Author | Batschelet, Edward. author |
---|---|
Title | Introduction to Mathematics for Life Scientists [electronic resource] / by Edward Batschelet |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-642-96080-2 |
Descript | online resource |
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 InequaHties -- 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 โNew Mathematicsโ -- 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 Ill -- 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 -- Chapters.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 -- Problems for Solution -- 10. Exponential and Logarithmic Functions II -- 10.1 Introduction -- 10.2 Integral of 1/x -- 10.3 Properties of Injc -- 10.4 The Inverse Function of Inx -- 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 yโ = ay -- 11.4 The Differential Equation yโ= ay+b -- 11.5 The Differential Equation yโ = 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 Probability -- 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 -- Problems for Solution -- 15. Complex Numbers -- 15.1 Introduction -- 15.2 The Complex Plane -- 15.3 Algebraic Operations -- 15.4 Exponential and Logarithmic Functions of Complex Variables -- 15.5 Quadratic Equations -- 15.6 Oscillations -- Problems for Solution -- Answers to Problems -- References -- Author and Subject Index