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Advanced LaTeX in Academia
(2021)

The derivation and understanding of Partial Differential Equations relies heavily on the fundamental knowledge of the first years of scientific education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills. Thus, it is a challenging topic for prospective engineers and scientists.
This volume provides a compact overview on the classical Partial Differential Equations of structural members in mechanics. It offers a formal way to uniformly describe these equations. All derivations follow a common approach: the three fundamental equations of continuum mechanics, i.e., the kinematics equation, the constitutive equation, and the equilibrium equation, are combined to construct the partial differential equations.

This book is the second edition of an introduction to modern computational mechanics based on the finite element method. It includes more details on the theory, more exercises, and more consistent notation; in addition, all pictures have been revised. Featuring more than 100 pages of new material, the new edition will help students succeed in mechanics courses by showing them how to apply the fundamental knowledge they gained in the first years of their engineering education to more advanced topics.
In order to deepen readers’ understanding of the equations and theories discussed, each chapter also includes supplementary problems. These problems start with fundamental knowledge questions on the theory presented in the respective chapter, followed by calculation problems. In total, over 80 such calculation problems are provided, along with brief solutions for each.
This book is especially designed to meet the needs of Australian students, reviewing the mathematics covered in their first two years at university. The 13-week course comprises three hours of lectures and two hours of tutorials per week.

This study aid on numerical optimization techniques is intended for university undergraduate and postgraduate mechanical engineering students. Optimization procedures are becoming more and more important for lightweight design, where weight reduction can, for example in the case of automotive or aerospace industry, lead to lower fuel consumption and a corresponding reduction in operational costs as well as beneficial effects on the environment. Based on the free computer algebra system Maxima, the authors present procedures for numerically solving problems in engineering mathematics as well as applications taken from traditional courses on the strength of materials. The mechanical theories focus on the typical one-dimensional structural elements, i.e., springs, bars, and Euler–Bernoulli beams, in order to reduce the complexity of the numerical framework and limit the resulting design to a low number of variables. The use of a computer algebra system and the incorporated functions, e.g., for derivatives or equation solving, allows a greater focus on the methodology of the optimization methods and not on standard procedures.
The book also provides numerous examples, including some that can be solved using a graphical approach to help readers gain a better understanding of the computer implementation.