Calculus, Vol I, 2ed (An Indian Adaptation)
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Calculus, Second Edition, strikes a perfect balance between theory and technique. Although it differs from the majority of contemporary texts, treating integration before differentiation is the most accurate historical representation of the relationship between the integral and the derivative. This introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept. ·Historical Introduction ·Basic Concepts of Set Theory ·Axioms for the Real-Number System ·Mathematical Induction, Summation Notation, and Related Topics ·Integral Calculus ·Applications of Integration ·Continuous Functions ·Differential Calculus ·Relation Between Integration and Differentiation ·The Logarithm, the Exponential, and the Inverse Trigonometric Functions ·Polynomial Approximations to Functions ·Differential Equations ·Complex Numbers ·Sequences, Infinite Series, Improper Integrals ·Sequences and Series of Functions ·Vector Algebra ·Applications of Vector Algebra to Analytic Geometry ·Calculus of Vector-Valued Functions ·Linear Spaces ·Linear Transformations and Matrices