Calculus For Biology and Medicine by Claudia Neuhauser PDF
By Claudia Neuhauser
ISBN-10: 0321644689
ISBN-13: 9780321644688
Calculus for Biology and drugs, 3rd Edition, addresses the wishes of readers within the organic sciences via exhibiting them how you can use calculus to investigate ordinary phenomena—without compromising the rigorous presentation of the maths. whereas the desk of contents aligns good with a standard calculus textual content, all of the suggestions are offered via organic and clinical functions. The textual content presents readers with the information and talents essential to study and interpret mathematical types of a various array of phenomena within the residing international. This ebook is acceptable for a large viewers, as all examples have been selected in order that no formal education in biology is required.
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EXAMPLE 5 A Chemical Reaction Consider the reaction rate of the chemical reaction A + B −→ AB in which the molecular reactants A and B form the molecular product AB. The rate at which this reaction proceeds depends on how often A and B molecules collide. The law of mass action states that the rate at which this reaction proceeds is proportional to the product of the respective concentrations of the reactants. Here, concentration means the number of molecules per fixed volume. 2 Elementary Functions 21 Note that k > 0, because [A], [B], and R are positive.
EXAMPLE 14 Solve x 2 + 4x + 5 = 0 Solution Using the quadratic formula, we obtain x 1, 2 = = −4 ± 42 − (4)(1)(5) (2)(1) −4 ± 16 − 20 2 = −4 ± −4 2 2 If we allowed solutions only in the real-number system, we would conclude that x + 4x + 5 = 0 has no solutions. But if we allow solutions in the complex number system, we find that x 1, 2 = −4 ± 4i 2 −4 ± 2i 2(−2 ± i) = = = −2 ± i 2 2 2 That is, x 1 = −2 + i and x 2 = −2 − i . 1 Preliminaries 13 The term b2 − 4ac under the square root sign in the quadratic formula is called the discriminant.
The constant, nonzero function has degree 0, the linear function has degree 1, and the 3 quadratic function has degree 2. Other examples are f (x) = 4x − 3x + 1, x ∈ R, 7 which is a polynomial of degree 3, and f (x) = 2 − x , x ∈ R, which is a polynomial of degree 7. 16, we display y = x n for n = 2 and 3. , symmetric about the origin) when n = 3. This property n holds in general: y = x is an even function when n is even and an odd function when n is odd. 1. 16 The graphs of y = x n for n = 2 and n = 3.
Calculus For Biology and Medicine by Claudia Neuhauser
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