Applied Mathematics for Science and Engineering

Preface

This book, Applied Mathematics for Science and Engineering, is the culmination of many years of experience preparing upper-division students in engineering and the physical sciences for graduate-level work (and particularly for subjects such as advanced transport phenomena). We strive to acquire key competencies that can be utilized to solve important practical problems of the type found in advanced coursework as well as those that may arise in a student's research program. The course is intended for engineers and scientists in the science/technology/engineering/mathematics (STEM) fields, and this book is my effort to fit the presentation of the material to the dominant learning styles of such students, many of whom are visual and tactile learners.

In the fall of 2013, the Programme for International Student Assessment (PISA) released its key findings from the 2012 examinations administered to 15-year-old students around the globe. The performance of students from the United States ranked about 26th in mathematics, far below the levels seen in Shanghai, Singapore, Hong Kong, Korea, Japan, and other countries. In the Country Notes, PISA observed that “students in the United States have particular weaknesses in performing mathematic tasks with higher cognitive demands, such as taking real-world situations, translating them into mathematical terms, and interpreting mathematical aspects in real-world problems.” This result has occurred despite the fact that the United States ...