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Creative Mathematics /
"Professor H.S. Wall wrote Creative Mathematics with the intention of leading students to develop their mathematical abilities, helping them learn the art of mathematics, and teaching them to create mathematical ideas. Creative Mathematics, according to Wall, "is not a compendium of mathem...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
|
| Colección: | Classroom resource materials.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover
- copyright page
- title page
- Foreword
- Preface
- Contents
- Short Biography of H.S. Wall
- 1 Numbers
- Sample Proofs
- 2 Ordered Number Pairs
- The Simple Graph L
- Problems
- The Logarithm
- Properties of L
- The Simple Graph E
- Powers and Roots
- 3 Slope
- Straight Lines
- Computation Formulas for L
- Computation of e
- Slope of a Simple Graph
- The Simple Graph I
- 4 Combinations of Simple Graphs
- Addition
- Multiplication
- Bracket Multiplication
- The Derivative
- 5 Theorems about Simple GraphsThe Conjectured Computation Formula
- The Addition Formulas for L and E
- The Simple Graphs S and C
- A Point Set which is not a Simple Graph
- Inequalities
- 6 The Simple Graphs of Trigonometry
- Addition Formulas for A
- Computation Problem for A
- The Simple Graphs K, C, S, and B
- Extension of S and C to the Set of all Numbers
- Connection with Triangles
- Property S
- 7 The Integral
- Property S
- Properties of Integrals
- Evaluation of Integrals
- A Theorem on Transformation of Integrals
- 8 Computation Formulas Obtained by Means of the IntegralComputation Formulas For L, A
- Computation Formulas for E, S, C
- The Binomial Theorem
- Length of a Simple Graph
- Length of an Arc of a Circle
- Polar Equations
- Analogy Between S, C and S, C
- 9 Simple Graphs Made to Order
- The Equation f ' = g · f + h
- The Equation f + kf = g
- The Equation f + pf' + qf = g
- 10 More about Integrals
- g-Length of an Interval
- Integral of a Simple Graph with Respect to a Simple Graph
- Properties of Int^b_a f dg
- Bounded Variation
- Extended IntegralsNumber Sequences
- Two Questions
- 11 Simple Surfaces
- Gradient
- Combination of Simple Surfaces
- More Simple Graphs Determined by a Simple Surface
- g-Area of a Rectangular Interval
- Maxima and Minima
- Integral of a Simple Surface with Respect to a Simple Surface
- Iterated Integrals
- Case Where f is not Continuous
- Integral over a Point Set
- Area of a Simple Surface
- Path Integrals
- Vectors
- Assorted Theorems and Problems
- 12 Successive Approximations
- Existence of Certain Numbers Established by Successive ApproximationsLemmas Concerning Sequences
- Simple Graphs Determined by Successive Approximations
- The Equation f ' â?? f = â??H
- Ordered Pairs of Simple Graphs Determined by Successive Approximations
- Particular Examples
- (A) The Simple Graphs S and C
- (B) The Equation f ' = I^2 + f^2
- (C) The Equation u f + v f ' + wf = g
- 13 Linear Spaces of Simple Graphs
- Linear Transformations in the Plane
- Axioms for Linear Space
- The Inner Product Space M[a, b]