A NUMERICAL APPROACH FOR SOLVING A CLASS OF
... Cubic B-spline functions were employed to solve a class of singular two-point boundary value problems. The removal of the singularity was achieved by using L’Hopital’s rule when the BC y ′ (0) = 0 is present, and Chebyshev polynomial around δ, the vicinity of the singularity, in the presence of the ...
... Cubic B-spline functions were employed to solve a class of singular two-point boundary value problems. The removal of the singularity was achieved by using L’Hopital’s rule when the BC y ′ (0) = 0 is present, and Chebyshev polynomial around δ, the vicinity of the singularity, in the presence of the ...
A counterexample concerning regularity properties for systems of
... Note that condition iii. implies that, for every U0 ∈ B, the number of shocks developed by the admissible solution cannot be locally finite. Owing to condition ii., this implies that the set of initial data such that the number of shocks of the admissible solution is locally finite cannot be dense i ...
... Note that condition iii. implies that, for every U0 ∈ B, the number of shocks developed by the admissible solution cannot be locally finite. Owing to condition ii., this implies that the set of initial data such that the number of shocks of the admissible solution is locally finite cannot be dense i ...
Relativistic Linear Restoring Force
... The dimensionless factor v/c gives us an additional knob – we can elect to set v c while maintaining finite relativistic energies (the v/c −→ 0 limit functions, in the retardation condition, much like the σ −→ ∞ limit). The other limit, v = c is the one on which we will focus on the grounds that: ...
... The dimensionless factor v/c gives us an additional knob – we can elect to set v c while maintaining finite relativistic energies (the v/c −→ 0 limit functions, in the retardation condition, much like the σ −→ ∞ limit). The other limit, v = c is the one on which we will focus on the grounds that: ...
Lecture 11: Graphs of Functions Definition If f is a function with
... Definition If f is a function with domain A, then the graph of f is the set of all ordered pairs {(x, f (x))|x ∈ A}, that is, the graph of f is the set of all points (x, y) such that y = f (x). This is the same as the graph of the equation y = f (x), discussed in the lecture on Cartesian co-ordinate ...
... Definition If f is a function with domain A, then the graph of f is the set of all ordered pairs {(x, f (x))|x ∈ A}, that is, the graph of f is the set of all points (x, y) such that y = f (x). This is the same as the graph of the equation y = f (x), discussed in the lecture on Cartesian co-ordinate ...
Forms of Linear Equations y m x
... m1 = m2 for parallel lines y = m1 x + b1 and y = m2 x + b2 ex) y = −3 x + 2 and y = −3 x − 4 Perpendicular Lines have slopes that are negative reciprocals ...
... m1 = m2 for parallel lines y = m1 x + b1 and y = m2 x + b2 ex) y = −3 x + 2 and y = −3 x − 4 Perpendicular Lines have slopes that are negative reciprocals ...
What is a linear relationship (straight line)? A linear relationship
... This is the least common way to represent a straight line. The word intercept here refers to both the x-intercept (a,0) and the y-intercept (0,b) of the straight line. This is the best way to represent a straight line if you want the readers to obtain two intercepts at the same time. To see b is the ...
... This is the least common way to represent a straight line. The word intercept here refers to both the x-intercept (a,0) and the y-intercept (0,b) of the straight line. This is the best way to represent a straight line if you want the readers to obtain two intercepts at the same time. To see b is the ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.