Mathematics for the Biological Sciences

by Arya, Jagdish C.; Lardner, Robin W.

• ISBN13: 9780135624395
• ISBN10: 0135624398
• Edition: 1st
• Format: Paperback
• Copyright: 1979-01-19
• Publisher: Pearson

Summary

This volume reviews differential and integral calculus for functions of one variable, differential calculus for several variables, differential equations, probability, difference equations, and matrices -- all with special emphasis on applications in the life sciences.

Table of Contents

Preface	xiii
Applications In The Life Sciences	xvii
Functions	1	(59)
Real Number System	2	(4)
Sets and Their Representation	6	(4)
Functions	10	(11)
Linear Functions	21	(7)
Linear Inequalities	28	(5)
Other Simple Functions	33	(14)
More on Functions	47	(5)
Limits as x→ ∞	52	(8)
Review Exercises for Chapter 1	58	(2)
The Derivative	60	(57)
Increments and Rates	61	(7)
Limits	68	(9)
More on Limits	77	(6)
Continuous Functions	83	(3)
The Derivative	86	(7)
Derivatives of Power Functions	93	(8)
Derivatives of Products and Quotients	101	(5)
Derivatives of Composite Functions	106	(6)
Higher Derivatives	112	(5)
Review Exercises for Chapter 2	115	(2)
Exponential And Logarithm Functions	117	(43)
Exponential Functions	118	(8)
Inverse Functions and Logarithms	126	(8)
Log-Log and Semi-log Plots	134	(11)
Natural Logarithms and Exponentials	145	(8)
Exponential Growth and Decay	153	(7)
Review Exercises for Chapter 3	157	(3)
Applications Of Derivatives	160	(64)
Analysis of Curves	161	(12)
Maxima and Minima	173	(13)
Applications of Maxima and Minima	186	(10)
Newton's Method	196	(9)
The Differentials dx and dy	205	(6)
Implicit Differentiation	211	(4)
Parametric Equations	215	(9)
Review Exercises for Chapter 4	221	(3)
Trigonometric Functions	224	(44)
Definitions and Elementary Uses	225	(9)
Limits of Trigonometric Functions	234	(5)
Derivatives of Trigonometric Functions	239	(9)
The Inverse Trigonometric Functions	248	(8)
Periodic Functions	256	(12)
Review Exercises for Chapter 5	266	(2)
Integration	268	(40)
Antiderivatives	269	(7)
Method of Substitution	276	(10)
Tables of Integrals	286	(6)
Method of Partial Fractions	292	(5)
Trigonometric Substitutions	297	(5)
Integration by Parts	302	(6)
Review Exercises for Chapter 6	306	(2)
The Definite Integral	308	(51)
Summation Notation	309	(8)
Areas under Curves	317	(5)
Definite Integrals	322	(8)
More on Areas	330	(8)
Volumes of Revolution	338	(6)
Centers of Mass	344	(9)
The Natural Logarithm	353	(6)
Review Exercises for Chapter 7	357	(2)
Probability	359	(69)
Sample Spaces and Events	360	(7)
Probability	367	(11)
Counting Methods	378	(10)
Applications in Genetics	388	(11)
The Binomial Distribution	399	(6)
Continuous Probability Distributions	405	(11)
The Normal Distribution	416	(12)
Review Exercises for Chapter 8	425	(3)
Functions Of Several Variables	428	(58)
Functions and Domains	429	(6)
Coordinates in Three Dimensions	435	(9)
Graphs in Three Dimensions	444	(7)
Partial Derivatives	451	(8)
Linear Approximations	459	(6)
Maxima and Minima	465	(8)
Method of Least Squares	473	(4)
Chain Rule	477	(9)
Review Exercises for Chapter 9	483	(3)
Differential Equations	486	(67)
Introductory Remarks	487	(5)
Exponential Functions Revisited	492	(8)
Separable Equations	500	(11)
Linear First-order Equations	511	(5)
Second-order Equations	516	(5)
Oscillatory Solutions	521	(6)
Systems of Differential Equations	527	(11)
Some More Advanced Models	538	(15)
Review Exercises for Chapter 10	549	(4)
Difference Equations	553	(39)
Discrete Time Models	554	(9)
The Logistic Model	563	(9)
Linear First-order Equations	572	(8)
Second-order Equations	580	(12)
Review Exercises for Chapter 11	590	(2)
Vectors And Matrices	592	(74)
Vectors in Two Dimensions	593	(11)
The Inner Product	604	(7)
Relative Velocities	611	(8)
Forces	619	(8)
Matrices	627	(7)
Applications of Matrices	634	(14)
Review Exercises for Chapter 12	644	(4)
APPENDICES
I Table of Standard Derivatives	648	(2)
II Table of Integrals	650	(9)
III Numerical Tables	659	(7)
Answers To Odd-Numbered Exercises	666	(38)
Index	704