Introduction to Mathematical Biology for Life Science Students

Chapter 1  First Order Scalar Differential Equations with Applications

§1.1    Linear equations

§1.2    Separation of variables

§1.3    Phase “plane” analysis : One-dimensional flow

§1.4    Logistic equation

§1.5    Uniform and nonuniform Oscillator, one-dimensional flow on circle

§1.6    Numerical Computation

Chapter 2  One-Dimensional Maps

§2.1    Introduction

§2.2    Logistic Map: Numerics

§2.3    Logistic Map: Analysis

§2.4    Periodic Windows

Chapter 3  Linear Algebra with Applications in Biology

§3.1    Basic operations of vectors

§3.2    Matrix notation and matrix multiplication

§3.3    Gaussian elimination

§3.4    Linear independence, basis and dimension

§3.5    Subspace and four fundamental subspaces

§3.6    Least square and curve fitting

§3.7    Properties of determinant

§3.8    Eigenvalues and eigenvectors

§3.9    Two dimensional linear flow

§3.10    Two dimensional phase portraits, Fixed points and linearization

§3.11    Predator-Prey models

§3.12    Competition models, Mutualism or Symbiosis

§3.13    Mathematical Model for Neuron Activity

§3.14    A Mathematical Model for Enzymatic Reactions

Chapter 4  Introduction to population genetics

§4.1    Hardy-Weinberg Law

§4.2    Selection

§4.3    Fundamental Theorem of Natural Selection