1 / 10

Solving Algebraic Equations

Math Review with Matlab:. Solving Algebraic Equations. Single Variable Transcendental Equations. S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn. Solving Transcendental Equations. Solve Command Polynomial Transcendental Example

hea
Download Presentation

Solving Algebraic Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math Review with Matlab: Solving AlgebraicEquations Single Variable Transcendental Equations S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn

  2. Solving TranscendentalEquations • Solve Command • Polynomial Transcendental Example • Poly2sym Command • Exponential Transcendental Example • Complex Solution Example

  3. Solve Command • The Symbolic Toolbox’s solvecommand is used to solve both transcendental and algebraic equations • solve(f) solves f in terms of the independent symbolic variable closest to x. f must be a symbolic expression or a entered as a text string enclosed by single quotes • solve(f1,f2,...,fn)is used to solve multiple equations by separating the symbolic equations by commas as follows

  4. Polynomial Transcendental Equation Example • Use Matlab’s Symbolic Toolbox solve command to solve the transcendental equation: » syms x » xs_sym=solve(x^2-3*x+2) xs_sym = [ 1] [ 2] » xs_dbl=double(xs) xs_dbl = 1 2

  5. Poly2Sym Command • The poly2sym(f) command converts a polynomial coefficient vector to symbolic polynomial expression in terms of the default symbolic variable x • The sym2poly command converts a symbolic polynomial expression to a polynomial coefficient vector • The poly2sym(f,'v') command converts a polynomial coefficient vector to symbolic polynomial expression in terms of the symbolic variable v

  6. Poly2sym Example • Example: » p=[5,2,-1,1,10]; Polynomial Vector » sym_exp=poly2sym(p) sym_exp = 5*x^4+2*x^3-x^2+x+10 Symbolic Expression » poly_vec=sym2poly(sym_exp) poly_vec = 5 2 -1 1 10 Polynomial Vector

  7. Complex Solution Real Solution Exponential Transcendental Equation Example • Use the solve command to solve the transcendental equation: » xs_sym=solve(exp(2*x)+3*exp(x)-54) xs_sym = [ log(-9)] [ log(6)] » xs_dbl=double(xs) xs_dbl = 2.1972 + 3.1416i 1.7918

  8. Verify Loge(-9) • In Matlab, log is the natural log of base e: • Verify ln(-a) is a complex number : • In this case -a = -9, so:

  9. Complex Solution Example • Solve the nonlinear equation: • Verify the result » syms x » rt = solve('x^2+exp(x)+5') rt = 3.5668799472626199482146544957277+ 4.8873680198538466074569067078051*i » z=subs('x^2+exp(x)+5',rt) z = .2e-30

  10. Summary • The solve command can be used to solve symbolic transcendental equations with real or complex solutions • poly2sym and sym2poly commands can be used to convertpolynomial vectors to/from symbolic expressions

More Related