scholarly journals Methods for fitting equations with two or more non-linear parameters

1976 ◽  
Vol 157 (2) ◽  
pp. 489-492 ◽  
Author(s):  
I A Nimmo ◽  
G L Atkins
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Linear Equations ◽  
Simultaneous Equations ◽  
The Other ◽  
Parameter Estimates ◽  
Non Linear ◽  
Non Linear Equations

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.

scholarly journals THE COMMON ERRORS IN THE LEARNING OF THE SIMULTANEOUS EQUATIONS

2020 ◽  
Vol 9 (2) ◽  
pp. 263
Author(s):  
Pg. Mohammad Adib Ridaddudin Pg. Johari ◽  
Masitah Shahrill
Keyword(s):  
Linear Equations ◽  
Simultaneous Equations ◽  
Government Schools ◽  
Brunei Darussalam ◽  
Non Linear ◽  
The Subject ◽  
The Common ◽  
Non Linear Equations ◽  
Mathematical Error

The purpose of this study is to understand the causes of common errors and misconceptions in the learning attainment of simultaneous equations, specifically on linear and non-linear equations with two unknowns. The participants consisted of 30 Year 9 students in one of the elite government schools in Brunei Darussalam. Further analyses of their work led to the categorisation of four factors derived from the recurring patterns and occurrences. These four factors are complicating the subject, wrong substitution of the subject, mathematical error and irrational error in solving the question. These factors usually cause participants to make errors or simply misconceptions that usually led them to errors in solving simultaneous equations.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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