Updated on March 16, 2024
| 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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