Differential and integral calculus . Volume 1 / / by R. Courant ; translated by E.J. McShane

• Autore: Courant Richard <1888-1972.>
• Pubblicazione: Hoboken, NJ, : Wiley, 1988
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (634 p.)
• Disciplina: 515
• Soggetto topico: Calculus; Differential calculus
• Altri autori: McShaneE. J <1904-> (Edward James)
• Note generali: Translation of: Vorlesungen uber Differential- und Integralrechnung.; Includes index.
• Nota di contenuto: Differential and Integral Calculus; CONTENTS; Introductory Remarks; Chapter I INTRODUCTION; 1. The Continuum of Numbers; 2. The Concept of Function; 3. More Detailed Study of the Elementary Functions; 4. Functions of an Integral Variable. Sequences of Numbers; 5. The Concept of the Limit of a Sequence; 6. Further Discussion of the Concept of Limit; 7. The Concept of Limit where the Variable is Continuous; 8. The Concept of Continuity; APPENDIX I; Preliminary Remarks; 1. The Principle of the Point of Accumulation and its Applications; 2. Theorems on Continuous Functions ; 3. Some Remarks on the Elementary FunctionsAPPENDIX II; 1. Polar Co-ordinates; 2. Remarks on Complex Numbers; Chapter II THE FUNDAMENTAL IDEAS OF THE INTEGRAL AND DIFFERENTIAL CALCULUS; 1. The Definite Integral; 2. Examples; 3. The Derivative; 4. The Indefinite Integral, the Primitive Function, and the Fundamental Theorems of the Differential and Integral Calculus; 5. Simple Methods of Graphical Integration; 6. Further Remarks on the Connexion between the Integral and the Derivative; 7. The Estimation of Integrals and the Mean Value Theorem of the Integral Calculus; APPENDIX ; 1. The Existence of the Definite Integral of a Continuous Function2. The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus; Chapter III DIFFERENTIATION AND INTEGRATION OF THE ELEMENTARY FUNCTIONS; 1. The Simplest Rules for Differentiation and their Applications; 2. The Corresponding Integral Formulae; 3. The Inverse Function and its Derivative; 4. Differentiation of a Function of a Function; 5. Maxima and Minima; 6. The Logarithm and the Exponential Function; 7. Some Applications of the Exponential Function ; 8. The Hyperbolic Functions9. The Order of Magnitude of Functions; APPENDIX; 1. Some Special Functions; 2. Remarks on the Differentiability of Functions; 3. Some Special Formulae; Chapter IV FURTHER DEVELOPMENT OF THE INTEGRAL CALCULUS; 1. Elementary Integrals; 2. The Method of Substitution; 3. Further Examples of the Substitution Method; 4. Integration by Parts; 5. Integration of Rational Functions; 6. Integration of Some Other Classes of Functions; 7. Remarks on Functions which are not Integrable in Terms of Elementary Functions; 8. Extension of the Concept of Integral. Improper Integrals ; APPENDIXThe Second Mean Value Theorem of the Integral Calculus; Chapter V APPLICATIONS; 1. Representation of Curves; 2. Applications to the Theory of Plane Curves; 3. Examples; 4. Some very Simple Problems in the Mechanics of a Particle; 6. Work; APPENDIX; 1. Properties of the Evolute; 2. Areas bounded by Closed Curves; Chapter VI TAYLOR'S THEOREM AND THE APPROXIMATE EXPRESSION OF FUNCTIONS BY POLYNOMIALS; 1. The Logarithm and the Inverse Tangent; 2. Taylor's Theorem; 3. Applications. Expansions of the Elementary Functions; 4. Geometrical Applications; APPENDIX ; 1. Example of a Function which cannot be expanded in a Taylor Series
• Sommario/riassunto: "This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this domain." -Amazon ReviewThis book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science and engineering, no matter whether he is a student of a university or technical college, a teacher, or an engineer. Courant leads the way straight to useful knowledge, and aims at making the subject easier to grasp, not only by giving proofs step by step
• Titolo autorizzato: Differential and integral calculus
• ISBN: 9786613298751; 9781283298759; 1283298759; 9781118033234; 111803323X; 9781118031490; 1118031490
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910139726403321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley classics library.