Textbook
Calculus, Volume 1, OneVariable Calculus with an Introduction to Linear Algebra , 2nd EditionJanuary 1991, ©1967

An introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiationthis is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the meanvalue 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.
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Historical Introduction.
Some Basic Concepts of the Theory of Sets.
A Set of Axioms for the Real Number System.
Mathematical Induction, Summation Notation, and Related Topics.
The Concepts of the Integral Calculus.
Some Applications of Differentiation.
Continuous Functions.
Differential Calculus.
The Relation between Integration and Differentiation.
The Logarithm, the Exponential, and the Inverse Trigonometric Functions.
Polynomial Approximations to Functions.
Introduction to 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 VectorValued Functions.
Linear Spaces.
Linear Transformations and Matrices.
Exercises.
Answers to Exercises.
Index.
Some Basic Concepts of the Theory of Sets.
A Set of Axioms for the Real Number System.
Mathematical Induction, Summation Notation, and Related Topics.
The Concepts of the Integral Calculus.
Some Applications of Differentiation.
Continuous Functions.
Differential Calculus.
The Relation between Integration and Differentiation.
The Logarithm, the Exponential, and the Inverse Trigonometric Functions.
Polynomial Approximations to Functions.
Introduction to 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 VectorValued Functions.
Linear Spaces.
Linear Transformations and Matrices.
Exercises.
Answers to Exercises.
Index.
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Purchase Options
Hardcover
Calculus, Volume 1, OneVariable Calculus with an Introduction to Linear Algebra , 2nd Edition
ISBN : 9780471000051
688 pages
January 1991, ©1967
$250.95 BUY
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