bimbo36 Posted January 23, 2016 Share Posted January 23, 2016 this is a noob question to most of you .. but i would like to have some clarity ... since i am still following computer oriented numerical methods .... last time , i opened up a thread about polynomials and numerical methods ... some of the things got clearer ... and some of the things got lost in the confusion of discussions ... the last thread was mostly a lot of basic questions about linear and non linear polynomial equations ... some of the things got clearer ... some not that clear .... anyway back to the question ... what are simultaneous equation ? what are systems of linear equations ? is it simply a bunch of polynomial equations ?? Link to comment Share on other sites More sharing options...
Janus Posted January 23, 2016 Share Posted January 23, 2016 Simultaneous equations are a set of equations that are true for the same variables. example: 2x+y=5 and 3x-2y=4 are simultaneous equations for the same values of x and y. x+2y-3z=10 2x-3y-4z=1 y-3x+z=-8 are simultaneous equations for the same values of x,y and z You can use simultaneous equations to solve for multiple variables. For N number of variables you need a minimum of N simultaneous equations. Link to comment Share on other sites More sharing options...
bimbo36 Posted January 23, 2016 Author Share Posted January 23, 2016 (edited) ok ..thanks for the reply .. i have many more basic questions and doubts regarding this numerical methods ... first of all ,,. what is the difference between linear equation .. ? and systems of linear equations ?? When we know the degree we can also give the polynomial a name:0 Constant 71 Linear 4x+32 Quadratic x^2−3x+23 Cubic 2x^3−5x^24 Quartic x^4+3x−2 this is a simple linear equation ... Linear 4x+3 ... because the degree of the polynomial is 1 ...then we have many linear equations ... where the degree of the polynomials is still 1 ...when we have many linear equations where the degree of the polynomial is 1 .. we have the following methods ... http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/13-LinEqs_Indirect.pdf now as for non linear equations ... When we know the degree we can also give the polynomial a name:Degree Name Example0 Constant 71 Linear 4x+32 Quadratic x2−3x+23 Cubic 2x3−5x24 Quartic x4+3x−2 any polynomial equation of degree greater than one can be called non linear equations ... right ?and its solving methods starts from the quadratic equation themselves i guess ...to methods like the mentioned below ... http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_2_Bisection.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_3_Newton.pdf but ... transcendental functionsdifferentiationintergrationdifferential equationall are non linear equations ... right ???do i use these methods to solve all of them ?? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdfhttp://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_2_Bisection.pdfhttp://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_3_Newton.pdf Edited January 23, 2016 by bimbo36 Link to comment Share on other sites More sharing options...
studiot Posted January 23, 2016 Share Posted January 23, 2016 Just to add to what Janus has said. It is not necessary for all the variables to appear in all the equations for them to be simultaneous, or for you to be able to solve them. Here is an example. s = ut + 0.5ft2 v = u + ft v2 = u2 +2fs f = (v-u)/t s = 0.5(v+u)t These are 5 equations with 5 variables, s, t, u, v and f which describe motion uder constant acceleration. They are simultaneous, even though t is the time variable, they all apply together. It is indeed necessary to have N equations for N variables, to be able to find a unique solution, if such a solution is possible. But N equations may not be sufficient since a solution may not be possible, even with N equations. Having more than N equations or less than N may also lead you into trouble since you may then have a choice of multiple solutions, even an infinite number. I would advise you to lay aside the issue of linear v non linear until you have thoroughly understood the meaning of simultaneous equations. 1 Link to comment Share on other sites More sharing options...
bimbo36 Posted January 23, 2016 Author Share Posted January 23, 2016 thanks ... i just got it confused with When we know the degree we can also give the polynomial a name:Degree Name Example0 Constant 71 Linear 4x+32 Quadratic x2−3x+23 Cubic 2x3−5x24 Quartic x4+3x−2 a linear equation .. ? and systems of linear equations ?? because i thought the gaussian elimination methods were for ...equations involving many linear equations ... this is a simple linear equation ... Linear 4x+3 ... because the degree of the polynomial is 1 ...then we have many linear equations ... where the degree of the polynomials is still 1 ...when we have many linear equations where the degree of the polynomial is 1 .. we have the following methods ... http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/13-LinEqs_Indirect.pdf Link to comment Share on other sites More sharing options...
