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This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus such as the real numbers, differentiation and integration, mean value theorems, the exponential function are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for . Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the...

This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus such as the real numbers, differentiation and integration, mean value theorems, the exponential function are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for . Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the...

This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The author’s enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much...

Positive psychology is the scientific study of how human beings prosper and thrive. This is the first book in SLA dedicated to theories in positive psychology and their implications for language teaching, learning and communication. Chapters examine the characteristics of individuals, contexts and relationships that facilitate learning: positive emotional states such as love, enjoyment and flow, and character traits such as empathy, hardiness and perseverance. The contributors present several innovative teaching ideas to bring out these characteristics among learners. The collection thus...