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Modern Calculus and Analystic Geometry by Richard A. Silverman



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Modern Calculus and Analystic Geometry by Richard A. Silverman , Harvard PH.D. in physics, author of numerous papers and books on mathematics as well as a renowned Russian science translator. This philosophy of this book can perhaps be summarized n the following two commandments "Motive all view ideas both mathematical and physical" and "Prove all theorems". Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student’s viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory — many of the answers are found at the end of the book; some of them worked out fully so that the entire process can be followed.

Modern Calculus and Analystic Geometry by Richard A. Silverman cover the following topics.

  • 1. Sets and Functions
    2. Number and Coordinates
    3. Graphs
    4. Limits
    5. Dervatives
    6. Well Behaved Functions
    7. Integrals
    8. Analystic Geometry in R2
    9. Curves and Vectors in R2
    10. Linear Algebra
    11. Analystic Geometry in R3
    12. Partial Differentiation
    13. Multiple Integration
    14. Further Computations
    15. Infinite Series

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