Differential Equations : An Introduction to Modern Methods and Applications (3 STU SOL)

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Differential Equations : An Introduction to Modern Methods and Applications (3 STU SOL)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 330 p.
  • 言語 ENG,ENG
  • 商品コード 9781118981252
  • DDC分類 515

Full Description


This is the Student Solutions Manual to accompany Differential EquationsAn Introduction to Modern Methods and Applications, 3rd Edition. Brannan/Boyce's Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition 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.

Contents

1 Introduction1.1 Mathematical Models and Solutions...11.2 Qualitative Methods: Phase Lines and Direction Fields...21.3 Definitions, Classification, and Terminology...82 First Order Differential Equations2.1 Separable Equations...112.2 Linear Equations: Method of Integrating Factors...162.3 Modeling with First Order Equations...232.4 Differences between Linear and Nonlinear Equations...302.5 Autonomous Equations and Population Dynamics...332.6 Exact Equations and Integrating Factors...362.7 Substitution Methods...423 Systems of Two First Order Equations3.1 Systems of Two Linear Algebraic Equations...493.2 Systems of Two First Order Linear Differential Equations...563.3 Homogeneous Linear Systems with Constant Coefficients...623.4 Complex Eigenvalues...793.5 Repeated Eigenvalues...873.6 A Brief Introduction to Nonlinear Systems...944 Second Order Linear Equations4.1 Definitions and Examples...1034.2 Theory of Second Order Linear Homogeneous Equations...1064.3 Linear Homogeneous Equations with Constant Coefficients...1084.4 Mechanical and Electrical Vibrations...1224.5 Nonhomogeneous Equations; Method of Undetermined Coefficients...1284.6 Forced Vibrations, Frequency Response, and Resonance...1344.7 Variation of Parameters...1395 The Laplace Transform5.1 Definition of the Laplace Transform...1495.2 Properties of the Laplace Transform...1545.3 The Inverse Laplace Transform...1595.4 Solving Differential Equations with Laplace Transforms...1635.5 Discontinuous Functions and Periodic Functions...1705.6 Differential Equations with Discontinuous Forcing Functions...1745.7 Impulse Functions...1855.8 Convolution Integrals and Their Applications...1935.9 Linear Systems and Feedback Control...2016 Systems of First Order Linear Equations6.1 Definitions and Examples...2056.2 Basic Theory of First Order Linear Systems...2096.3 Homogeneous Linear Systems with Constant Coefficients...2116.4 Nondefective Matrices with Complex Eigenvalues...2286.5 Fundamental Matrices and the Exponential of a Matrix...2406.6 Nonhomogeneous Linear Systems...2496.7 Defective Matrices...2557 Nonlinear Differential Equations and Stability7.1 Autonomous Systems and Stability...2637.2 Almost Linear Systems...2697.3 Competing Species...2837.4 Predator-Prey Equations...2937.5 Periodic Solutions and Limit Cycles...3027.6 Chaos and Strange Attractors: The Lorenz Equations...3108 Numerical Methods8.1 Numerical Approximations: Euler's Method...3158.2 Accuracy of Numerical Methods...3178.3 Improved Euler and Runge-Kutta Methods...3218.4 Numerical Methods for Systems of First Order Equations...3269 Series Solutions of Second Order Linear Equations9.1 Review of Power Series...3319.2 Series Solutions Near an Ordinary Point, Part I...3349.3 Series Solutions Near an Ordinary Point, Part II...3499.4 Regular Singular Points...3559.5 Series Solutions Near a Regular Singular Point, Part I...3619.6 Series Solutions Near a Regular Singular Point, Part II...3689.7 Bessel's Equation...37710 Orthogonal Functions, Fourier Series, and Boundary Value Problems10.1 Orthogonal Systems in the Space PC[a,b]...38310.2 Fourier Series...38510.3 Elementary Two-Point Boundary Value Problems...39410.4 General Sturm-Liouville Boundary Value Problems...39810.5 Generalized Fourier Series and Eigenfunction Expansions...40710.6 Singular Sturm-Liouville Boundary Value Problems...41510.7 Convergence Issues...41811 Elementary Partial Differential Equations11.1 Heat Conduction in a Rod: Homogeneous Case...43111.2 Heat Conduction in a Rod: Nonhomogeneous Case...44311.3 The Wave Equation: Vibrations of an Elastic String...45011.4 The Wave Equation: Vibrations of a Circular Membrane...45911.5 Laplace's Equation...459