Pure Mathematics

Oxford University (OX)

Here are the best resources to pass Pure Mathematics. Find Pure Mathematics study guides, notes, assignments, and much more.

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FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
  • FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

  • Class notes • 13 pages • 2021
  • Recall that a nite sequence has the form fyngN n=0 and an in nite sequence has the form fyng1 n=0. A di erence equation of order m has the form (1) yn+m = F(n; yn; yn+1; : : : ; yn+m
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FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
  • FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

  • Class notes • 19 pages • 2021
  • An ordinary di erential equation of order k has the form (1) F  x; y; dy dx ; d2y dx2 ; : : : ; dky dxk  = 0; where F is a function of k+2 variables. We will usually write ODE as an abreviation for ordinary di erential equation. A function y(x) is a solution of the ODE (1) in the interval a < x < b if it satis es the equation (1) for all x in this interval. We will usually be interested in solving an initial value problem. For an ODE of order k, this has the form Reca...
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Derivatives in Several Variables
  • Derivatives in Several Variables

  • Summary • 12 pages • 2021
  • These notes introduce the notion of derivatives for functions of several variables. It is worthwhile to rst recall the derivative of a real-valued function of a single variable. Let f : R ! R, and xed x0 2 R. The classical de nition of f having a derivative f0(x0) at x0 is that the limit Notice that any linear map from R to itself is just multiplication by some constant a. This is the important conceptual leap we must make: the derivative of a function at a point is not a number, or a ve...
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Trigonometry - summary of all Trigonometry - summary of all
  • Trigonometry - summary of all

  • Summary • 12 pages • 2019
  • In these notes one can find almost everything important about trigonometry: definitions and concepts, formulas and exercises; solved(to understand the methodology) and unsolved (to practice by yourself).
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Quadratic equations
  • Quadratic equations

  • Class notes • 2 pages • 2013
  • In this document, the quadratic formula (for roots of x) and x- and y-values of the turning point is derived from a general quadratic equation.
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