Prelude to analysis / Paul C. Rosenbloom, Seymour Schuster.
Series Prentice-Hall mathematics seriesEditor: Englewood Cliffs, N.J. : Prentice-Hall, 1966Descripción: xix, 473 p. ; 23 cmTema(s): MathematicsOtra clasificación: 00-01 (00A06 26-01)Chapter One Introduction, [1] 1.1 Nature of mathematics, [2.] 1.2 Mathematics in modem society, career opportunities, [8.] 1.3 Outline of the course, [11.] 1.4 Examples of deductive sciences, [25.] Chapter Two The Real Number Line, [36] 2.1 Descartes9 brainstorm, [37.] 22 The number line; integers, [37.] 23 Rationals on the number line, [39.] 2.4 Irrationals on the number line, [41.] 2.5 The number line postulate, [44.] 2.6 Order, [49.] 2.7 Change of coordinates, [51.] Chapter Three Algebraic Structures, [57] 3.1 Introduction, [58.] 3.2 Addition and multiplication, [58.] 3.3 Subtraction and division, [62.] 3.4 Postulates for the algebraic structure of [67.] 33 Field properties (second version), [75.] 3.6 Examples of fields, [81.] 3.7 Abelian groups, [92.] 3.8 (Optional) The affine line and its group, [99.] 3.9 Ordered fields, [105.] 3.10 Gaining algebraic experience, [110.] 3.11 Some points of logic and language, [113.] Chapter Four Coordinates in the Plane, [121] 4.1 Points and number pairs, [122.] 4.2 Some practical problems in graphing other coordinate systems, [126.] 43 Graph of y = x + a, [134.] 4.4 The graph of y = ax, [139.] 43 The graph of ax + by + c 0,146. Chapter Five Functions, [154] 5.1 Introduction, [155.] 52 Defining functions, [160.] 5.3 Defining functions (continued), [166.] 5.4 Properties, [171.] 5.5 Sequences, [175.] 5.6 Relations, [179.] 5.7 Inverse Junctions, [187.] Chapter Six Vectors, [192] 6.1 Translations and vectors, [193.] 6.2 Coordinate representation, [197.] 6.3 Composition of translations and sums of vectors, [199.] 6.4 Other basic operations with vectors, [204.] 6.5 Applications to geometry of the line, [217.] 6.6 Analytic and vector proofs in geometry, [221.] 6.7 Abstract vector spaces, [230.] 6.8 Work. The dot product, [234.] 6.9 Further applications of the dot product, [241.] Chapter Seven Numerical Solution of Equations, [246] 7.1 Exact solution of two-by-two equations, [247.] 7.2 Logical analysis of linear systems, [257.] 73 Systems of more than two linear equations, [264.] 7.4 Approximate solutions, [268.] 7.5 Interpretation by transformation, [273.] 7.6 Transformations of vectors. Linearity, [283.] 7.7 Algebra of matrices, [299.] 7.8 Approximating solutions by iteration, [306.] 79 Falling body. Iteration and error estimates for square roots, [321.] 7.10 General quadratic equations, [331.] 7.11 The Bernoulli iteration, [343.] Chapter Eight Estimation of Errors, [351] 8.1 Linear equations, [352.] 8.2 Matrix methods, [355.] 8.3 Quadratic equations, [361.] 8.4 Computation of roots. Newton's method, [365.] Chapter Nine Convergence, [371] 9.1 The limit concept, [372.] 9.2 The Cauchy criterion, [385.] 9.3 Monotonic sequences, [397.] 9.4 Least upper bound, [406.] 9.5 Limit theorems, [413.] Chapter Ten Mathematical Induction, [425] 10.1 The principle of induction, [426.] 10.2 A description of L+. Well-ordering, [440.] 10.3 Division in L [452.] Index, [467]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode |
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Instituto de Matemática, CONICET-UNS | 26 R813 (Browse shelf) | Available | A-8131 |
