Name: Differential Equations: An Introduction to Modern Methods and Applications
Author: James R. Brannan, William E. Boyce
ISBN: 9781118531778

Chapter 1.1 - Mathematical Models And Solutions Chapter 1.2 - Qualitative Methods: Phase Lines And Direction Fields Chapter 1.3 - Definitions, Classification, And Terminology Chapter 2.1 - Separable Equations Chapter 2.2 - Linear Equations: Method Of Integrating Factors Chapter 2.3 - Modeling With First Order Equations Chapter 2.4 - Differences Between Linear And Nonlinear Equations Chapter 2.5 - Autonomous Equations And Population Dynamics Chapter 2.6 - Exact Equations And Integrating Factors Chapter 2.7 - Substitution Methods

Chapter 2.P1 - Harvesting A Renewable Resource Chapter 2.P2 - A Mathematical Model Of A Groundwater Contaminant Source Chapter 2.P3 - Monte Carlo Option Pricing: Pricing Financial Options By Flipping A Coin Chapter 3.1 - Systems Of Two Linear Algebraic Equations Chapter 3.2 - Systems Of Two First Order Linear Differential Equations Chapter 3.3 - Homogeneous Linear Systems With Constant Coefficients Chapter 3.4 - Complex Eigenvalues Chapter 3.5 - Repeated Eigenvalues Chapter 3.6 - A Brief Introduction To Nonlinear Systems Chapter 3.P1 - Estimating Rate Constants For An Open Two-compartment Model Chapter 3.P2 - A Blood–brain Pharmacokinetic Model Chapter 4.1 - Definitions And Examples Chapter 4.2 - Theory Of Second Order Linear Homogeneous Equations Chapter 4.3 - Linear Homogeneous Equations With Constant Coefficients Chapter 4.4 - Mechanical And Electrical Vibrations Chapter 4.5 - Nonhomogeneous Equations; Method Of Undetermined Coefficients Chapter 4.6 - Forced Vibrations, Frequency Response, And Resonance Chapter 4.7 - Variation Of Parameters Chapter 4.P1 - A Vibration Insulation Problem Chapter 4.P2 - Linearization Of A Nonlinear Mechanical System Chapter 4.P3 - A Spring-mass Event Problem Chapter 4.P4 - Euler–lagrange Equations Chapter 5.1 - Definition Of The Laplace Transform Chapter 5.2 - Properties Of The Laplace Transform Chapter 5.3 - The Inverse Laplace Transform Chapter 5.4 - Solving Differential Equations With Laplace Transforms Chapter 5.5 - Discontinuous Functions And Periodic Functions Chapter 5.6 - Differential Equations With Discontinuous Forcing Functions Chapter 5.7 - Impulse Functions Chapter 5.8 - Convolution Integrals And Their Applications Chapter 5.9 - Linear Systems And Feedback Control Chapter 5.P1 - An Electric Circuit Problem Chapter 5.P2 - The Watt Governor, Feedback Control, And Stability Chapter 6.1 - Definitions And Examples Chapter 6.2 - Basic Theory Of First Order Linear Systems Chapter 6.3 - Homogeneous Linear Systems With Constant Coefficients Chapter 6.4 - Nondefective Matrices With Complex Eigenvalues Chapter 6.5 - Fundamental Matrices And The Exponential Of A Matrix Chapter 6.6 - Nonhomogeneous Linear Systems Chapter 6.7 - Defective Matrices Chapter 6.P1 - Earthquakes And Tall Buildings Chapter 6.P2 - Controlling A Spring-mass System To Equilibrium Chapter 7.1 - Autonomous Systems And Stability Chapter 7.2 - Almost Linear Systems Chapter 7.3 - Competing Species Chapter 7.4 - Predator–prey Equations Chapter 7.5 - Periodic Solutions And Limit Cycles Chapter 7.6 - Chaos And Strange Attractors: The Lorenz Equations Chapter 7.P1 - Modeling Of Epidemics Chapter 7.P2 - Harvesting In A Competitive Environment Chapter 7.P3 - The R ̈ossler System Chapter 8.1 - Numerical Approximations: Euler’s Method Chapter 8.2 - Accuracy Of Numerical Methods Chapter 8.3 - Improved Euler And Runge–kutta Methods Chapter 8.4 - Numerical Methods For Systems Of First Order Equations Chapter 8.P1 - Designing A Drip Dispenser For A Hydrology Experiment Chapter 8.P2 - Monte Carlo Option Pricing: Pricing Financial Options By Flipping A Coin Chapter A.1 - Matrices Chapter A.2 - Systems Of Linear Algebraic Equations, Linear Independence, And Rank Chapter A.3 - Determinants And Inverses Chapter A.4 - The Eigenvalue Problem

Book Details

The modern landscape of technology and industry demands an equally modern approach to differential equations in the classroom. Designed for a first course in differential equations, the third edition of Brannan/Boyce’s Differential Equations: An Introduction to Modern Methods and Applications is consistent with the way engineers and scientists use mathematics in their daily work. The text emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problem-solvers in today’s workplace. Section exercises throughout the text provide hands-on experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.