Calculus in a new key:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Swarthmore, Pa.
APL Pr.
1976
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 286 Seiten. |
| ISBN: | 0917326059 |
Staff View
MARC
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| 300 | |a 286 Seiten. | ||
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Record in the Search Index
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| adam_text | Contents CHAPTER 0. INTRODUCTION 0.1 Notation, 2 0.2 Expressions, Identities, and Proofs, 9 0.3 Function Definition, 10 0.4 Examples, 12 CHAPTER 1. THE DERIVATIVE 1.1 Differences and Sums, 13 1.2 Graph Sketching, 14 1.3 Difference-Quotients, 14 Rules for Difference-Quotients, 16 The Binomial Theorem, 19 1.4 Cline Functions, 20 The Definition of Cline Functions, 21 Rules for Cline Functions, 22 1.5 Derivatives, 23 The Definition of the Derivative, 24 Rules for Derivatives, 25 1.6 The Derivative as Rate of Change, 26 1.7 Integrals, 29 Rules for Integrals, 29 CHAPTER 2. THE MATRIX PRODUCT 2.1 The Definition of the Matrix Product, 32 2.2 A Markov Process, 34 2.3 Matrix Product Equations, 36 Triangular Matrices, 36 The Primary Dyadic Function ША, 39 2.4 Extended Domains of Monadic Functions, 40 Linear Functions, 42 The Determinant, 44 2.5 The Geometry of Vectors, 45 CHAPTER 3. POLYNOMIALS 3.1 Introduction, 48 Functions on Polynomials, 49 3.2 The Sum of Polynomials, 51 3.3 The Product of Polynomials, 51 3.4 The Composition of Polynomials, 54 3.5 Reciprocal Polynomials, 55 3.6 Other Expressions for Polynomials, 58 3.7 Fitting Polynomials, 60 CHAPTER 4. APPLICATIONS OF THE DERIVATIVE 4.1 Introduction, 62 4.2 Applications of the Derivative, 63 Critical Arguments, 63 Monotonie Functions, 64 Tangent Line Approximations, 66 A Rootfinder, 67 4.3 Functions of Bounded Variation, 70
4.4 4.5 Applications of the Second Derivative, 74 Flection and Concavity, 74 Quadratic Approximations, 77 Taylor Polynomials, 77 Taylor Coefficient Functions, 79 Rules for Taylor Coefficient Functions, 80 Pythagorean Functions, 82 CHAPTER 5. THE DEFINITE INTEGRAL 5.1 Riemann Sums, 84 , 5.2 Water Pressure, 87 ■ 5.3 Estimating Areas, 89 Signed Areas, 93 5.4 Definite Integrals, 95 The Definition of the Definite Integral, 96 Rules for Definite Integrals, .96 Fundamental Theorems of the Calculus, 98 The Definite Integral of the Function ω*Ν, 101 5.5 Approximations of Definite Integrals, 102 84 CHAPTER 6. ELEMENTARY TRANSCENDENTAL FUNCTIONS 107 6.1 Introduction, 107 Quotients and Products,. 107 6.2 Growth and Decay Functions, 113 Growth and Decay Functions: Another Approach, 117 Primary Growth and Decay Functions, 118 Electrical Circuits, 119 6.3 The Circular Functions, 121 The Addition Formula for COS, 125 The Addition Formula for SIN, 126 The Derivatives of the Circular Functions, 127 Primary Circular Functions, 130 Mechanical Vibrations, 130 6.4 Hyperbolic Functions, 132 6.5 Approximate Solutions of Differential Equations, 132 CHAPTER 7. INVERSE FUNCTIONS 136 7.1 Introduction, 136 7.2 The Inverse Function of *a, 141 The Primary Function ®ω, 143 Polynomial Approximations to the Function ®ω, 143 The Dyadic Power and Logarithm Functions, 144 7.3 Inverse Functions of a*N, 145 7.4 Inverse Circular Functions, 146 7.5 Inverse Hyperbolic Functions, 148 7.6 Inverse Linear Functions, 149 CHAPTER 8. DIFFERENTIATION AND INTEGRATION 8.1 Introduction, 151 8.2 A Derivative Function, 153
8.3 Some Integrals, 163 Rules for Integrals, 163 8.4 Integration by Parts, 164 8.5 Integration by Substitution, 166 8.6 Integration of Rational Functions, 168 EXERCISES 172 APPENDIX A 280 REFERENCES 282 151 INDEX 283
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| adam_txt |
Contents CHAPTER 0. INTRODUCTION 0.1 Notation, 2 0.2 Expressions, Identities, and Proofs, 9 0.3 Function Definition, 10 0.4 Examples, 12 CHAPTER 1. THE DERIVATIVE 1.1 Differences and Sums, 13 1.2 Graph Sketching, 14 1.3 Difference-Quotients, 14 Rules for Difference-Quotients, 16 The Binomial Theorem, 19 1.4 Cline Functions, 20 The Definition of Cline Functions, 21 Rules for Cline Functions, 22 1.5 Derivatives, 23 The Definition of the Derivative, 24 Rules for Derivatives, 25 1.6 The Derivative as Rate of Change, 26 1.7 Integrals, 29 Rules for Integrals, 29 CHAPTER 2. THE MATRIX PRODUCT 2.1 The'Definition of the Matrix Product, 32 2.2 A Markov Process, 34 2.3 Matrix Product Equations, 36 Triangular Matrices, 36 The Primary Dyadic Function ША, 39 2.4 Extended Domains of Monadic Functions, 40 Linear Functions, 42 The Determinant, 44 2.5 The Geometry of Vectors, 45 CHAPTER 3. POLYNOMIALS 3.1 Introduction, 48 Functions on Polynomials, 49 3.2 The Sum of Polynomials, 51 3.3 The Product of Polynomials, 51 3.4 The Composition of Polynomials, 54 3.5 Reciprocal Polynomials, 55 3.6 Other Expressions for Polynomials, 58 3.7 Fitting Polynomials, 60 CHAPTER 4. APPLICATIONS OF THE DERIVATIVE 4.1 Introduction, 62 4.2 Applications of the Derivative, 63 Critical Arguments, 63 Monotonie Functions, 64 Tangent Line Approximations, 66 A Rootfinder, 67 4.3 Functions of Bounded Variation, 70
