bimbo36

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 ... ??

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 were the simultaneous equations .... let me arrange a few things for my understandings sake ... first let me start with .. the usual equations ... then we have simulaneous equations ...which looks like these ... 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 ???

thanks ... i just got it confused with a linear equation .. ? and systems of linear equations ?? because i thought the gaussian elimination methods were for ...equations involving many linear equations ... 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

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 ?? 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 ... 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 functions differentiation intergration differential equation all 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.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

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 ??

hello studiot , thanks for all the help , support and questions... why i dont work with problems right now is because , i was a bit weak in algebra in general ... i was also looking for small problems to begin working with examples ... thank god , i found this excellent beginner book on algebra .... i am also ... going to buy two more books from an online store ... with the help of those two books .. i am going to work on examples of algebra and calculus .... later , after i get those books... i will start working on differential equations too ... right now i am not touching that subject .... i am glad i got a better overall picture of this subject ... now its time to practise from basics.... with the help of those books ....

let me rearrange few things one more time .... f(x) = polynomial ?? f(x) = transcendental ?? f(x) = polynomial of degree one ?? therefore linear ? Solution of Linear Equations? Direct Methods ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf f(x) = polynomial of degree one ?? therefore linear ? Solution of Linear Equations? Indirect Methods ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/13-LinEqs_Indirect.pdf f(x) = polynomial greater than degree one ?? therefore non linear ?? solving nonlinear equations ? Fixed Point ?http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdf f(x) = polynomial greater than degree one ?? therefore non linear ?? solving nonlinear equations ? Bisection ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_2_Bisection.pdf f(x) = polynomial greater than degree one ?? therefore non linear ?? solving nonlinear equations ? Newton ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_3_Newton.pdf is this right so far ?? its better than getting stuck .... atleast things are going to get better in 2016 ....

f(x) = polynomial ?? f(x) = transcendental ?? f(x) = polynomial of degree one ?? therefore linear ? f(x) = polynomial greater than degree one ?? therefore non linear ?? also all the above mentioned stuff about a linear change against a non linear change ???

this once again has messed up my head succesfully ... and i am confused again .. about the linear and non linear ... does this mean that only a polynomial of degree 1 is linear in nature and a quadratic equation of degree 2 , is non linear in nature ???? http://ads.harvard.edu/books/1990fnmd.book/ http://ads.harvard.edu/books/1990fnmd.book/chapt2.pdf so everything other than a polynomial of degree one ... is considered non linear in nature ??? then the method to solve these sort of problem ... must be like this ... right ??? Solution of Linear Equations Direct Methods http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf Solution of Linear Equations Indirect Methods http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/13-LinEqs_Indirect.pdf ??? then what does it mean to solve non linear equations ?? does that mean any polynomial other than degree 1 is non linear ???

thanks for the suggestions ... sorry i could not find those books anywhere ... currently i dont have a CC ... and i dont think i can make use of cash on delivery even if i ordered that book , since its a bit far away .... by this time i managed to read a lot of pdf and ebooks ... most of it lacked worked out examples ... but this thread has turned out to be something very usefull for me , even though it looks a bit messy ... that is because in my humble opinion , this is a big subject and organizing these subjects properly in my head was a bit of a hard task ... let me revise these things i have managed to learn and organize into this one post ... first of all , there is this HELM workbooks ...i find it very usefull for a person like me , who is not a maths expert ... but who is willing to spent time learning ... https://learn-pilot.lboro.ac.uk/archive/olmp/olmp_resources/pages/wbooks_fulllist.html http://www21.zippyshare.com/v/eMWFsoho/file.html and my confusions about linear , non linear maths is a bit less now ... https://books.google.com.sa/books/about/Computer_Oriented_Numerical_Methods_1E.html?id=J1J9W7EDdmcC BSc maths numerical methods http://www.universityofcalicut.info/SDE/BSc_maths_numerical_methods.pdf i also found these two links , which i find very related to my syllabus ... it is a bit more organized than many of the books ... http://www.caee.utexas.edu/prof/mckinney/ce311k/assign.html http://www.ce.utexas.edu/prof/mckinney/ce311k/assign_ce311k.html ... this is how much i have managed to organize so far ... now to work on some example problems... let me see if i can find few examples for all these methods .... ???

