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• Classes of functions
  '''THEOREM.''' A linear polynomial ...h $f(x+T)$ and work our way to $f(x)$, identically. For example, no linear polynomial $f(x)=mx+b,\ m\ne 0$, is periodic:
  143 KB (24,052 words) - 13:11, 23 February 2019
• Vector and complex variables
  '''Definition.''' The ''characteristic polynomial'' of an $2\times 2$ matrix $A$ is defined to be: *the eigenvalues are the real roots of the (quadratic) characteristic polynomial $\chi_A$, and, therefore,
  113 KB (18,750 words) - 02:33, 10 December 2018
• Series
  ...lar value of $x$, we can find a special analog of the standard form of the polynomial for each $x=a$. The polynomials are still sums of powers just not of $x$ bu '''Proposition.''' For each real number $a$, every degree $n$ polynomial $P$ can be represented in the form ''centered at $x=a$'', i.e.,
  113 KB (19,100 words) - 23:07, 3 January 2019
• Operations on functions
  '''Example.''' To find the inverse of a linear polynomial A linear polynomial,
  142 KB (23,566 words) - 02:01, 23 February 2019
• Limits and continuity
  Any polynomial can be built from $x$ and constants by multiplication and addition. Therefo [[image:cubic polynomial.png| center]]
  107 KB (18,743 words) - 17:00, 10 February 2019
• Precalculus exercises
  *Suppose $f$ is a polynomial of degree $55$ and its leading term is $-1$. Describe the long term behavio *For the polynomial $f(x)=-2x^2(x+2)^2(x^2+1)$, find its $x$-intercepts.
  17 KB (2,933 words) - 19:37, 30 July 2018
• College Algebra -- Fall 2016
  '''MTH 130 College Algebra.''' 3 hrs. Polynomial, rational, exponential, and logarithmic functions. Graphs, systems of equat * 2.4 Higher Degree Polynomial Equations
  10 KB (1,078 words) - 19:07, 16 December 2016
• Limits: transition from discrete to continuous
  Any polynomial can be built from $x$ and constants by multiplication and addition. Therefo [[image:cubic polynomial.png| center]]
  51 KB (9,271 words) - 20:02, 8 September 2016
• Differentiation
  In other words, our “function of functions” has the same property as a linear polynomial: *The derivative of a constant polynomial is zero:
  82 KB (14,116 words) - 19:50, 6 December 2018
• Systems of ODEs
  The analysis starts with the characteristic polynomial: Recall that the characteristic polynomial of matrix $F$ is
  63 KB (10,958 words) - 14:27, 24 November 2018
• College Algebra by Ratti and McWaters
  3. Polynomial and Rational Functions 3.2 [[Polynomial]] Functions
  2 KB (269 words) - 18:53, 16 November 2011
• Calculus exercises: part II
  *Estimate the coefficients of the Taylor polynomial $T_1$ of order $1$ centered at $a=1$ of the function $f$ shown above. Provi *What degree Taylor polynomial one would need to approximate $e^{.01}$ within $.001$? (Answers may vary an
  15 KB (2,591 words) - 17:15, 8 March 2018
• The derivative
  We know from Chapter 3 that under a linear polynomial $f(x)=mx+b$ with $m>0$, the distance is increased by a factor of $m$ or dec *the derivative of a quadratic polynomial is linear, and
  75 KB (13,000 words) - 15:12, 7 December 2018
• Eigenvalues and eigenvectors of linear operators
  The ''characteristic polynomial'' of matrix $A$ is This is a polynomial of $\lambda$!
  12 KB (1,971 words) - 01:09, 12 October 2011
• College Algebra -- Fall 2013
  '''MTH 130 College Algebra.''' 3 hrs. Polynomial, rational, exponential, and logarithmic functions. Graphs, systems of equat Chapter 5. Polynomial and Rational Functions
  6 KB (752 words) - 04:19, 13 December 2013
• College Algebra -- Fall 2014
  ''MTH 130 College Algebra.'' 3 hrs. Polynomial, rational, exponential, and logarithmic functions. Graphs, systems of equat Chapter 5. Polynomial and Rational Functions
  6 KB (850 words) - 16:52, 29 November 2014
• College Algebra by Sullivan
  5. Polynomial and Rational Functions 5.1 Polynomial Functions and Models
  3 KB (349 words) - 16:29, 8 August 2013
• Perron–Frobenius theorem
  #$r$ is a simple [[root]] of the [[characteristic polynomial]] of A and its [[eigenspace]] is 1-dimensional (the geometric multiplicity #r is a simple root of the characteristic polynomial of A and its [[eigenspace]] is 1-dimensional (the geometric multiplicity of
  2 KB (239 words) - 15:08, 25 August 2011
• Precalculus with Scientific Applications -- Spring 2016
  ...lus with Scientific Applications.''' Functions used in calculus including polynomial, rational, exponential, logarithmic, and trigonometric. Systems of equation * 4. POLYNOMIAL AND RATIONAL FUNCTIONS.
  7 KB (890 words) - 16:32, 20 April 2016
• Inner product spaces: part 1
  Its [[Taylor polynomial]] of degree $3$ is Consider the quadratic polynomial of $t$:
  14 KB (2,404 words) - 15:04, 13 October 2011

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