LEADER 05373nam 2200697Ia 450 001 9910141248003321 005 20200520144314.0 010 $a9786613298744 010 $a9781283298742 010 $a1283298740 010 $a9781118033241 010 $a1118033248 010 $a9781118031483 010 $a1118031482 035 $a(MiAaPQ)EBC818699 035 $a(PPN)16971943X 035 $a(CKB)2670000000122557 035 $a(Perlego)2757816 035 $a(EXLCZ)992670000000122557 100 $a20111102d1988 uy 0 101 0 $aeng 135 $auran|---||a|| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential and integral calculus$hVolume II /$fby R. Courant ; translated by E. J. McShane 205 $aWiley classics library ed. 210 $a[New York] $cInterscience Publishers$d1988 215 $a1 recurso en línea (696 p.) 225 1 $aWiley classics library 300 $aTranslation of: Vorlesungen uber Differential- und Integralrechnung. 300 $aOriginally published: 2nd ed., 1937. 300 $aIncludes indexes. 311 1 $a9780471608400 311 1 $a0471608408 311 1 $a9780471178200 311 1 $a0471178209 327 $aDifferential and Integral Calculus; CONTENTS; Chapter I PRELIMINARY REMARKS ON ANALYTICAL GEOMETRY AND VECTOR ANALYSIS; 1. Rectangular Co-ordinates and Vectors; 2. The Area of a Triangle, the Volume of a Tetrahedron, the Vector Multiplication of Vectors; 3. Simple Theorems on Determinants of the Second and Third Order; 4. Affine Transformations and the Multiplication of Determinants; Chapter II FUNCTIONS OF SEVERAL VARIABLES AND THEIR DERIVATIVES; 1. The Concept of Function in the Case of Several Variables; 2. Continuity; 3. The Derivatives of a Function 327 $a4. The Total Diflerential of a Function and its Geometrical Meaning5. Functions of Functions (Compound Functions) and the Introduction of New Independent Variables; 6. The Mean Value Theorem and Taylor's Theorem for Functions of Several Variables; 7. The Application of Vector Methods; APPENDIX; 1. The Principle of the Point of Accumulation in Several Dimensions and its Applications; 2. The Concept of Limit for Functions of Several Variables; 3. Homogeneous Functions; Chapter III DEVELOPMENTS AND APPLICATIONS OF THE DIFFERENTIAL CALCULUS; 1. Implicit Functions 327 $a2. Curves and Surfaces in Implicit Form3. Systems of Functions, Transformations, and Mappings; 4. Applications; 5. Families of Curves, Families of Surfaces, and their Envelopes; 6. Maxima and Minima; APPENDIX; 1. Sufficient Conditions for Extreme Values; 2. Singular Points of Plane Curves; 3. Singular Points of Surfaces; 4. Connexion between Euler's and Lagrange's Representations of the Motion of a Fluid; 5. Tangential Representation of a Closed Curve; Chapter IV MULTIPLE INTEGRALS; 1. Ordinary Integrals as Functions of a Parameter 327 $a2. The Integral of a Continuous Function over a Region of the Plane or of Space3. Reduction of the Multiple Integral to Repeated Single Integrals; 4. Transformation of Multiple Integrals; 5. Improper Integrals; 6. Geometrical Applications; 7. Physical Applications; APPENDIX; 1. The Existence of the Multiple Integral; 2. General Formula for the Area (or Volume) of a Region bounded by Segments of Straight Lines or Plane Areas (Guldin's Formula). The Polar Planimeter; 3. Volumes and Areas in Space of any Number of Dimensions; 4. Improper Integrals as Functions of a Parameter 327 $a5. The Fourier Integral6. The Eulerian Integrals (Gamma Function); 7. Differentiation and Integration to Fractional Order. Abel's Integral Equation; 8. Note on the Definition of the Area of a Curved Surface; Chapter V INTEGRATION OVER REGIONS IN SEVERAL DIMENSIONS; 1. Line Integrals; 2. Connexion between Line Integrals and Double Integrals in the Plane. (The Integral Theorems of Gauss, Stokes, and Green); 3. Interpretation and Applications of the Integral Theorems for the Plane; 4. Surface Integrals; 5. Gauss's Theorem and Green's Theorem in Space; 6. Stokes's Theorem in Space 327 $a7. The Connexion between Differentiation and Integration for Several Variables 330 $aDifferential and Integral Calculus, Volume 2:"Unlike modern mathematicians who pursue their research apart from engineering or physical applications, Richard Courant was adverse to abstract theories and vague theorems. The topics covered in this set will provide the reader with a solid background to understanding the mathematics of heat conduction, electricity and magnetism, fluid dynamics and elasticity." -Amazon Review This book includes not only calculational techniques, but also an introduction to real analysis, good mathematical reasoning, and proof 410 0$aWiley classics library. 606 $aCalculus 606 $aDifferential calculus 606 $aCalculus, Integral 615 0$aCalculus. 615 0$aDifferential calculus. 615 0$aCalculus, Integral. 686 $aB0220$2Inspec 700 $aCourant$b Richard$f1888-1972.$0447721 701 $aMcShane$b E. J$g(Edward James),$f1904-$041778 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141248003321 996 $aDifferential and integral calculus$91910728 997 $aUNINA