E-raamat: Mathematical Methods for Life Sciences

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 LHopitals 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. Newtons 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. Cauchys 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.

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.