《Advanced Engineering Mathematics》(第七版)是一本全面介绍工程数学核心概念和技术的经典教材，适用于高年级本科生和研究生。书中涵盖了线性代数、常微分方程、偏微分方程等主题，并提供了丰富的实例与习题，帮助读者深入理解并掌握理论知识及其实际应用。
This seventh edition of Advanced Engineering Mathematics differs from the sixth in four key aspects. Firstly, based on reviews and user feedback, new content has been included:
- Orthogonal projections and least squares approximations for vectors and functions provide a unifying theme by recognizing partial sums of eigenfunction expansions as projections onto subspaces, along with understanding lines of best fit to data points.
- Introduction to orthogonalization processes and the generation of orthogonal bases.
- LU factorization techniques for matrices.
- Linear transformations and their matrix representations.
- Application of Laplace transforms in solving Bessels equation and addressing problems related to wave motion and diffusion.
- Expanded coverage on properties and applications of Legendre polynomials and Bessel functions, including solutions to Kepler’s problem and a model depicting alternating current flow.
- Heavisides formula for calculating inverse Laplace transforms.
- A complex integral formula for the inverse Laplace transform, applied in studying heat diffusion within a slab.
- Vector operations conducted in orthogonal curvilinear coordinates.
- Utilization of vector integral theorems to develop Maxwell’s equations.
- Application of the convolution property of the Laplace transform to solve replacement scheduling problems.
5星
