Modelling with Ordinary Differential Equations

Abstract

Introduction: Mathematical Modelling. Boundary Value Problems. Direction Fields. Finding Zeros. Exercises. First Order Differential Equations: Population Growth: The Malthus Model. Least Squares Method of Curve Fitting. Population Growth: The Logistic Model. Harvesting. Optimization of Profit. Epidemics. Potato Blight. Free Fall with Air Resistance. Power. Rockets. Exercises. Projects. Mathematical Background. Numerical Methods: Existence Theorem. Euler Algorithm. Error Analysis. Runge-Kutta Algorithm. Fruitflies. Exercises. Projects. Mathematical Background. Laplace Transforms: Linear Transforms. Properties of Laplace Transforms. Solving Differential Equations with Laplace Transforms. Table of Laplace Transforms. Exercises. Projects. Mathematical Background. Simultaneous Linear First Order Differential Equations: Projectile Trajectories with Air Resistance. Romantic Relationships. Neutron Flow. Electrical Networks. Marriage. Residential Segregation. Exercises. Projects. Mathematical Background. Second Order Linear Differential Equations: Mechanical Vibrations. Electrical Networks. The Ignition System of an Automobile. Simultaneous Equations. Exercises. Projects. Mathematical Background. Non-Linear Second Order Differential Equations: The Pendulum without Damping. The Pendulum with Damping. Population of Interacting Species. Exercises. Mathematical Background. Table of Integrals. Answers. References. Index.