Updated on March 16, 2024

Understanding the subtle distinctions brought by different adjectives when used with the noun 'equations' is crucial for any mathematics student or professional. Whether an equation is described as 'differential,' 'linear,' 'simultaneous,' 'following,' 'partial,' or 'nonlinear,' each adjective unravels a new layer of complexity and nuance. For instance, a 'linear equation' suggests a direct proportionality and simpler relationships, whereas a 'nonlinear equation' implies more complexity, often requiring sophisticated methods to solve. 'Simultaneous equations' denote more than one equation being dealt with together, introducing the challenge of finding a solution that satisfies all at once. Dive deeper into the fascinating world of equations with our comprehensive list of adjectives that highlight their distinct characteristics and complexities.

differential | The complex differential equations can be solved using the Laplace transform. |

linear | Students find it easy to solve linear equations |

simultaneous | The simultaneous equations were x + y = 5 and x - y = 1. |

following | |

partial | Solving partial equations is a common task in mathematics and physics. |

nonlinear | We can solve nonlinear equations using numerical methods. |

above | |

ordinary | You are solving the problems of ordinary equations |

basic | The basic equations of science are essential for understanding the universe. |

mathematical | The scientist concluded that, based on the mathematical equations the experiment would fail. |

integral | The solution to integral equations requires advanced mathematical techniques. |

constitutive | The constitutive equations of a material are mathematical equations that describe the relationship between stress and strain. |

general | The resulting equations are general equations applicable to any random structure and any particular type of hypothetical function. |

normal | The normal equations are a system of linear equations that can be used to find the least squares solution to a linear regression problem. |

simple | Simple equations can be solved using basic algebraic operations. |

fundamental | The fundamental equations of Newtonian mechanics are the three laws of motion. |

independent | |

quadratic | Solving quadratic equations can be challenging, but with the right techniques, it becomes manageable. |

structural | The structural equations model showed that the independent variables had a significant effect on the dependent variable. |

corresponding | In this study, these methods were validated using corresponding equations from first principles. |

empirical | Our team is going to use empirical equations to predict the outcome. |

similar | These similar equations can be solved by substitution. |

dynamic | The dynamic equations of the system were solved using a finite difference scheme. |

dimensional | Dimensional equations are mathematical equations that express the relationships between the dimensions of different physical quantities. |

original | These original equations are the first of their kind. |

homogeneous | |

dynamical | The dynamical equations governing the oscillatory system are derived. |

appropriate | Solve the appropriate equations |

kinetic | The kinetic equations are a set of equations used to describe the motion of molecules in a gas. |

stochastic | Stochastic equations are differential equations in which the coefficients are stochastic processes. |

linearized | The linearized equations can be solved by Gaussian elimination. |

classical | In classical equations acceleration is defined as the change in velocity over a specific time interval. |

additional | The additional equations are now available. |

complex | The mathematician worked on complex equations for hours. |

separate | We need to solve the separate equations for x and y. |

functional | Functional equations are equations that describe the relationship between a function and its arguments. |

preceding | The preceding equations are used to calculate the drag force acting on a body. |

finite | Only finite equations are considered in this study. |

elliptic | The elliptic equations describe the basic laws governing a wide range of phenomena in the physical world. |

relevant | The relevant equations are listed in the appendix. |

hydrodynamic | The hydrodynamic equations are a system of partial differential equations that describe the flow of fluids. |

parametric | The parametric equations of a curve are a set of equations that express the coordinates of the points on the curve in terms of one or more parameters. |

characteristic | Eigenvalues of the matrix are found from characteristic equations |

cubic | Solving cubic equations is a challenging but rewarding mathematical endeavor. |

hyperbolic | Hyperbolic equations are partial differential equations that describe waves. |

exact | Exact equations are helpful for solving differential equations of the form M(x,y)dx + N(x,y)dy = 0. |

parabolic | The researchers used parabolic equations to model the propagation of sound waves in the atmosphere. |

multiple | |

theoretical | The researchers used theoretical equations to predict the behavior of the system. |

generalized | I will infer the underlying generalized equations from your collected data. |

canonical | The canonical equations of a circle are x^2+y^2 = r^2. |

foregoing | The foregoing equations are used to calculate the velocity and acceleration of the object. |

dependent | Solving the first three equations will allow you to find a solution for the rest of the dependent equations |

complicated | With the help of complicated equations scientists have discovered the mysteries of the universe. |

lagrange | The Lagrange equations are a system of differential equations that describe the motion of a mechanical system. |

primitive | The primitive equations are a set of equations used to describe the large-scale motion of the atmosphere and ocean. |

balanced | Balanced equations are mathematical equations that represent chemical reactions where the number of atoms of each element is the same on both sides of the equation. |

macroscopic | Macroscopic equations describe the behavior of matter on a large scale. |

predictive | Predictive equations are mathematical tools used to estimate future events or outcomes based on past observations and current data. |

algebraic | Algebraic equations are constructed from variables, constants, and mathematical operators. |

state | State equations are used in control systems to describe the dynamics of a system. |

shallow | The shallow equations are a set of equations that describe the flow of water in a shallow body of water. |

recursive | Recursive equations are equations in which the unknown function appears on both sides of the equation. |

thermodynamic | Entropy of a system is described mathematically by thermodynamic equations |

incompressible | These equations constitute a system of 6 incompressible equations for the 6 unknown functions. |

scalar | We solve the scalar equations over a finite field by using the Berlekamp-Massey algorithm. |

discrete | The discrete equations were solved using a Gauss-Seidel iterative method. |

numerical | The numerical equations were solved by the mathematician. |

phenomenological | The phenomenological equations provide a mathematical framework for describing the behavior of a physical system. |

conditional | |

electromagnetic | The theory of electromagnetism is based on Maxwell's electromagnetic equations |

relativistic | Astronomers must use relativistic equations to account for gravitational time dilation when they calculate the motions of neutron stars. |

behavioral | The behavioral equations for the system are very complex. |

kinematic | The kinematic equations describe the motion of an object with constant acceleration. |

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