4.4 4.5 Applications of the Second Derivative, 74 Flection and Concavity, 74 Quadratic Approximations, 77 Taylor Polynomials, 77 Taylor Coefficient Functions, 79 Rules for Taylor Coefficient Functions, 80 Pythagorean Functions, 82 CHAPTER 5. THE DEFINITE INTEGRAL 5.1 Riemann Sums, 84 , 5.2 Water Pressure, 87 ■ ' 5.3 Estimating Areas, 89 Signed Areas, 93 5.4 Definite Integrals, 95 The Definition of the Definite Integral, 96 Rules for Definite Integrals, .96 Fundamental Theorems of the Calculus, 98 The Definite Integral of the Function ω*Ν, 101 5.5 Approximations of Definite Integrals, 102 84 CHAPTER 6. ELEMENTARY TRANSCENDENTAL FUNCTIONS 107 6.1 Introduction, 107 Quotients and Products,. 107 6.2 Growth and Decay Functions, 113 Growth and Decay Functions: Another Approach, 117 Primary Growth and Decay Functions, 118 Electrical Circuits, 119 6.3 The Circular Functions, 121 The Addition Formula for COS, 125 The Addition Formula for SIN, 126 The Derivatives of the Circular Functions, 127 Primary Circular Functions, 130 Mechanical Vibrations, 130 6.4 Hyperbolic Functions, 132 6.5 Approximate Solutions of Differential Equations, 132 CHAPTER 7. INVERSE FUNCTIONS 136 7.1 Introduction, 136 7.2 The Inverse Function of *a, 141 The Primary Function ®ω, 143 Polynomial Approximations to the Function ®ω, 143 The Dyadic Power and Logarithm Functions, 144 7.3 Inverse Functions of a*N, 145 7.4 Inverse Circular Functions, 146 7.5 Inverse Hyperbolic Functions, 148 7.6 Inverse Linear Functions, 149 CHAPTER 8. DIFFERENTIATION AND INTEGRATION 8.1 Introduction, 151 8.2 A Derivative Function, 153
8.3 Some Integrals, 163 Rules for Integrals, 163 8.4 Integration by Parts, 164 8.5 Integration by Substitution, 166 8.6 Integration of Rational Functions, 168 EXERCISES 172 APPENDIX A 280 REFERENCES 282 151 INDEX 283 |
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| index_date | 2024-07-02T16:03:19Z |
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| isbn | 0917326059 |
| language | English |
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| spelling | Orth, D. L. Verfasser aut Calculus in a new key Swarthmore, Pa. APL Pr. 1976 286 Seiten. txt rdacontent n rdamedia nc rdacarrier APL (langage de programmation) ram Mathématiques - Informatique ram calcul inriac dérivation inriac dérivée inriac fonction intégrale inriac fonction inverse inriac fonction transcendante inriac intégrale définie inriac polynôme inriac produit matriciel inriac Calculus Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015084833&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orth, D. L. Calculus in a new key APL (langage de programmation) ram Mathématiques - Informatique ram calcul inriac dérivation inriac dérivée inriac fonction intégrale inriac fonction inverse inriac fonction transcendante inriac intégrale définie inriac polynôme inriac produit matriciel inriac Calculus Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Calculus in a new key |
| title_auth | Calculus in a new key |
| title_exact_search | Calculus in a new key |
| title_exact_search_txtP | Calculus in a new key |
| title_full | Calculus in a new key |
| title_fullStr | Calculus in a new key |
| title_full_unstemmed | Calculus in a new key |
| title_short | Calculus in a new key |
| title_sort | calculus in a new key |
| topic | APL (langage de programmation) ram Mathématiques - Informatique ram calcul inriac dérivation inriac dérivée inriac fonction intégrale inriac fonction inverse inriac fonction transcendante inriac intégrale définie inriac polynôme inriac produit matriciel inriac Calculus Analysis (DE-588)4001865-9 gnd |
| topic_facet | APL (langage de programmation) Mathématiques - Informatique calcul dérivation dérivée fonction intégrale fonction inverse fonction transcendante intégrale définie polynôme produit matriciel Calculus Analysis |
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