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By Ibn Khaldun
The Muqaddimah, frequently translated as "Introduction" or "Prolegomenon," is an important Islamic heritage of the premodern international. Written through the nice fourteenth-century Arab student Ibn Khaldûn (d. 1406), this enormous paintings laid down the principles of numerous fields of information, together with philosophy of heritage, sociology, ethnography, and economics. the 1st whole English translation, by means of the eminent Islamicist and interpreter of Arabic literature Franz Rosenthal, was once released in 3 volumes in 1958 as a part of the Bollingen sequence and obtained speedy acclaim in the US and out of the country. A one-volume abridged model of Rosenthal's masterful translation was once first released in 1969.
This new version of the abridged model, with the addition of a key part of Rosenthal's personal creation to the three-volume variation, and with a brand new advent by way of Bruce B. Lawrence, will reintroduce this seminal paintings to twenty-first-century scholars and students of Islam and of medieval and old historical past.
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Extra info for The Muqaddimah: An Introduction to History
Sample text
10 Notes and References . . . . . . . . . . . . . . . . . . . 676 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 14 Numerical Solutions of Boundary Value Problems . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 2 Conditioning . . . . . . . . . . . . . . . . . . . . . . . 3 A Method to Solve BVPODE . . . . . . . .
4 Trigonometric interpolation . . . . . . . . . . . . . . . . . . . 409 A solution of the van der Pol equation . . . . . . . . . . . . . . 410 Periodogram for the van der Pol equation . . . . . . . . . . . . . 410 Periodogram for a forced van der Pol equation . . . . . . . . . . . 4 An approximation to a definite integral by a finite Riemann sum . . . 420 The graph of an integrand for W on 0 ≤ v ≤ π . . . . . . . . . . . 433 The graph of 1/(1 + u64 ) on 0 ≤ u ≤ 1 .
7 The Method of Modified Equations . . . . . . . . . . . . . . 1 Correlations and Structure in the Residual . . . . . . . 2 Finding a Modified Equation . . . . . . . . . . . . . 8 Geometric Integration . . . . . . . . . . . . . . . . . . . 9 Other Methods . . . . . . . . . . . . . . . . . . . . . . 10 Notes and References . . . . . . . . . . . . . . . . . . . 676 Problems .