A cookbook of mathematics by Vinogradov V.

By Vinogradov V.

Show description

Read Online or Download A cookbook of mathematics PDF

Similar mathematical & statistical books

Computation of Multivariate Normal and t Probabilities (Lecture Notes in Statistics)

This booklet describes lately constructed equipment for actual and effective computation of the necessary likelihood values for issues of or extra variables. It comprises examples that illustrate the chance computations for quite a few purposes.

Excel 2013 for Environmental Sciences Statistics: A Guide to Solving Practical Problems (Excel for Statistics)

This can be the 1st booklet to teach the services of Microsoft Excel to coach environmentall sciences records effectively.  it's a step by step exercise-driven advisor for college kids and practitioners who have to grasp Excel to resolve useful environmental technology problems.  If realizing records isn’t your most powerful go well with, you're not particularly mathematically-inclined, or while you are cautious of pcs, this is often the correct publication for you.

Lectures on the Nearest Neighbor Method (Springer Series in the Data Sciences)

This article offers a wide-ranging and rigorous evaluate of nearest neighbor tools, some of the most very important paradigms in laptop studying. Now in a single self-contained quantity, this ebook systematically covers key statistical, probabilistic, combinatorial and geometric rules for realizing, interpreting and constructing nearest neighbor tools.

Recent Advances in Modelling and Simulation

Desk of Content01 Braking technique in autos: research of the Thermoelastic Instability PhenomenonM. Eltoukhy and S. Asfour02 Multi-Agent structures for the Simulation of Land Use switch and coverage InterventionsPepijn Schreinemachers and Thomas Berger03 Pore Scale Simulation of Colloid DepositionM.

Additional info for A cookbook of mathematics

Sample text

With respect to l, we have: pf11 (l, k0 ) ∂l = 1 or ∂w ∂l 1 = . ) For another economic application see the section ‘Constrained Optimization’. 9 Concavity, Convexity, Quasiconcavity and Quasiconvexity Definition 42 A function z = f (x1 , . . , xn ) is concave if and only if for any pair of distinct points u = (u1 , . . , un ) and v = (v1 , . . , vn ) in the domain of f and for any θ ∈ (0, 1) θf (u) + (1 − θ)f (v) ≤ f (θu + (1 − θ)v) and convex if and only if θf (u) + (1 − θ)f (v) ≥ f (θu + (1 − θ)v).

Nonclassical optimization, also known as mathematical programming, tackles problems with inequality constraints like g(x1 , . . , xn ) ≤ c. Mathematical programming includes linear programming and nonlinear programming. In linear programming, the objective function and all inequality constraints are linear. When either the objective function or an inequality constraint is nonlinear, we face a problem of nonlinear programming. In the following, we restrict our attention to non-linear programming.

The conditions for concavity and convexity are necessary and sufficient, while those for strict concavity (strict convexity) are only sufficient. Definition 43 A set S in Rn is convex if for any x, y ∈ S and any θ ∈ [0, 1] the linear combination θx + (1 − θ)y ∈ S. Definition 44 A function z = f (x1 , . . , xn ) is quasiconcave if and only if for any pair of distinct points u = (u1 , . . , un ) and v = (v1 , . . , vn ) in the convex domain of f and for any θ ∈ (0, 1) f (v) ≥ f (u) =⇒ f (θu + (1 − θ)v) ≥ f (u) and quasiconvex if and only if f (v) ≥ f (u) =⇒ f (θu + (1 − θ)v) ≤ f (v).

Download PDF sample

Rated 4.06 of 5 – based on 19 votes