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Everything about Equation solving
Finding values for variables that make an equation true
In mathematics, to solve an equation is to find the solutions of an equation, which are the values that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values such that, when substituted for the unknowns, the equation becomes an equality. A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Equation solvingA 5-minute orientation
- Skim a recent paper: Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equationsInfluential work since 2022
- Pick up a classic book: How to solve itThe most-reprinted book on the subject
- Read the landmark paper: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equationsCited 20,944 times
- Go sideways: EquationA closely related topic
- Go sideways: System of linear equationsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Method for Solving the Korteweg-deVries Equation
Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models
Solving the KPZ equation
Flexibility in problem solving: The case of equation solving
ON SOLVING THE UNSATURATED FLOW EQUATION
ON SOLVING THE UNSATURATED FLOW EQUATION
Solving Burgers’ equation with quantum computing
🆕 Influential since 2022
Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations
Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations
Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems
Variational Physics-informed Neural Operator (VINO) for solving partial differential equations
📚 Books worth reading
How to solve itGeorge Pólya · 1945
Advanced Problem Solving with MapleWilliam P. Fox, William C. Bauldry · 2019- 📕Advanced Problem Solving Using MapleWilliam P. Fox, William Bauldry · 2020
Algebra 2McGraw-Hill · 1998
Equal, shmequalVirginia L. Kroll · 2005- 📕The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equationsStanley Osher · 1989
Metody řešení matematických úloh IJiří Herman · 2000- 📕Pseudo-time methods for contrained optimization problems governed by PDEShlomo Ta'asan · 1995
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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