S. Lipschutz, et al.'s Beginning Finite Mathematics [Theory and Problems of] PDF

By S. Lipschutz, et al.

Show description

Read or Download Beginning Finite Mathematics [Theory and Problems of] PDF

Similar mathematics books

Download e-book for iPad: Conceptual Mathematics: A First Introduction to Categories by F. William Lawvere, Stephen Hoel Schanuel

The belief of a "category"--a type of mathematical universe--has led to a impressive unification and simplification of arithmetic. Written through of the best-known names in express good judgment, Conceptual arithmetic is the 1st ebook to use different types to the main easy arithmetic.

Download e-book for iPad: Count Like an Egyptian: A Hands-on Introduction to Ancient by David Reimer

The maths of historical Egypt used to be essentially diverse from our math this present day. opposite to what humans may possibly imagine, it wasn’t a primitive forerunner of contemporary arithmetic. in truth, it can’t be understood utilizing our present computational tools. count number Like an Egyptian presents a enjoyable, hands-on advent to the intuitive and often-surprising artwork of historic Egyptian math.

Extra info for Beginning Finite Mathematics [Theory and Problems of]

Sample text

2jnπ k + dj sin 2jnπ k , 42 1. 24 [23]. 5) which describes a population with a propensity to simple exponential growth at low densities and a tendency to decrease at high densities. The quantity λ = exp(r(1 − x(n))) could be considered the densitydependent reproductive rate of the population. This model is plausible for a single-species population that is regulated by an epidemic disease at high density. The nontrivial fixed point of this equation is given by x∗ = 1. Now, ′ f (1) = 1 − r. Hence x∗ = 1 is asymptotically stable if 0 < r ≤ 2 (check r = 2).

For most biological species, however, none of the above cases is valid as the population increases until it reaches a certain upper limit. Then, due to the limitations of available resources, the creatures will become testy and engage in competition for those limited resources. This competition is proportional to the number of squabbles among them, given by y 2 (n). A more reasonable model would allow b, the proportionality constant, to be greater than 0, y(n + 1) = µy(n) − by 2 (n). 3) x(n + 1) = µx(n)(1 − x(n)) = f (x(n)).

Consider Baker’s map defined by ⎧ 1 ⎪ ⎨2x for 0 ≤ x ≤ , 2 B(x) = 1 ⎪ ⎩2x − 1 for < x ≤ 1. 2 (i) Draw the function B(x) on [0,1]. (ii) Show that x ∈ [0, 1] is an eventually fixed point if and only if it is of the form x = k/2n , where k and n are positive integers,2 with 0 ≤ k ≤ 2n − 1. 13. Find the fixed points and the eventually fixed points of x(n + 1) = f (x(n)), where f (x) = x2 . 14. 7 that is not in the form k/2n . 15. 7. Show that if x = k/2n , where k and n are positive integers with 0 < k/2n ≤ 1, then x is an eventually fixed point.

Download PDF sample

Beginning Finite Mathematics [Theory and Problems of] by S. Lipschutz, et al.


by Donald
4.1

Rated 4.24 of 5 – based on 29 votes