i am sorry ... i am currently working as an accountant somewhere ... and i dont get so much free time to work on example problems ... i am only trying to get an overalll picture of my syllabus .... i might work on examples after i get an overall grip on this whole subject .... sorry i could not find both the books ... its unavailable at local online stores ... in the meanwhile ... i managed to put together a book with the help of nitro pro 10 ... i joined all the pdf files from HELM , helping engineers learn mathematics website ... https://learn-pilot.lboro.ac.uk/archive/olmp/olmp_resources/pages/wbooks_fulllist.html http://www21.zippyshare.com/v/eMWFsoho/file.html here is the link to the free content .... currently i am refering to that book ... because the book has nice simple explanations .... one thing i am looking at right now , is numerical differentiation https://learn-pilot.lboro.ac.uk/archive/olmp/olmp_resources/pages/workbooks_1_50_jan2008/Workbook31/31_3_num_diff.pdf and numerical integration .... https://learn-pilot.lboro.ac.uk/archive/olmp/olmp_resources/pages/workbooks_1_50_jan2008/Workbook31/31_2_num_int.pdf i think i have only two more sections to looks into ... after this ... that is differential equations and "algebraic and transcendental equations" .... i dont know what both of it is .... right now ??? http://www.universityofcalicut.info/SDE/BSc_maths_numerical_methods.pdf Algebraic and Transcendental Equations Numerical Solutions of Ordinary Differential Equations i guess this is really it ... ???? no more numerical methods left to learn .... ???

Computer Oriented Numerical Methods https://books.google.com.sa/books/about/Computer_Oriented_Numerical_Methods_1E.html?id=J1J9W7EDdmcC&redir_esc=y this one ...

i was studying this because my syllabus had it ... we had computer oriented numerical methods in c ...i am trying to making it a bit simpler with the help of this thread , and the conversations we are having is very helpful ... i havent solved much integration or differentiation problems before ... because i was busy trying to understand the code and the languages .. back in the days , i had no idea what i was trying to solve ... there was not much depth for this subject ... it was a bit uninteresting too ... which is why i am trying to learn this from scratch .... you replies are helping ... because i can reply back with something even though its drifiting away from the subject sometimes .... i wish i could start from the basics and go to the methods of differentiation and integration ... differentiation rules integration rules the only thing i can think of is that , i get a bunch of polynomials again after differentiation or integration ???? where to from it ??? i know i am going away and away from the original topic ... that is because i have not found any example problems with explanations to work with ... or even look at ... i tried reading a lot of books ... but none of it had proper examples ....

differentiation or integration , which comes first ? many books starts with integration , then moves on to explain differentiation ... i was reading this book roughly ... A Graduate Introduction to Numerical Methods_ From the Viewpoint of Backward Error Analysis when i tried to copy paste a few definitions some of the things are not showing up properly , due to this Latex issues ... even the book starts with integration , then moves to differentiation ... i thought differentiation was the easy part and integration the hard part ... anyway .. let me try to copy paste a few things from the book .. starting with differentiation itself ... i like these definitons at one place ... atleast its helping me ... let me see if this thread can get all the definitions i want atleast roughly .... http://www.personal.soton.ac.uk/jav/soton/HELM/helm_workbooks.html http://www.nucleartheory.net/Essential_Maths/helm_workbooks_jan2008.pdf http://www.personal.soton.ac.uk/jav/soton/HELM/workbooks/workbook_11/11_1_intro_diffn.pdf http://www.personal.soton.ac.uk/jav/soton/HELM/workbooks/workbook_11/11_2_use_tbl_derivs.pdf http://www.personal.soton.ac.uk/jav/soton/HELM/workbooks/workbook_13/13_1_basic_cncpts_intgrn.pdf Numerical Differentiation and Finite Differences Numerical Integration

thanks for the reply and the link ... at this moment , even i dont know what i am looking for .. ??? it feels like i am refreshing ...differentiation , integration and differential equations ... because i am not at all familiar with the numerical methods associated with differentiation , integration or differential equations ... but i found something nice online .... Calculus http://www.mathsisfun.com/calculus/index.html Calculus in Context http://www.math.smith.edu/Local/cicintro/ http://www.math.smith.edu/Local/cicintro/book.pdf thought i would share it here ... and also this book ... http://www.mif.vu.lt/~stepanauskas/AM1/Tom%20Apostol%20-%20Calculus%20vol.1%20-%20One-variable%20Calculus,%20with%20an%20Introduction%20to%20Linear%20Algebra%20%281975%29.pdf i am not sure which path is the next , because i dont know what the names of the methods are called ? or how many type of methods there are for numerical methods associated with differentiation , integration and differential equation ....

ok thanks , i have never come across the term affine before ... which is why the confusions ?? where do i get some good online material for numerical differentiation or numerical integration ??

