Non-linear partial differential equations. Are you offering to help me? If not, why did you ask?
Sample problems in differential equations often include finding the solution to first-order equations, such as separable equations or linear equations. For example, solving the equation ( \frac{dy}{dx} = y - x ) involves using integrating factors or separation of variables. Other common problems include second-order linear differential equations, like ( y'' + 3y' + 2y = 0 ), where the characteristic equation helps find the general solution. Applications may involve modeling real-world phenomena, such as population growth or the motion of a pendulum.
The WKB (Wentzel-Kramers-Brillouin) method is a semiclassical approximation used to find solutions to linear differential equations, particularly in quantum mechanics and wave phenomena. It involves assuming a solution in the form of an exponential function, where the exponent is a rapidly varying phase. By substituting this form into the differential equation and applying asymptotic analysis, one can derive an approximate solution valid in regions where the potential changes slowly. This method is particularly useful for solving Schrödinger equations and other second-order linear differential equations in physics.
I'm not altogether clear about what you mean. However, the term 'linear programming' means a category of optimisation problems in which both the objective function and the constraints are linear. Please see the link.
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
Charles Andrews Swanson has written: 'Comparison and oscillation theory of linear differential equations' -- subject(s): Differential equations, Linear, Linear Differential equations, Numerical solutions
Kent Franklin Carlson has written: 'Applications of matrix theory to systems of linear differential equations' -- subject(s): Differential equations, Linear, Linear Differential equations, Matrices
Avron Douglis has written: 'Ideas in mathematics' -- subject(s): Mathematics 'Dirichlet's problem for linear elliptic partial differential equations of second and higher order' -- subject(s): Differential equations, Linear, Differential equations, Partial, Dirichlet series, Linear Differential equations, Partial Differential equations
Marcus Pivato has written: 'Linear partial differential equations and Fourier theory' -- subject(s): Partial Differential equations, Linear Differential equations, Fourier transformations
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
Fred Brauer has written: 'Linear mathematics; an introduction to linear algebra and linear differential equations' -- subject- s -: Linear Algebras, Linear Differential equations 'Mathematical models in population biology and epidemiology' -- subject- s -: Mathematical models, Population biology, Epidemiology 'Problems and solutions in ordinary differential equations' -- subject- s -: Differential equations, Problems, exercises
Algebraic equations, trigenometric equations, linear equations, geometric equations, partial differential equations, differential equations, integrals to name a few.
Rudolph Ernest Langer has written: 'On the asymptotic solutions of ordinary linear differential equations about a turning point' -- subject(s): Differential equations, Linear, Linear Differential equations 'Nonlinear problems' -- subject(s): Nonlinear theories, Congresses 'A first course in ordinary differential equations' -- subject(s): Differential equations 'Partial differential equations and continuum mechanics' -- subject(s): Congresses, Differential equations, Partial, Mathematical physics, Mechanics, Partial Differential equations 'Boundary problems in differential equations' -- subject(s): Boundary value problems, Congresses
Roberto Conti has written: 'Linear differential equations and control' -- subject(s): Control theory, Linear Differential equations
Arthur Sylvester Peters has written: 'Lectures on linear algebra' -- subject(s): Differential equations, Linear, Linear Differential equations 'Linear algebra' -- subject(s): Algebra
J. Lewowicz has written: 'Asymptotic directions of the solutions of linear differential equations' -- subject(s): Asymptotic theory, Linear Differential equations
Paul C. Rosenbloom has written: 'Linear partial differential equations' -- subject(s): Linear Differential equations, Partial Differential equations 'The elements of mathematical logic' -- subject(s): Symbolic and mathematical Logic