Introduction to Mathematics for Life Scientists.

1. Real Numbers. - 1.1 Introduction. - 1.2 Classification and Measurement. - 1.3 A Problem with Percentages. - 1.4 Proper and Improper Use of Percentages. - 1.5 Algebraic Laws. - 1.6 Relative Numbers. - 1.7 Inequalities. - 1.8 Mean Values. - 1.9 Summation. - 1.10 Powers. - 1.11 Fractional Powers. - 1.12 Calculations with Approximate Numbers. - 1.13 An Application. - 1.14 Survey. - Problems for Solution. - 2. Sets and Symbolic Logic. - 2.1 "New Mathematics". - 2.2 Sets. - 2.3 Notations and Symbols. - 2.4 Variable Members. - 2.5 Complementary Set. - 2.6 The Union. - 2.7 The Intersection. - 2.8 Symbolic Logic. - 2.9 Negation and Implication. - 2.10 Boolean Algebra. - Problems for Solution. - 3. Relations and Functions. - 3.1 Introduction. - 3.2 Product Sets. - 3.3 Relations. - 3.4 Functions. - 3.5 A Special Linear Function. - 3.6 The General Linear Function. - 3.7 Linear Relations. - Problems for Solution. - 4. The Power Function and Related Functions. - 4.1 Definitions. - 4.2 Examples of Power Functions. - 4.3 Polynomials. - 4.4 Differences. - 4.5 An Application. - 4.6 Quadratic Equations. - Problems for Solution. - 5. Periodic Functions. - 5.1 Introduction and Definition. - 5.2 Angles. - 5.3 Polar Coordinates. - 5.4 Sine and Cosine. - 5.5 Conversion of Polar Coordinates. - 5.6 Right Triangles. - 5.7 Trigonometric Relations. - 5.8 Polar Graphs. - 5.9 Trigonometric Polynomials. - Problems for Solution. - 6. Exponential and Logarithmic Functions I. - 6.1 Sequences. - 6.2 The Exponential Function. - 6.3 Inverse Functions. - 6.4 The Logarithmic Functions. - 6.5 Applications. - 6.6 Scaling. - 6.7 Spirals. - Problems for Solution. - 7. Graphical Methods. - 7.1 Nonlinear Scales. - 7.2 Semilogarithmic Plot. - 7.3 Double-Logarithmic Plot. - 7.4 Triangular Charts. - 7.5 Nomography. - 7.6 Pictorial Views. - Problems for Solution. - 8. Limits. - 8.1 Limits of Sequences. - 8.2 Some Special Limits. - 8.3 Series. - 8.4 Limits of Functions. - 8.5 The Fibonacci Sequence. - Problems for Solution. - 9. Differential and Integral Calculus. - 9.1 Growth Rates. - 9.2 Differentiation. - 9.3 The Antiderivative. - 9.4 Integrals. - 9.5 Integration. - 9.6 The Second Derivative. - 9.7 Extremes. - 9.8 Mean of a Continuous Function. - 9.9 Small Changes. - 9.10 Techniques of Integration. - Problems for Solution. - 10. Exponential and Logarithmic Functions II. - 10.1 Introduction. - 10.2 Integral of 1/x. - 10.3 Properties of ln x. - 10.4 The Inverse Function of ln x. - 10.5 The General Definition of a Power. - 10.6 Relationship between Natural and Common Logarithms. - 10.7 Differentiation and Integration. - 10.8 Some Limits. - 10.9 Applications. - 10.10 Approximations and Series Expansions. - 10.11 Hyperbolic Functions. - Problems for Solution. - 11. Ordinary Differential Equations. - 11.1 Introduction. - 11.2 Geometric Interpretation. - 11.3 The Differential Equation y' = ay. - 11.4 The Differential Equation y' = ay+b. - 11.5 The Differential Equation y' = ay2+ by+ c. - 11.6 The Differential Equation dy/dx = k * y/x. - 11.7 A System of Linear Differential Equations. - 11.8 A System of Nonlinear Differential Equations. - 11.9 Classification of Differential Equations. - Problems for Solution. - 12. Functions of Two or More Independent Variables. - 12.1 Introduction. - 12.2 Partial Derivatives. - 12.3 Maxima and Minima. - 12.4 Partial Differential Equations. - Problems for Solution. - 13. Probability. - 13.1 Introduction. - 13.2 Events. - 13.3 The Concept of Probability. - 13.4 The Axioms of Probability Theory. - 13.5 Conditional Probabilities. - 13.6 The Multiplication Rule. - 13.7 Counting. - 13.8 Binomial Distribution. - 13.9 Random Variables. - 13.10 The Poisson Distribution. - 13.11 Continuous Distributions. - Problems for Solution. - 14. Matrices and Vectors. - 14.1 Notations. - 14.2 Matrix Algebra. - 14.3 Applications. - 14.4 Vectors in Space. - 14.5 Applications. - 14.6 Determinants. - 14.7 Inverse of a Matrix. - 14.8 Linear Dependence. - 14.9 Eigenvalues and Eigenvectors. - Problems for Solution. - 15. Complex Numbers. - 15.1 Introduction. - 15.2 The Complex Plane. - 15.3 Algebraic Operations. - 15.4 Exponential Functions of Complex Variables. - 15.5 Quadratic Equations. - 15.6 Oscillations. - Problems for Solution. - Appendix (Tables A to K). - Solutions to Odd Numbered Problems. - References. - Author and Subject Index.