Author | LeCuyer, Edward J. author |
---|---|
Title | Introduction to College Mathematics with A Programming Language [electronic resource] / by Edward J. LeCuyer |
Imprint | New York, NY : Springer New York, 1978 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9422-8 |
Descript | 420 p. online resource |
1 Set theory -- 1.1 Sets -- 1.2 Operations with Sets -- 1.3 A set theory drill and practice program (optional) -- 1.4 Boolean algebra -- 1.5 The number of elements in a set -- 2 Logic -- 2.1 Statements and logical operations -- 2.2 Conditional statements -- 2.3 Logical equivalence -- 2.4 Arguments -- 3 Vectors and matrices -- 3.1 Vectors -- 3.2 Operations with vectors -- 3.3 Matrices -- 3.4 Operations with matrices -- 3.5 Properties of matrices -- 4 Systems of linear equations -- 4.1 Linear equations -- 4.2 Two-by-two systems of linear equations -- 4.3 Elementary row operations -- 4.4 Larger systems of linear equations -- 4.5 Row reduced form -- 4.6 The inverse of a matrix -- 4.7 Inverses in APL -- 4.8 Applications -- 5 Determinants -- 5.1 Definition of a determinant -- 5.2 A Program for evaluation of determinants -- 5.3 Cofactors -- 5.4 Adjoints and inverses -- 5.5 Cramerโs rule -- 6 Functions and graphing -- 6.1 Definition of a function -- 6.2 Graphing -- 6.3 Linear functions -- 6.4 Quadratic functions -- 6.5 Polynomials -- 6.6 Rational functions -- 7 Exponential and logarithmic functions -- 7.1 Exponential functions -- 7.2 Applications of exponential functions -- 7.3 Logarithmic functions -- 7.4 Properties and applications of logarithms -- 8 Differential calculus -- 8.1 The limit of a function -- 8.2 Slope of a curve and the definition of derivative at a point -- 8.3 Differentiating polynomials -- 8.4 Applications of derivatives -- 8.5 More rules of differentiation (optional) -- 8.6 Theory of maxima, minima -- 8.7 Applied maxima, minima -- 8.8 Curve sketching using derivatives -- 9 Integral calculus -- 9.1 Antidifferentiation -- 9.2 Some formulas for antidifferentiation -- 9.3 Area under a curve -- 9.4 The definite integral -- 9.5 The fundamental theorem of calculus -- 9.6 More applications of integration -- 10 Probability -- 10.1 Axioms of probability -- 10.2 More rules of probability -- 10.3 Permutations and combinations -- 10.4 The hypergeometric distribution -- 10.5 The binomial distribution -- 10.6 The Poisson distribution -- 11 Statistics -- 11.1 Random samples and frequency distributions -- 11.2 Measures of central tendency -- 11.3 Measures of dispersion -- 11.4 The normal distribution -- 11.5 The sampling distribution of the mean -- 12 The trigonometric functions -- 12.1 Angles -- 12.2 The trigonometric functions -- 12.3 The trigonometric functions in APL -- 12.4 Graphs of the trigonometric functions -- 12.5 The inverse trigonometric functions -- 12.6 Solving right triangles -- 12.7 Solving oblique triangles -- A.0 Using APL on a computer terminal -- A.1 Introduction to APL -- A.2 Program definition -- A.3 Branching -- A.4 Program revision and editing procedures -- A.5 The trace command -- Solutions to exercises -- Program index