User Manual
Page 266
... variable. Finds candidate values of integrand values). Calculates the numerical derivative of an expression with respect to a specified variable. ‰ integrate limit G sum Π product fMin fMax arcLen taylor nDeriv nInt deSolve impDif Integrates an expression with respect to a ...specified variable. Evaluates an expression at discrete variable values within a range and then calculates the product. Returns the arc length of an expression with respect ...
... variable. Finds candidate values of integrand values). Calculates the numerical derivative of an expression with respect to a specified variable. ‰ integrate limit G sum Π product fMin fMax arcLen taylor nDeriv nInt deSolve impDif Integrates an expression with respect to a ...specified variable. Evaluates an expression at discrete variable values within a range and then calculates the product. Returns the arc length of an expression with respect ...
User Manual
Page 443
...=2. 17. The exact solution to zoom in so that you can examine the differences in more detail. You can use C to scroll up to the Graph screen. In the Window Editor, set the Window variables. yscl=10. xmin=39.7 xmax=40.3 xscl=.1 ymin=85.5 ymax=86 yscl=.1 xres=2 19. Return to... 1 and Plot 2. In the Window Editor, set the Window variables to the differential equation is given below. ymax=120. Note: The fuzzy line on the graph indicates differences between the RK and Euler values. 18. 15. y1 = (100ùe^(x/10))/(e^(x/10)+9) Note: You can use...
...=2. 17. The exact solution to zoom in so that you can examine the differences in more detail. You can use C to scroll up to the Graph screen. In the Window Editor, set the Window variables. yscl=10. xmin=39.7 xmax=40.3 xscl=.1 ymin=85.5 ymax=86 yscl=.1 xres=2 19. Return to... 1 and Plot 2. In the Window Editor, set the Window variables to the differential equation is given below. ymax=120. Note: The fuzzy line on the graph indicates differences between the RK and Euler values. 18. 15. y1 = (100ùe^(x/10))/(e^(x/10)+9) Note: You can use...
User Manual
Page 444
... to trace each solution to xc = 40, you solve many 1st- Press ... Differential Equation Graphing 444 You can find that: • The exact solution (y1) is 85.8486, rounded to time = 40. Example of the deSolve( ) Function The deSolve( ) function lets you can also use the Data/Matrix Editor to open the errorlog...
... to trace each solution to xc = 40, you solve many 1st- Press ... Differential Equation Graphing 444 You can find that: • The exact solution (y1) is 85.8486, rounded to time = 40. Example of the deSolve( ) Function The deSolve( ) function lets you can also use the Data/Matrix Editor to open the errorlog...
User Manual
Page 445
... between the variable and parentheses. For a particular solution, refer to t. deSolve(y' = 1/1000 yù(100Ny),t,y) For ', type 2 È. deSolve(1stOr2ndOrderODE, independentVar, dependentVar) Using the logistic 1st-order differential equation, find the general solution for y with respect to the Technical Reference module. Differential Equation Graphing 445 Example For a general solution, use 1/1000 instead of .001...
... between the variable and parentheses. For a particular solution, refer to t. deSolve(y' = 1/1000 yù(100Ny),t,y) For ', type 2 È. deSolve(1stOr2ndOrderODE, independentVar, dependentVar) Using the logistic 1st-order differential equation, find the general solution for y with respect to the Technical Reference module. Differential Equation Graphing 445 Example For a general solution, use 1/1000 instead of .001...
User Manual
Page 446
...184;. Note: If you got a different constant (@2, etc.), solve for that constant. @1 represents a constant. You may get a different constant (@2, etc.). For @, type @ 89 H 2R Differential Equation Graphing 446 Before using deSolve( ), clear any existing t and y variables. a) Press C to define a function. Otherwise, an error occurs. 1. In the Home screen @ " "use solve( ) ...Note: Press 2 A to move to find the general solution. 2. Then press ¸ to find the @1 constant. For an initial condition y=10 with t=0, use deSolve( ) to autopaste it into the entry line.
...184;. Note: If you got a different constant (@2, etc.), solve for that constant. @1 represents a constant. You may get a different constant (@2, etc.). For @, type @ 89 H 2R Differential Equation Graphing 446 Before using deSolve( ), clear any existing t and y variables. a) Press C to define a function. Otherwise, an error occurs. 1. In the Home screen @ " "use solve( ) ...Note: Press 2 A to move to find the general solution. 2. Then press ¸ to find the @1 constant. For an initial condition y=10 with t=0, use deSolve( ) to autopaste it into the entry line.
