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second-degree polynomial. second derivative. second derivative test. second-order differential equation. series. shell integration. Simpson's rule. sine. sine wave. slope field. squeeze theorem. sum rule in differentiation. sum rule in integration. summation. supplementary angle. surface area. system of linear equations.
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
Sometimes other equivalent versions of the test are used. In cases 1 and 2, the requirement that f xx f yy − f xy 2 is positive at (x, y) implies that f xx and f yy have the same sign there. Therefore, the second condition, that f xx be greater (or less) than zero, could equivalently be that f yy or tr(H) = f xx + f yy be greater (or less ...
Because the degree of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two. [11] Two terms with the same indeterminates raised to the same powers are called "similar terms" or "like terms", and they can be combined, using the distributive law, into a single term whose coefficient is the sum of the ...
The resulting polynomial is not a linear function of the coordinates (its degree can be higher than 1), but it is a linear function of the fitted data values. The determinant, permanent and other immanants of a matrix are homogeneous multilinear polynomials in the elements of the matrix (and also multilinear forms in the rows or columns).
The expression + + , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two. In elementary mathematics a polynomial and its associated polynomial function are rarely distinguished and the terms quadratic function and quadratic polynomial are nearly synonymous and ...
The defining property of the Vandermonde polynomial is that it is alternating in the entries, meaning that permuting the by an odd permutation changes the sign, while permuting them by an even permutation does not change the value of the polynomial – in fact, it is the basic alternating polynomial, as will be made precise below.
The largest zero of this polynomial which corresponds to the second largest zero of the original polynomial is found at 3 and is circled in red. The degree 5 polynomial is now divided by () to obtain = + + which is shown in yellow. The zero for this polynomial is found at 2 again using Newton's method and is circled in yellow.