A Course in Ordinary Differential Equations, Second Edition teaches students how to use analytical and numerical solution methods in typical engineering, physics, and mathematics applications. Lauded for its extensive computer code and student-friendly approach, the first edition of this popular textbook was the first on ordinary differential equations (ODEs) to include instructions on using MATLAB®, Mathematica®, and Maple(TM). This second edition reflects the feedback of students and professors who used the first edition in the classroom. Thiis version adds two new chapters to the current text.…mehr
A Course in Ordinary Differential Equations, Second Edition teaches students how to use analytical and numerical solution methods in typical engineering, physics, and mathematics applications. Lauded for its extensive computer code and student-friendly approach, the first edition of this popular textbook was the first on ordinary differential equations (ODEs) to include instructions on using MATLAB®, Mathematica®, and Maple(TM). This second edition reflects the feedback of students and professors who used the first edition in the classroom. Thiis version adds two new chapters to the current text.
Stephen A. Wirkus is an associate professor of mathematics at Arizona State University, where he has been a recipient of the Professor of the Year Award and NSF AGEP Mentor of the Year Award. He has published over 30 papers and technical reports. He completed his Ph.D. at Cornell University under the direction of Richard Rand. Randall J. Swift is a professor of mathematics and statistics at California State Polytechnic University, Pomona, where he has been a recipient of the Ralph W. Ames Distinguished Research Award. He has authored more than 80 journal articles, three research monographs, and three textbooks. He completed his Ph.D. at the University of California, Riverside under the direction of M.M. Rao.
Inhaltsangabe
Traditional First-Order Differential Equations Introduction to First-Order Equations Separable Differential Equations Linear Equations Some Physical Models Arising as Separable Equations Exact Equations Special Integrating Factors and Substitution Methods Bernoulli Equation Homogeneous Equations of the Form g(y=x) Geometrical and Numerical Methods for First-Order Equations Direction Fields the Geometry of Differential Equations Existence and Uniqueness for First-Order Equations First-Order Autonomous Equations Geometrical Insight Graphing Factored Polynomials Bifurcations of Equilibria Modeling in Population Biology Nondimensionalization Numerical Approximation: Euler and Runge-Kutta Methods An Introduction to Autonomous Second-Order Equations Elements of Higher-Order Linear Equations Introduction to Higher-Order Equations Operator Notation Linear Independence and the Wronskian Reduction of Order the Case n = 2 Numerical Considerations for nth-Order Equations Essential Topics from Complex Variables Homogeneous Equations with Constant Coe cients Mechanical and Electrical Vibrations Techniques of Nonhomogeneous Higher-Order Linear Equations Nonhomogeneous Equations Method of Undetermined Coe cients via Superposition Method of Undetermined Coe cients via Annihilation Exponential Response and Complex Replacement Variation of Parameters Cauchy-Euler (Equidimensional) Equation Forced Vibrations Fundamentals of Systems of Differential Equations Useful Terminology Gaussian Elimination Vector Spaces and Subspaces The Nullspace and Column Space Eigenvalues and Eigenvectors A General Method, Part I: Solving Systems with Real and Distinct or Complex Eigenvalues A General Method, Part II: Solving Systems with Repeated Real Eigenvalues Matrix Exponentials Solving Linear Nonhomogeneous Systems of Equations Geometric Approaches and Applications of Systems of Differential Equations An Introduction to the Phase Plane Nonlinear Equations and Phase Plane Analysis Systems of More Than Two Equations Bifurcations Epidemiological Models Models in Ecology Laplace Transforms Introduction Fundamentals of the Laplace Transform The Inverse Laplace Transform Laplace Transform Solution of Linear Differential Equations Translated Functions, Delta Function, and Periodic Functions The s-Domain and Poles Solving Linear Systems Using Laplace Transforms The Convolution Series Methods Power Series Representations of Functions The Power Series Method Ordinary and Singular Points The Method of Frobenius Bessel Functions Boundary-Value Problems and Fourier Series Two-Point