Introduction to College Mathematics with A Programming Language

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 Cramer's 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.