Introduction to Mathematics for Life Scientists
A few decades ago mathematics played a modest role in life sciences. Today, however, a great variety of mathematical methods is applied in biology and medicine. Practically every mathematical procedure that is useful in physics, chemistry, engineering, and economics has also found an important appli...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1975, 1975
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| Edition: | 2nd ed. 1975 |
| Series: | Springer Study Edition
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- *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 In 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
- 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
- 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
- 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 PoissonDistribution
- 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 and Logarithmic 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