Cinzia Bisi, Rita Fioresi

Mathematical Methods for Life Sciences (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book introduces calculus, and other key mathematical methods, to students from applied sciences. Special attention is paid to real-world applications, and for every concept, many concrete examples are provided.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 246
• Erscheinungstermin: 19. Januar 2024
• Englisch
• ISBN-13: 9781003824602
• Artikelnr.: 69570051

Autorenporträt

Cinzia Bisi is a Professor of Geometry at the Department of Mathematics and Computer Sciences at the University of Ferrara, Italy. She has wide experience in teaching mathematics and statistics to students in the Department of Life Sciences. She has an interest in the areas of pure and applied mathematics.

Rita Fioresi is a professor of Geometry at the FaBiT Department at the University of Bologna, Italy. She has written textbooks in linear algebra, and her research interests are primarily in the areas of pure and applied mathematics.

Inhaltsangabe

1. Functions in applied sciences. 1.1. The concept of function. 1.2. Linear
functions. 1.3. Polynomial functions. 1.4. Rational functions and algebraic
functions. 1.5. The exponential and logarithmic functions. 1.6. Malthusian
Law. 1.7. Elementary trigonometric functions. 1.8. Exercises with
solutions. 1.9. Suggested Exercises. 2. Limits and Derivatives. 2.1.
Limits. 2.2. Properties of limits and standard limits. 2.3. Indeterminate
forms. 2.4. Continuity. 2.5. Derivative of a function. 2.6. Derivability
and Continuity. 2.7. De L'Hopital's Rule. 2.8. Derivative of the Inverse
Function. 2.9. Exercises with solutions. 2.10. Suggested Exercises. 2.11.
Appendix: Derivation rules. 2.12. Appendix: Derivatives. 2.13. Appendix:
Theorems on limits. 3. Applications of the derivative. 3.1. The linear
approximation. 3.2. The derivative as rate of change. 3.3. Local Maxima and
Minima. 3.4. Graph sketching. 3.5. Optimization. 3.6. Exercises with
SolutionsSuggested Exercises. 3.7. Appendix: Theorems of differential
calculus. 4. Integrals. 4.1. The Definite Integral. 4.2. Properties of the
definite integral. 4.3. The Fundamental Theorem of Calculus. 4.4.
Integration by substitution. 4.5. Integration by parts. 4.6. Integration of
rational functions. 4.7. Integration of trigonometric functions. 4.8.
Applications. 4.9. Exercises with solutions. 4.10. Suggested Exercises.
4.11. Appendix: Indefinite integrals. 4.12. Appendix: Theorems on integral
calculus. 5. First order differential equations. 5.1. First order
equations. 5.2. The Cauchy problem. 5.3. Direction field. 5.4. Separable
Equations. 5.5. Newton's law of cooling. 5.6. Linear equations. 5.7. Mixing
problems. 5.8. Malthusian laws and population dynamics. 5.9. Homogeneous
equations. 5.10. Autonomous differential equations. 5.11. The Logistics
Model. 5.12. Solution of the logistic equation. 5.13. Exercises with
solutions. 5.14. Suggested exercises. 6. Second order differential
equations. 6.1. Cauchy's Theorem. 6.2. The Wronskian. 6.3. Homogeneous
linear equations. 6.4. Linear equations. 6.5. Linear equations with
constant coefficients. 6.6. Equations with constant coefficients: the
general case. 6.7. Simple harmonic motion. 6.8. Harmonic motion with
external force. 6.9. Damped harmonic motion. 6.10. Exercises with
Solutions. 6.11. Suggested Exercises. 6.12. Appendix: Linear Systems. 7.
Elementary Statistics. 7.1. Populations and Variables. 7.2. Absolute
Frequencies and Percentages. 7.3. Graphical representation of data. 7.4.
Mode, Average, and Median. 7.5. Variance and standard deviation. 7.6.
Quartiles and Interquartile Range. 7.7. Normal Distribution. 7.8. Exercises
with solutions. 7.9. Suggested Exercises. A. Solutions of some exercises.