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Second Year Calculus From Celestial Mechanics to Special Relativity

Aus der Reihe Readings in Mathematics

56,99 €

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Beschreibung

This textbook covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The exercises and observations of mathematical symmetry studied in the text enable the student to better understand the interaction of physics and mathematics....

Beschreibung

This textbook covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The exercises and observations of mathematical symmetry studied in the text enable the student to better understand the interaction of physics and mathematics.

Produktdetails

Einband

Taschenbuch
Erscheinungsdatum

08.08.1991
Abbildungen

404 p.
Verlag Springer Us

Produktdetails

Einband

Taschenbuch
Erscheinungsdatum

08.08.1991
Abbildungen

404 p.
Verlag Springer Us
Seitenzahl

404
Maße (L/B/H)

23,5/15,5/2,2 cm
Gewicht

610 g
Auflage

1991
Sprache

Englisch
ISBN

978-0-387-97606-8
Herstelleradresse

Springer-Verlag GmbH
Europaplatz 3
69115 Heidelberg
DE

Email: ProductSafety@springernature.com

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  • Produktbild: Second Year Calculus
  • Produktbild: Second Year Calculus
  • 1 F=ma.- 1.1 Prelude to Newton’s Principia.- 1.2 Equal Area in Equal Time.- 1.3 The Law of Gravity.- 1.4 Exercises.- 1.5 Reprise with Calculus.- 1.6 Exercises.- 2 Vector Algebra.- 2.1 Basic Notions.- 2.2 The Dot Product.- 2.3 The Cross Product.- 2.4 Using Vector Algebra.- 2.5 Exercises.- 3 Celestial Mechanics.- 3.1 The Calculus of Curves.- 3.2 Exercises.- 3.3 Orbital Mechanics.- 3.4 Exercises.- 4 Differential Forms.- 4.1 Some History.- 4.2 Differential 1-Forms.- 4.3 Exercises.- 4.4 Constant Differential 2-Forms.- 4.5 Exercises.- 4.6 Constant Differential k-Forms.- 4.7 Prospects.- 4.8 Exercises.- 5 Line Integrals, Multiple Integrals.- 5.1 The Riemann Integral.- 5.2 Line Integrals.- 5.3 Exercises.- 5.4 Multiple Integrals.- 5.5 Using Multiple Integrals.- 5.6 Exercises.- 6 Linear Transformations.- 6.1 Basic Notions.- 6.2 Determinants.- 6.3 History and Comments.- 6.4 Exercises.- 6.5 Invertibility.- 6.6 Exercises.- 7 Differential Calculus.- 7.1 Limits.- 7.2 Exercises.- 7.3 Directional Derivatives.- 7.4 The Derivative.- 7.5 Exercises.- 7.6 The Chain Rule.- 7.7 Using the Gradient.- 7.8 Exercises.- 8 Integration by Pullback.- 8.1 Change of Variables.- 8.2 Interlude with Lagrange.- 8.3 Exercises.- 8.4 The Surface Integral.- 8.5 Heat Flow.- 8.6 Exercises.- 9 Techniques of Differential Calculus.- 9.1 Implicit Differentiation.- 9.2 Invertibility.- 9.3 Exercises.- 9.4 Locating Extrema.- 9.5 Taylor’s Formula in Several Variables.- 9.6 Exercises.- 9.7 Lagrange Multipliers.- 9.8 Exercises.- 10 The Fundamental Theorem of Calculus.- 10.1 Overview.- 10.2 Independence of Path.- 10.3 Exercises.- 10.4 The Divergence Theorems.- 10.5 Exercises.- 10.6 Stokes’ Theorem.- 10.7 Summary for R3.- 10.8 Exercises.- 10.9 Potential Theory.- 11 E = mc2.- 11.1 Prelude to Maxwell’s Dynamical Theory.-11.2 Flow in Space-Time.- 11.3 Electromagnetic Potential.- 11.4 Exercises.- 11.5 Special Relativity.- 11.6 Exercises.- Appendices.- A An Opportunity Missed 361.- B Bibliography 365.- C Clues and Solutions 367.- Index 382.