Book:Michael C. Gemignani/Calculus and Statistics

An unabridged republication was issued in 2006 by Dover Publications.

Subject Matter

 * Calculus
 * Probability Theory
 * Statistics

Contents

 * Chapter 1 The basic Concepts of Function and Probability
 * 1.1 Sets and functions
 * 1.2 The notion of probability
 * 1.3 The basic laws of probability
 * 1.4 More basic facts about probabilities


 * Chapter 2 Some Specific Probabilities
 * 2.1 Sampling without replacement but with regard to order
 * 2.2 Sampling without replacement or regard to order
 * 2.3 Sampling with replacement and with regard to order
 * 2.4 Bayes' Theorem


 * Chapter 3 Random Variables. Graphs
 * 3.1 Random variables. Admissible ranges
 * 3.2 Graphs of equalities and inequalities
 * 3.3 Properties of functions and graphs
 * 3.4 Continuity
 * 3.5 Summation notation
 * 3.6 Probability distributions


 * Chapter 4 The Derivative
 * 4.1 The limit of a function
 * 4.2 The derivative of a function
 * 4.3 Basic rules for finding a derivative
 * 4.4 The Chain Rule. Implicit differentiation


 * Chapter 5 Applications of the Derivative
 * 5.1 Maxima and minima
 * 5.2 More about maxima and minima. Increasing and decreasing functions
 * 5.3 Some theorems about continuous functions
 * 5.4 Higher derivatives and their applications
 * 5.5 The density function of a continuous distribution. The mode


 * Chapter 6 Sequences and Series
 * 6.1 Sequences and series
 * 6.2 Tests for convergence of series
 * 6.3 Power series
 * 6.4 Taylor's series. Interval of convergence


 * Chapter 7 Integration
 * 7.1 The definite integral. Area under a graph
 * 7.2 The fundamental theorem of the calculus
 * 7.3 Some basic integrals. The indefinite integral
 * 7.4 Integration by parts and change of variable
 * 7.5 Improper integrals. Tables of integrals
 * 7.6 Numerical methods of integration


 * Chapter 8 The Integral and Continuous Variates
 * 8.1 Measures of central tendency
 * 8.2 Variation from the norm
 * 8.3 Probability of extreme values. Moment-generating functions


 * Chapter 9 Some Basic Discrete Distributions
 * 9.1 The rectangular and hypergeometric distributions
 * 9.2 The binomial distribution
 * 9.3 Distributions involving the number of trials until success
 * 9.4 The Poisson distribution


 * Chapter 10 Other Important Distributions
 * 10.1 The normal distribution
 * 10.2 Student's $t$-distribution
 * 10.3 More about the $t$-distribution
 * 10.4 $\chi^2$-distribution
 * 10.5 Some other distributions


 * Chapter 11 Hypothesis Testing
 * 11.1 Statistical inference
 * 11.2 More about critical regions
 * 11.3 Some remarks on the design of experiments
 * 11.4 An example


 * Chapter 12 Functions of Several Variables
 * 12.1 Multivariate functions
 * 12.2 Partial differentiation
 * 12.3 Multiple integration


 * Chapter 13 Regression and Correlation
 * 13.1 Linear regression
 * 13.2 Measures of correlation
 * 13.3 The coefficient of correlation
 * 13.4 The significance of $r$ and $r^2$


 * Appendix
 * Table 1 Common logarithms
 * Table 2 Areas under the standard normal curve
 * Table 3 Critical values of chi square
 * Table 4 Critical values of $t$
 * Table 5 Critical values of $F$
 * Table 6 Exponential functions
 * Table 7 $z = \frac12 \ln \left({\dfrac {1 + r} {1 - r} }\right)$
 * Table 8 Squares, square roots, and reciprocals from $1$ to $1000$


 * Answers to the Exercises
 * General Index
 * Index of Symbols
 * Table of Integrals