sets incorporate the use of such leading software packages as MAPLE. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight-parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Special Functions, Partial Differential Equations, Complex Analysis, and Historical Notes.

Benefits:

...show moreBenefits:

- NEW! Throughout the text, students are invited to experiment with computations involving mathematical models and topics under discussion: for example, the effects of forcing terms and physical parameters on solution of wave and heat equations, and of filters on signal output.
- NEW! Expanded treatment of Fourier transforms, including windowing, filtering, and the N-point discrete Fourier transforms are included.
- NEW! Expanded treatment of special functions and orthogonal polynomials, with special attention to eigenfunction expansions and completeness of eigenfunctions leads to a discussion of the Haar wavelets.
- NEW! New material on partial differential equations, including nonhomogenous heat and wave equations, the method of characteristics, and a chapter on Dirichlet and Neumann problems are included.
- NEW! Expanded treatment of systems of linear and nonlinear ordinary differential equations and analysis of critical points and stability are included.
- NEW! Expanded problem sets, including the introduction of sequences of problems that make use of such software packages such as MAPLE. Some problems also call on students to use computer analysis to explore relationships between solutions of mathematical models and the phenomena they model - just as they will in their careers.
- NEW! More example problems are included throughout, particularly emphasizing computations based on the underlying theory.
- Mathematical models of many phenomena are pursued in depth, with the objective of analyzing factors that influence behavior as well as predicting future behavior.
- The computer plays a prominent role throughout the text. Computer graphics are used to display such concepts as direction field, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals.

Benefits:

- NEW! Throughout the text, students are invited to experiment with computations involving mathematical models and topics under discussion: for example, the effects of forcing terms and physical parameters on solution of wave and heat equations, and of filters on signal output.
- NEW! Expanded treatment of Fourier transforms, including windowing, filtering, and the N-point discrete Fourier transforms are included.
- NEW! Expanded treatment of special functions and orthogonal polynomials, with special attention to eigenfunction expansions and completeness of eigenfunctions leads to a discussion of the Haar wavelets.
- NEW! New material on partial differential equations, including nonhomogenous heat and wave equations, the method of characteristics, and a chapter on Dirichlet and Neumann problems are included.
- NEW! Expanded treatment of systems of linear and nonlinear ordinary differential equations and analysis of critical points and stability are included.
- NEW! Expanded problem sets, including the introduction of sequences of problems that make use of such software packages such as MAPLE. Some problems also call on students to use computer analysis to explore relationships between solutions of mathematical models and the phenomena they model - just as they will in their careers.
- NEW! More example problems are included throughout, particularly emphasizing computations based on the underlying theory.
- Mathematical models of many phenomena are pursued in depth, with the objective of analyzing factors that influence behavior as well as predicting future behavior.
- The computer plays a prominent role throughout the text. Computer graphics are used to display such concepts as direction field, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals.

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