Lecture Notes on Mathematical Methods

Department of Aerospace and Mechanical Engineering University of Notre Dame, Indiana, USA, 2012. — 501 pages. These are lecture notes for AME 60611 Mathematical Methods I, the first of a pair of courses on applied mathematics taught in the Department of Aerospace and Mechanical Engineering of the University of Notre Dame. Most of the students in this course are beginning graduate students in engineering coming from a variety of backgrounds. The course objective is to survey topics in applied mathematics, including multidimensional calculus, ordinary differential equations, perturbation methods, vectors and tensors, linear analysis, linear algebra, and non-linear dynamic systems. In short, the course fully explores linear systems and considers effects of non-linearity, especially those types that can be treated analytically. The companion course, AME 60612, covers complex variables, integral transforms, and partial differential equations. These notes emphasize method and technique over rigor and completeness; the student should call on textbooks and other reference materials. It should also be remembered that practice is essential to learning; the student would do well to apply the techniques presented by working as many problems as possible. The notes, along with much information on the course, can be found at http://www.nd.edu/∼powers/ame.60611. At this stage, anyone is free to use the notes under the auspices of the Creative Commons license below. These notes have appeared in various forms over the past years. An especially general tightening of notation and language, improvement of figures, and addition of numerous small topics was implemented in 2011. Fall 2011 students were also especially diligent in identifying additional areas for improvement. We would be happy to hear further suggestions from you.