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Preface

The subject is for undergraduate materials scientists and engineers who wish to learn about the mathematics that is essential to their chosen field.

Materials science and engineering is a discipline that combines knowledge of chemistry, mechanics, and physics and then applies them to the study of materials and their properties. It is a challenging and diverse enterprise--obtaining expertise in a large set of diverse subjects--but a career devoted to diverse study and applications will be very rewarding and fulfilling.

Mathematics is the language that binds together disparate topics in physics, engineering, and chemistry. While it is possible to become an excellent materials scientist and engineer without some working knowledge of a large subset of mathematical topics, it is much easier to master this discipline with mathematics to guide you. Through mathematics, you will discover that some topics have similarities that are not obvious--and not taught to you as being similar. Such similarities and analogies will make learning much, much easier--and I think much more enjoyable.

MIT's Department of Materials Science and Engineering has determined that students benefit from a background and a working knowledge of many more mathematics topics that pertain specifically to MS&E than are taught in a one-semester subject in the mathematics department. It is reasonable to ask, ``Is this subject a substitute for a mathematics subject such as linear algebra or partial differential equations taught by a mathematics professor as part of the mathematics department?'' No, this is not a replacement for such a subject and I encourage you to take subjects in mathematics in the future. This subject is designed to be very broad in scope and therefore its depth in any one topic is limited.

I do believe very strongly that you will enjoy studying math more after taking this introduction and that the mathematical background you will receive this semester will make your materials science education richer and more rewarding.

I have designed this subject to help you learn as much essential mathematics as possible in a short time. To this end, this subject has several unusual aspects that you will need to know.