Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations.

The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) that reinforce ideas and provide insight into more advanced problems. A Student Solutions Manual is also available.

It offers comprehensive coverage of frequently used integrals, functions and fundamental mathematical results. The contents are selected and organized to suit the needs of students, scientists, and engineers. It contains tables of Laplace and Fourier transform pairs. There is a new section on numerical approximation, and new section on the z-transform. There is easy reference system.

- Review of Prerequisites.
- Vectors and Vector Spaces.
- Matrices and Systems of Linear Equations.
- Eigenvalues, Eigenvectors and Diagonalization.
- First Order Differential Equations.
- Second and Higher Order Linear Differential Equations and Systems.
- The Laplace Transform.
- Series Solutions of Differential Equations, Special Functions and Sturm-Liouville Equations.
- Fourier Series.
- Fourier Integrals and the Fourier Transform.
- Vector Differential Calculus.
- Vector Integral Calculus.
- Analytic Functions.
- Complex Integration.
- Laurent Series, Residues and Contour Integration.
- The Laplace Inversion Integral.
- Conformal Mapping and Applications to Boundary Value Problems.
- Partial Differential Equations.
- Numerical Mathematics.

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