studiot Posted January 23, 2016 Share Posted January 23, 2016 Studiot post#4 I would advise you to lay aside the issue of linear v non linear until you have thoroughly understood the meaning of simultaneous equations. Link to comment Share on other sites More sharing options...
bimbo36 Posted January 24, 2016 Author Share Posted January 24, 2016 ok .. i sort of understand simultaneous equations ... and you use numerical methods such as gaussian elimination to solve it ... the types of equations were confusing me ... i thought a bunch of usual polynomial linear equations ...such as these Linear 4x+3 were the simultaneous equations .... let me arrange a few things for my understandings sake ... first let me start with .. the usual equations ... When we know the degree we can also give the polynomial a name:Degree Name Example0 Constant 71 Linear 4x+32 Quadratic x2−3x+23 Cubic 2x3−5x24 Quartic x4+3x−2 then we have simulaneous equations ...which looks like these ... x+2y-3z=102x-3y-4z=1y-3x+z=-8 these two numerical methods can be applied to it if you have to deal with equations like these ... http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/13-LinEqs_Indirect.pdf now could somebody please tell me to what sort of equations do i apply the rest of the three methods mentioned below ??? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_2_Bisection.pdf http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_3_Newton.pdf are those methods for ?? transcendental functions ??differentiation ???intergration ??differential equation ??? Link to comment Share on other sites More sharing options...
studiot Posted January 24, 2016 Share Posted January 24, 2016 Studiot post#4 I would advise you to lay aside the issue of linear v non linear until you have thoroughly understood the meaning of simultaneous equations. Link to comment Share on other sites More sharing options...
bimbo36 Posted January 24, 2016 Author Share Posted January 24, 2016 well i think i sort of understand what simultaneous equations are studiot , and i think we can use the numerical method gaussian elimination to solve such equations ?? am i getting it wrong somewhere ... ?? Link to comment Share on other sites More sharing options...
studiot Posted January 24, 2016 Share Posted January 24, 2016 You don't seem to have read my post#4. How would you use gaussian elimination to solve that system? These equations and their solution are not special and are taught in high school. Link to comment Share on other sites More sharing options...
bimbo36 Posted January 24, 2016 Author Share Posted January 24, 2016 (edited) but our questions in college were mostly oriented toward c program ... it was called computer oriented numerical methods in C ... the application of the methods were more important , rather than the quality of the questions .... you mean those u v t are like x y z ... and therefore those are simultaneous equations... right ? i learned few of those in high school physics class .. but dont remember it well now ... it must have been like 15 years ago ... but after leaving college .. i am still following a subject which i failed badly ... the computer oriented numerical methods in c .... because programming was hard .. mathematics was hard ... the combination of these two subjects were even harder .... Edited January 24, 2016 by bimbo36 Link to comment Share on other sites More sharing options...
bimbo36 Posted January 27, 2016 Author Share Posted January 27, 2016 (edited) can i have a little bit of help ... with this fixed point iteration method ??? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdf http://www.universityofcalicut.info/SDE/BSc_maths_numerical_methods.pdf i am sorry if this looks like a mess ... but fixed point iteration is the last method i am going to follow in numerical methods .. some help or directions please before i completly quit this subject ... ??? Edited January 27, 2016 by bimbo36 Link to comment Share on other sites More sharing options...
bimbo36 Posted January 29, 2016 Author Share Posted January 29, 2016 (edited) i am stuck with methods after methods for solving non linear equations ...i think i sort of understand how equations are re arranged in fixed point iterations ...are these methods somehow similiar ?? fixed point iterationthe bisection methodthe newton raphson methodthe secant method http://www.maths.dit.ie/~dmackey/lectures/Roots.pdf does these methods always involve re arranging equations ... to fit certain formulas ??? i am sorry for making all this look like spam ... i am also sorry for deviating from the original topic ... but these all looks very similar .... Edited January 29, 2016 by bimbo36 Link to comment Share on other sites More sharing options...
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