User Manual
Page 447
... obtain the particular solution shown. or - @ 8Í What Order Equation Are You Graphing? 4. Many problems may be related to solve this problem directly. You can help you have difficulties graphing a differential equation, this section can also use deSolve( ) to your Fields graph format setting. If the equation is: 1st-order Valid Fields settings are...
... obtain the particular solution shown. or - @ 8Í What Order Equation Are You Graphing? 4. Many problems may be related to solve this problem directly. You can help you have difficulties graphing a differential equation, this section can also use deSolve( ) to your Fields graph format setting. If the equation is: 1st-order Valid Fields settings are...
User Manual
Page 782
... Listing of Operations Algebra Calculus Graphics Lists This section lists the TI-89 Titanium functions and instructions in functional groups along with the page numbers... 889 895 ‰() (integrate) 907 Π() (product) 908 G() (sum) 908 arcLen() 788 avgRC() 789 d() 805 deSolve() 808 fMax() 821 fMin() 821 ImpDif() 831 limit() 834 nDeriv() 845 nInt() 847 ' (prime) 910 seq() 869 taylor... 900 ZoomTrig 790 Circle 792 793 CyclePic 803 812 DrawParm 813 813 DrwCtour 814 822 Graph 829 835 LineTan 836 846 PtChg 856 856 ptTest() 856 857 PxlCrcl 857 857 PxlOff...
... Listing of Operations Algebra Calculus Graphics Lists This section lists the TI-89 Titanium functions and instructions in functional groups along with the page numbers... 889 895 ‰() (integrate) 907 Π() (product) 908 G() (sum) 908 arcLen() 788 avgRC() 789 d() 805 deSolve() 808 fMax() 821 fMin() 821 ImpDif() 831 limit() 834 nDeriv() 845 nInt() 847 ' (prime) 910 seq() 869 taylor... 900 ZoomTrig 790 Circle 792 793 CyclePic 803 812 DrawParm 813 813 DrwCtour 814 822 Graph 829 835 LineTan 836 846 PtChg 856 856 ptTest() 856 857 PxlCrcl 857 857 PxlOff...
User Manual
Page 808
...symbol is an integer suffix from memory. 2! a ¸ (a+2)^2 ¸ DelVar a ¸ (a+2)^2 ¸ 2 16 Done (a + 2)ñ deSolve() MATH/Calculus menu deSolve(1stOr2ndOrderOde, independentVar, dependentVar) ⇒ a general solution Note: To type a prime symbol ( ' ), press 2 È. In other cases, use ClrHome...solutions. Returns an equation that different methods introduce arbitrary constants at different points in the calculation, which may produce different general solutions. deSolve(y'=(cos(y))^2ùx,x,y) ¸ tan(y)= xñ 2 +@3 When comparing your results with...
...symbol is an integer suffix from memory. 2! a ¸ (a+2)^2 ¸ DelVar a ¸ (a+2)^2 ¸ 2 16 Done (a + 2)ñ deSolve() MATH/Calculus menu deSolve(1stOr2ndOrderOde, independentVar, dependentVar) ⇒ a general solution Note: To type a prime symbol ( ' ), press 2 È. In other cases, use ClrHome...solutions. Returns an equation that different methods introduce arbitrary constants at different points in the calculation, which may produce different general solutions. deSolve(y'=(cos(y))^2ùx,x,y) ¸ tan(y)= xñ 2 +@3 When comparing your results with...
User Manual
Page 809
...is used , the default tolerance is ignored. • If you use the form: dependentVar' (initialIndependentValue) = initial1stDerivativeValue deSolve(2ndOrderOde and boundaryCondition1 and boundaryCondition2, independentVar, dependentVar) ⇒ a particular solution Returns a particular solution that have no ...ode|y'=impdif(soln,x,y) ¸ stored values. Otherwise, tol is calculated as: 5Eë 14 ù max(dim(squareMatrix)) ù rowNorm(squareMatrix) det([a,b;c,d]) ¸ aød ìbøc det...
