Preface Aims, scope, and outline of the book; mathematical and ecological preparation required .Part I. Introduction and Mathematical Preliminaries.Chapter 1. Introduction Why do mathematical ecology? Understanding and predicting Theoretical problems vs. empirical problems Common errors of perception of mathematical models Mathematical models are analogues of biological systems Approaches to mathematical ecology .Chapter 2. Mathematical Prologue Numbers, operations, and closure Matrix Algebra and Linear Systems Limits, derivatives, differential equations Eigenvalues and eigenvectors Taylor Series Numerical methods (Runga-Kutta) .

Part II. Linear Models of Single Populations.Chapter 3. Non-structured Models: Homogeneous populations Exponential growth, exponential decay . Equilibrium, eigenvalue, stability, and bifurcation of exponential model Geometric model . Equilibrium, eigenvalue, stability, and bifurcation of geometric model Relationship between exponential and geometric models .Chapter 4. Structured Linear Models: Relaxing assumption of population homogeneity Age structure .

Euler's equation. Leslie matrix. Historical background: Peter Leslie and Elton's ecologists. The Leslie matrix. Eigenvalues and eigenvectors of the Leslie matrix. Stable age distribution and population growth rates Stage structure . Life-stage models. Dominant eigenvalue and eigenvector Markov models of landscapes .

Historical background: Markov. The Markov matrix. Dominant eigenvalue and eigenvector Semimarkov models: relaxing assumption of constancy of transition probabilities . Sojourn functions. An age-stage model of a landscape.Part III. Non-Linear Models of Single Populations.Chapter 5.

The logistic model: Continuous time Historical background: Verhulst, Pearl Deriving the logistic model: relaxing assumption of constant birth and death in the exponential model .What K and r are.Why K and r are correlated Equilibrium, eigenvalues, and stability of the logistic model Transcritical bifurcation in the logistic model Other ways of representing density-dependence and generalized logistic models .Chapter 6. Harvesting in the continuous time logistic model Harvesting functions: a precursor of "functional responses" .