This book aims to help learners of English first to identify and then to say the sounds of the language correctly. The author stresses the importance of intensive listening, to enable the student to recognize similarities and differences between sounds, and to place a sound in its particular group. Practice drills for the student cover the repetition of minimal pairs and using the problem sounds in words and sentences, both in isolation and contrast.
Urdu: An Essential Grammar is a reference guide to the most important aspects of the language as it is used by native speakers today. The complexities of Urdu are set out in short, readable sections. Explanations contain minimal jargon and emphasis has been placed on the aspects of Urdu that pose a particular challenge for English-speaking students.
These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research.