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| 26 R495-2 Matemáticas técnicas / | 26 R682 Convex analysis / | 26 R682 Convex analysis / | 26 R813 Prelude to analysis / | 26 R888 Real analysis / | 26 R888-2 Real analysis / | 26 R888-3 Real analysis / |
Chapter One --
Introduction, [1] --
1.1 Nature of mathematics, [2.] --
1.2 Mathematics in modem society, career opportunities, [8.] --
1.3 Outline of the course, [11.] --
1.4 Examples of deductive sciences, [25.] --
Chapter Two --
The Real Number Line, [36] --
2.1 Descartes9 brainstorm, [37.] --
22 The number line; integers, [37.] --
23 Rationals on the number line, [39.] --
2.4 Irrationals on the number line, [41.] --
2.5 The number line postulate, [44.] --
2.6 Order, [49.] --
2.7 Change of coordinates, [51.] --
Chapter Three --
Algebraic Structures, [57] --
3.1 Introduction, [58.] --
3.2 Addition and multiplication, [58.] --
3.3 Subtraction and division, [62.] --
3.4 Postulates for the algebraic structure of [67.] --
33 Field properties (second version), [75.] --
3.6 Examples of fields, [81.] --
3.7 Abelian groups, [92.] --
3.8 (Optional) The affine line and its group, [99.] --
3.9 Ordered fields, [105.] --
3.10 Gaining algebraic experience, [110.] --
3.11 Some points of logic and language, [113.] --
Chapter Four --
Coordinates in the Plane, [121] --
4.1 Points and number pairs, [122.] --
4.2 Some practical problems in graphing other coordinate systems, [126.] --
43 Graph of y = x + a, [134.] --
4.4 The graph of y = ax, [139.] --
43 The graph of ax + by + c 0,146. --
Chapter Five --
Functions, [154] --
5.1 Introduction, [155.] --
52 Defining functions, [160.] --
5.3 Defining functions (continued), [166.] --
5.4 Properties, [171.] --
5.5 Sequences, [175.] --
5.6 Relations, [179.] --
5.7 Inverse Junctions, [187.] --
Chapter Six --
Vectors, [192] --
6.1 Translations and vectors, [193.] --
6.2 Coordinate representation, [197.] --
6.3 Composition of translations and sums of vectors, [199.] --
6.4 Other basic operations with vectors, [204.] --
6.5 Applications to geometry of the line, [217.] --
6.6 Analytic and vector proofs in geometry, [221.] --
6.7 Abstract vector spaces, [230.] --
6.8 Work. The dot product, [234.] --
6.9 Further applications of the dot product, [241.] --
Chapter Seven --
Numerical Solution of Equations, [246] --
7.1 Exact solution of two-by-two equations, [247.] --
7.2 Logical analysis of linear systems, [257.] --
73 Systems of more than two linear equations, [264.] --
7.4 Approximate solutions, [268.] --
7.5 Interpretation by transformation, [273.] --
7.6 Transformations of vectors. Linearity, [283.] --
7.7 Algebra of matrices, [299.] --
7.8 Approximating solutions by iteration, [306.] --
79 Falling body. Iteration and error estimates for square roots, [321.] --
7.10 General quadratic equations, [331.] --
7.11 The Bernoulli iteration, [343.] --
Chapter Eight --
Estimation of Errors, [351] --
8.1 Linear equations, [352.] --
8.2 Matrix methods, [355.] --
8.3 Quadratic equations, [361.] --
8.4 Computation of roots. Newton's method, [365.] --
Chapter Nine --
Convergence, [371] --
9.1 The limit concept, [372.] --
9.2 The Cauchy criterion, [385.] --
9.3 Monotonic sequences, [397.] --
9.4 Least upper bound, [406.] --
9.5 Limit theorems, [413.] --
Chapter Ten Mathematical Induction, [425] --
10.1 The principle of induction, [426.] --
10.2 A description of L+. Well-ordering, [440.] --
10.3 Division in L [452.] --
Index, [467] --
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