Advanced Calculus : An Introduction to Modern Analysis

摘要: Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well students who need in their field of study,with introduction the theory and applications elementary analysis. The text presents, inan accessible form, a carefully maintained balance between abstract concepts applied results ofsignificance that serves bridge gap two- or three-cemester calculus sequence andsenior/graduate level courses appplications ordinary partial differentialequations, complex variables, numerical methods, measure integration theory.The book focuses on topological concepts, such compactness, connectedness, metric spaces,and topics from analysis including Fourier series, analysis, integration, generalizedfunctions, Laplace transforms. Applications genetics, spring systems,enzyme transfer, thorough classical vibrating string, heat andbrachistochrone problems illustrate this book's usefulness non-mathematics major. Extensiveproblem sets found throughout test student's understanding andhelp develop ability handle more mathematical ideas.Advanced Analysis is intended for junior- senior-levelundergraduate mathematics, biology, engineering, physics, other related disciplines.An excellent textbook one-year course calculus, methods employed thistext will increase students' maturity prepare them solidly senior/graduatelevel topics. wealth materials allows instructor select are ofspecial interest student. A three ll?lester required successfuluse book.