1550078481-Ordinary_Differential_Equations__Roberts_

CSODE User's Guide EXAMPLE Calculation of the Roots of a Cubic Polynomial with Complex Coefficients Find the roots of the cubic ...

504 Ordinary Differential Equations On the right-hand side of Figure A.5, the coefficients of the polynomial and the roots of th ...

CSODE User's Guide 505 Then we enter the nonzero entries of A in the 2 x 2 array which appears and which is initially filled wit ...

506 Ordinary Differential Equations By clicking on the button labeled CALCULATE THE EIGENVALUES AND EIGENVECTORS OF A NEW MATRIX ...

CSODE User's Guide 507 EIGEN r;)@~ EISEN finds aD eigenvalues: and eigenvedots of a real. square inatrix A of order N whete 2 ( ...

508 Ordinary Differential Equations The four computer programs GRAPH, DIRFIELD, SOLVEIVP, and SOLVESYS contained in CSODE requir ...

CSODE User's Guide 509 Table A.1 Intrinsic Basic Functions Basic Function Mathematical Comments Notation Notation abs(x) lxl Abs ...

510 Ordinary Differential Equations Table A.2 Additional Mathematical Functions Functions Computation in BASIC Comments Arccos x ...

CSODE User's Guide 511 graphed and the interval [Xmin, Xmax] on which the function is to be evalu- ated. It is usually a good id ...

512 Ordinary Differential Equations on the monitor as shown in Figure A.9. The graphing information box shown in Figure A.9 also ...

CSODE User's Guide 513 Xmax, Y min, Y max}. Another option is for you to click on the third option button: New Function and then ...

514 Ordinary Differential Equations EXAMPLE Graphing the Direction Field of the Differential Equation y' = x - y Use DIRFIELD to ...

CSODE User's Guide 515 [NOTE: If we had wanted to graph the direction field on a different rectan- gle, we would have changed th ...

516 Ordinary Differential Equations EXAMPLE Solving the Initial Value Problem: y' = x - y; y(O) = 2 on the interval [- 1 , 4] Us ...

CSODE User's Guide 517 " SOLVEIVP S~IE3 SOINEIVP calculates anc;I graphs the solution of>the initial value problem: y'· ~ f(J ...

518 Ordinary Differential Equations Clicking the OPTIONS button at the top right-hand side of the graph, we see that the fourth ...

CSODE User's Guide 519 Iii SOLVEIVP ~(!IJl:i SOLVEIVP calculates ana graphs the solution of the in~ial value problem: y' = f{•. ...

520 Ordinary Differential Equations Using SOLVESYS The computer program SOLVESYS will attempt to solve numerically the system in ...

CSODE User's Guide 521 In order to use SOLVESYS to solve the system IVP (3), we double click the CSODE icon and when the program ...

522 Ordinary Differential Equations o;; SOLVESYS J!!ifill!!i Ymin"--~,.....:.~~-'- 1 ~~~l~~-'-~~'--~-'"~~-'-~~~I~~-'-~--' Xmin y ...