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This book is intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed. Each chapter starts with a concise summary of the main results that should be kept in mind and used for the exercises in that chapter, which is then followed by a selection of solved problems. A selection of exercises without solutions rounds out each chapter. The primary focus is on functions of one real variable, but some differential calculus of functions of two or more variables is also included. As for basic ordinary differential equations, separation of variables, linear first order and constant coefficients ODEs are discussed.