Top Phonics Readers (4) To the Shop! with Audio APP (1版)

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【簡介】 Description Top Phonics Readers is a 5-book series developed for young learners who are already familiar with the English alphabet. Top Phonics Readers can be used as a stand-alone reading series, or as a supplement to Seed Learning’s Top Phonics textbook series. In these books, students practise and gain experience in recognizing and saying short vowel sounds, long vowel sounds, double-letter consonant sounds, and double-letter vowel sounds. The 20 leveled readers of the series provide invaluable phonics practice through fun and engaging stories designed especially for the emerging reader. The themes of the stories have been chosen to appeal to young learners. Features 4 stories per book – a total of 20 stories Contextual practice of words commonly studied in phonics series The ideal accompaniment to Top Phonics Strategic introduction of sight words to increase reading fluency Glossary of target words at the back of each book 【目錄】

Introduction to the Calculus of Variations (4版)

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【簡介】 The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology. This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions. This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels. 【目錄】