is that definition wrong ... ?? i myself have no idea about the depth of these definitions ... but i am getting a rough overall picture of all these things ... which for me at this stage is very helpful ... but i cannot find much definition or online notes for , numerical differentiation or numerical integration ... not sure where to find a simple description of these ...

thanks ... i just keep finding a lot of definitions from a lot of sites ... now if only i could find some examples like these for Numerical differentiation and Numerical integration ...that would make my life a bit more easier ...

this is how my syllabus looked like ... i am trying to organize these in a proper way .. based of my understanding so far , and with a little bit of help from a graph ... i am not sure if am organizing this right ... i thought why not give it a try ... Numerical Methods and errors Interpolation Numerical Solution of a system of Linear Equations Root Finding and Nonlinear Sets of Equations Solution of Algebraic and Transcendental Equations Numerical Differentiation Numerical Integration Numerical Solution of Ordinary differential equations Curve fitting Numerical Solution of problems associated with Partial Differential Equations does this non linear sets of equations simply means , equations involving differentiation and integration ???

i am happy that i could organize a part of this vast subject atleast like this ... if those matrix equations and polynomials are all part of the linear system ... i wonder what non linear systems are ... i donno if i should continue in this thread , or start a seperate thread for non linear systems ... because the coversation was a little bit of fun and was very helpfull ... i already read some books , pdfs and got some definitions from it ... let me quote it here ... my point is to organize these things in a better way , so that i can have a better understanding of these things .. i am not sure where these are all going right now .... ???

the problem was , back in the days ... programming was a bit hard ... especially trying to code something for numerical methods in c ... i had this book ... Numerical Recipes Flannery, Press, Teukolsky and Vetterling but i lost it , somehow ... i think i lost interest too ... since both the programming and the maths involved in it was hard ... noawadays , programming doesnt look that hard ... but the maths is ... this one for example ... this one with a little bit of effort and time ... can be turned into a program in C ... for example a matrix operation with c program ... i need to figure out how to turn a polynomial into a good matrix equation ... with its coefficients and all ... this will take a bit of time .... i think the coefficients becomes the elements of the matrix , in this case ... http://www.slideshare.net/SendashPangambam/solvng-linear-equations-37190053 let me see if i can focus on the ... anyway thanks again for the book recomendations...

actually the subject i was following was called computer oriented numerical method ... with some examples of c programming language trying to solve some methods of numerical methods ... there was lots of different types of numerical methods in it ... like newton raphson method , bisection method ...secant method ...regula falsi method ...mullers method ..horners method ...trapezoidal formula ..trapezoidal rule ... etc etc ... and in the end i am supposed to write computer programs for it in C language ... which was and still is a difficult task for me ... but it also had this one ... but it also had these ones,with matrix operations ... which looked like a bit more easier ones to put it into computer programs in C ... which is what i was looking for ... the simpler ones ... the rest seems like a mess ... anyway thanks a lot for taking the time to reply ... its this part from that website where i will be focusing on ... http://ads.harvard.edu/books/1990fnmd.book/chapt2.pdf because i think without much difficulty , this part can be made into a program in C ...

yea , i read that .. still a bit difficult for me to grasp everything written in it .. the pdf book has some simpler explanations ... for example ... right now am not sure how many methods there are for polynomial approximations ... i just googled " methods of polynomial approximation " .. and found this site ... http://ads.harvard.edu/books/1990fnmd.book/ isnt this a bit like the noob friendly part of the polynomials and numerical method ??? i am not that familiar with other methods ...

its the amount of terms , that is currently confusing me ... it does not seem to end ... sorry i feel very new to numerical methods .. even though we had this subject in college , along with computer programs in c ... let me change a few things , in your reply ... so that it makes a little bit more sense to me ... for my understanding .... i had to refresh a lot of terms ... to understand this one ... including terms like ... monomial binomial trinomial polynomial degree coeficients linear quadratic cubic quartic ... base , now more stuffs ... is this learning of terms ever going to end ? sorry i am a noob .. how does a simple question look like ? i have seen polynomial coefficients arranged into matrix equations for solving purposes ... i dont remember what it was called now ... because i dont have that book with me right now ... i might have to collect it from someone else .... this conversation is helping by the way ... even though i keep getting lost ....

i found a book online ... which explains a lot about what i was looking for ... http://www.statsci.org/webguide/smyth/pubs/EoB/bap064-.pdf this is something i found when i searched Polynomial Approximation , in google can somebody tell me , where to from here ??