By Peter Freyd

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**Extra info for Abelian categories. An introduction to the theory of functors**

**Sample text**

10) 2. Associative law of ⊗: 3. 12) 4. Distributive law: 5. Multiplication cancelling division: xˆ ⊗ (yˆ x) ˆ = y. 15. As a result of these failures, mathematicians find it very difficult to work directly in floating-point arithmetic—its algebraic structure is weak and unfamiliar. However, thanks to the discussion above, we know how to translate a problem involving floating-point operations into a problem involving only real arithmetic on real quantities (x, Δ x, δ x, . ). This approach allows us to use the mathematical structures that we are familiar with in algebra and analysis.

601 The region in the z = hλ plane where backward Euler has a monotonic decrease as k → ∞ . . . . . . . . . . . . . . . . . . 602 Asymmetry of error in approximation of exp(x) by a polynomial . . . 603 Analytic continuation . . . . . . . . . . . . . . . . . . . . . 607 Residual of the Taylor polynomials of S (dotted line) and I . . . . . . 611 The region in the z = hλ plane, where the second-order implicit Taylor series method has a monotonic decrease as k → ∞ .

2 Conditioning . . . . . . . . . . . . . . . . . . . . . . . 3 A Method to Solve BVPODE . . . . . . . . . . . . . . . . 1 Solution on a Uniform Mesh . . . . . . . . . . . . . 2 Solution on an Adapted Mesh . . . . . . . . . . . . 4 How Does It Work, and Why Does It Work? . . . . . . . . . 1 Equidistribution, the Theory . . . . . . . . . . . . . 2 Solution of the Minimax Problem .