Problems in Calculus of One Variable

The 'Classic Text Series' is the only of its kind selection of classic pieces of work that started off as bestseller and continues to be the bestseller even today. These classic texts have been designed so as to work as elementary textbooks which play a crucial role in building the concepts from scratch as in-depth knowledge of concepts is necessary for students preparing for various entrance exams.The present book on Problems in Calculus of One Variable covers the in-depth study of mathematical analysis based on many years of the author's experience. The author has presented this book with an aim to train the students in active approach to mathematical exercises, as is done at a seminar. The present book has been divided into eight chapters namely Introduction to Mathematical Analysis, Differentiation of Functions, Application of Differential Calculus to investigation of Functions, Indefinite Integrals, Basic Method of Integration, Basic Classes of Integrable Functions, The Definite Integrals, Applications of the Definite Integral and Improper Integrals. Each chapter in the book begins with a theoretical introduction of the topics containing the principal definitions, theorems and formulas followed by solved examples based on the topics discussed. The solved examples have been covered topic wise along with the explanation of concepts for immediate and effective understanding of the concepts. The standard computational exercises are supplemented by examples and problems explaining the theory, promoting its deeper understanding and stimulating precise mathematical thinking. Some counter-examples explaining the need for certain conditions in the formulation of basis theorems are also included in the book. At the end of each chapter, unsolved practice exercises have been provided to help aspirants revise the concepts discussed in the chapter. At the end of the book answers and solutions to the unsolved practice exercises have also been provided for better comprehension of the concepts.As the book contains relevant theoretical content along with ample number of solved as well as unsolved problems covering the varied aspects of mathematical analysis, it for sure will help the students master their concepts of Problems in Calculus of One Variable.