Boundary-Value Problems Orthogonal Functions and Fourier Series Even, Odd, and Discontinuous Functions Simple Eigenvalue-Eigenfunction Problems Sturm-Liouville Theory Generalized Fourier Series Partial Differential Equations Separable Linear Partial Differential Equations Heat Equation Wave Equation Laplace Equation Non-Homogeneous Boundary Conditions Non-Cartesian Coordinate Systems A An Introduction to MATLAB, Maple, and Mathematica MATLAB Some Helpful MATLAB Commands Programming with a script and a function in MATLAB Maple Some Helpful Maple Commands Programming in Maple Mathematica Some Helpful Mathematica Commands Programming in Mathematica B Selected Topics from Linear Algebra A Primer on Matrix Algebra Matrix Inverses, Cramer's Rule Calculating the Inverse of a Matrix Cramer's Rule Linear Transformations Coordinates and Change of Basis Similarity Transformations Computer Labs: MATLAB, Maple, Mathematica Answers to Odd Problems
Traditional First-Order Differential Equations Introduction to First-Order Equations Separable Differential Equations Linear Equations Some Physical Models Arising as Separable Equations Exact Equations Special Integrating Factors and Substitution Methods Bernoulli Equation Homogeneous Equations of the Form g(y=x) Geometrical and Numerical Methods for First-Order Equations Direction Fields the Geometry of Differential Equations Existence and Uniqueness for First-Order Equations First-Order Autonomous Equations Geometrical Insight Graphing Factored Polynomials Bifurcations of Equilibria Modeling in Population Biology Nondimensionalization Numerical Approximation: Euler and Runge-Kutta Methods An Introduction to Autonomous Second-Order Equations Elements of Higher-Order Linear Equations Introduction to Higher-Order Equations Operator Notation Linear Independence and the Wronskian Reduction of Order the Case n = 2 Numerical Considerations for nth-Order Equations Essential Topics from Complex Variables Homogeneous Equations with Constant Coe cients Mechanical and Electrical Vibrations Techniques of Nonhomogeneous Higher-Order Linear Equations Nonhomogeneous Equations Method of Undetermined Coe cients via Superposition Method of Undetermined Coe cients via Annihilation Exponential Response and Complex Replacement Variation of Parameters Cauchy-Euler (Equidimensional) Equation Forced Vibrations Fundamentals of Systems of Differential Equations Useful Terminology Gaussian Elimination Vector Spaces and Subspaces The Nullspace and Column Space Eigenvalues and Eigenvectors A General Method, Part I: Solving Systems with Real and Distinct or Complex Eigenvalues A General Method, Part II: Solving Systems with Repeated Real Eigenvalues Matrix Exponentials Solving Linear Nonhomogeneous Systems of Equations Geometric Approaches and Applications of Systems of Differential Equations An Introduction to the Phase Plane Nonlinear Equations and Phase Plane Analysis Systems of More Than Two Equations Bifurcations Epidemiological Models Models in Ecology Laplace Transforms Introduction Fundamentals of the Laplace Transform The Inverse Laplace Transform Laplace Transform Solution of Linear Differential Equations Translated Functions, Delta Function, and Periodic Functions The s-Domain and Poles Solving Linear Systems Using Laplace Transforms The Convolution Series Methods Power Series Representations of Functions The Power Series Method Ordinary and Singular Points The Method of Frobenius Bessel Functions Boundary-Value Problems and Fourier Series Two-Point Boundary-Value Problems Orthogonal Functions and Fourier Series Even, Odd, and Discontinuous Functions Simple Eigenvalue-Eigenfunction Problems Sturm-Liouville Theory Generalized Fourier Series Partial Differential Equations Separable Linear Partial Differential Equations Heat Equation Wave Equation Laplace Equation Non-Homogeneous Boundary Conditions Non-Cartesian Coordinate Systems A An Introduction to MATLAB, Maple, and Mathematica MATLAB Some Helpful MATLAB Commands Programming with a script and a function in MATLAB Maple Some Helpful Maple Commands Programming in Maple Mathematica Some Helpful Mathematica Commands Programming in Mathematica B Selected Topics from Linear Algebra A Primer on Matrix Algebra Matrix Inverses, Cramer's Rule Calculating the Inverse of a Matrix Cramer's Rule Linear Transformations Coordinates and Change of Basis Similarity Transformations Computer Labs: MATLAB, Maple, Mathematica Answers to Odd Problems
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