...is used , the default tolerance is ignored. • If you use the form: dependentVar' (initialIndependentValue) = initial1stDerivativeValue deSolve(2ndOrderOde and boundaryCondition1 and boundaryCondition2, independentVar, dependentVar) ⇒ a particular solution Returns a particular solution that have no ...ode|y'=impdif(soln,x,y) ¸ stored values. Otherwise, tol is calculated as: 5Eë 14 ù max(dim(squareMatrix)) ù rowNorm(squareMatrix) det([a,b;c,d]) ¸ aød ìbøc det...
User Manual
Page 910
...; Returns dd+(mm/60)+(ss.ss/3600). All unit names must begin with an underscore. deSolve(y''=y^(ë 1/2) and y(0)=0 and y'(0)=0,t,y) ¸ 2øy 3/4 3 =t _ (underscore) ¥ key expression_unit 3_m 4 _ft ¸ Designates the units for best results in calculations such as hours/minutes/seconds. 25.221... 51/2 ' (prime) 2 È key variable ' variable '' Enters a prime...
...; Returns dd+(mm/60)+(ss.ss/3600). All unit names must begin with an underscore. deSolve(y''=y^(ë 1/2) and y(0)=0 and y'(0)=0,t,y) ¸ 2øy 3/4 3 =t _ (underscore) ¥ key expression_unit 3_m 4 _ft ¸ Designates the units for best results in calculations such as hours/minutes/seconds. 25.221... 51/2 ' (prime) 2 È key variable ' variable '' Enters a prime...
User Manual
Page 979
.... 596, 600, 809 denominator 795 derivatives 79 first derivative, d 806 first derivative, d( ) .79, 247, 265, 267 numeric derivative, nDeriv( ) 266, 846 Derivatives (graph math tool) . 331, 334, 346 353 deSolve( ), solution 266, 444, 809 det( ), matrix determinant 810 diag( ), matrix diagonal 811 dialog box CLOCK 41 edit categories 33 menu indicator 53...modifier key (8) description 13 status 38 differential equations DIRFLD, direction field . . . . 415, 423 first order 425, 444 FLDOFF, field off . . . . 415, 424, 451 graphing 410-452 initial conditions 421 second order 427, 444 9
.... 596, 600, 809 denominator 795 derivatives 79 first derivative, d 806 first derivative, d( ) .79, 247, 265, 267 numeric derivative, nDeriv( ) 266, 846 Derivatives (graph math tool) . 331, 334, 346 353 deSolve( ), solution 266, 444, 809 det( ), matrix determinant 810 diag( ), matrix diagonal 811 dialog box CLOCK 41 edit categories 33 menu indicator 53...modifier key (8) description 13 status 38 differential equations DIRFLD, direction field . . . . 415, 423 first order 425, 444 FLDOFF, field off . . . . 415, 424, 451 graphing 410-452 initial conditions 421 second order 427, 444 9
User Manual
Page 1001
...946 slope field, SLPFLD . . . . . 415, 423, 448 SLPFLD, slope field . . . . . 415, 423, 448 Smart Graph 318 SocialSt (social studies) category . . . . 31 software version 233 Solution Method graph format 414 solution, deSolve 266, 444, 809 solve( ), solve 77, 83, 446, 879 solve, solve( ) 77, 83, 240, 242, 243, 247, ...512, 514 exiting 509 setting 506 switch, switch 617, 886 switching 512 Split Screen mode 188, 924 split-screen mode active graph 38 exiting 64 Number of graphs 62 returning from within an App . . . . . 31 selecting active App 64 setting 59 setting initial Apps 61 ...
...946 slope field, SLPFLD . . . . . 415, 423, 448 SLPFLD, slope field . . . . . 415, 423, 448 Smart Graph 318 SocialSt (social studies) category . . . . 31 software version 233 Solution Method graph format 414 solution, deSolve 266, 444, 809 solve( ), solve 77, 83, 446, 879 solve, solve( ) 77, 83, 240, 242, 243, 247, ...512, 514 exiting 509 setting 506 switch, switch 617, 886 switching 512 Split Screen mode 188, 924 split-screen mode active graph 38 exiting 64 Number of graphs 62 returning from within an App . . . . . 31 selecting active App 64 setting 59 setting initial Apps 61 ...