tải lên: 13/08/2014, 02:21

... n v m = λ n v m (8. 83) On the other hand, if we dotted Eq (8. 78) on the left with the bra-vector , we obtain: H v m = λ m v m = λ m v m (8. 84) Now compare Eqs (8. 83) and (8. 84) They are equal, ... ilamp=circuit872(RL) M=[1 0 0 0;1 -1 -5 0 0;0 -1 -1 00 0; 0 -3 00;0 -RL 0;0 0 -1 -1 ]; Vs=[5;0;0;0;0;0]; VI=M\Vs; ilamp=VI(5); Then, from the command window, we proceed b...

Ngày tải lên: 13/08/2014, 02:21

... transformations, in 2-D, are respectively: s Sx =  x 0 0 1  (9. 8) 1 Sy =  0 0 sy   (9. 9) In-Class Exercises Pb 9. 12 Find the transformation matrix for simultaneously compressing the x-coordinate ... 2, while expanding the y-coordinate by a factor of Apply this transformation to the trapezoid of Example 9. 1 and plot the result Pb 9. 13 Find the inverse matrices for Sx...

Ngày tải lên: 13/08/2014, 02:21

... Solution: The number of ways of selecting 10 items from a batch of 100 items is: N= 100 ! 100 ! 100 = = C10 10! (100 − 10) ! 10! 90! n where Ck is the binomial coefficient and represents the number of combinations ... (10. 43) Again, using Eqs (10. 37) and (10. 43), we have: P( Ai B) = P(B Ai )P( Ai ) (10. 44) P(B) Now, substituting Eq (10. 41) in the denominator of Eq (10. 44),...

Ngày tải lên: 13/08/2014, 02:21

Ngày tải lên: 19/10/2013, 20:15

... commands to get one started on MATLAB Detailed descriptions and usages of the commands can be obtained from the MATLAB help facility or from MATLAB manuals Table 1.2 Some Basic MATLAB Commands ... 1.1 MATLAB BASIC OPERATIONS When MATLAB is invoked, the command window will display the prompt >> MATLAB is then ready for entering data or executing commands To quit MATLAB, type t...

Ngày tải lên: 23/10/2013, 16:15

Ngày tải lên: 23/10/2013, 18:15

... “FrontMatter.” Electronics and Circuit Analysis using MATLAB Ed John Okyere Attia Boca Raton: CRC Press LLC, 1999 © 1999 by CRC PRESS LLC ELECTRONICS and CIRCUIT ANALYSIS using MATLAB JOHN Electrical ... electrical and electronic circuits and systems Organization The book is divided into three parts: Introduction to MATLAB, Circuit analysis applications using...

Ngày tải lên: 27/10/2013, 23:15