Essentials of calculus for business and economics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Harper & Row
1978
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 442, 37 S. graph. Darst. |
| ISBN: | 0060439475 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
PREFACE xi
1 REAL NUMBERS, GRAPHS, AND FUNCTIONS 1
1.1 Sets, Real Numbers, and Inequalities 1
1.2 The Number Plane and Graphs of Equations 14
1.3 Equations of a Line 26
1.4 Functions and Their Graphs 35
1.5 Operations on Functions, Types of Functions, and Applications 43
1.6 Demand and Supply Equations 50
viii CONTENTS
2 LIMITS AND CONTINUITY 57
2.1 The Limit of a Function 57
2.2 One Sided Limits 66
2.3 Infinite Limits 10
1A Limits at Infinity 19
2.5 Continuity of a Function at a Number 88
2.6 Theorems on Continuity and Continuity on an Interval 93
3 THE DERIVATIVE 205
3.1 The Tangent Line and the Derivative 205
3.2 Differentiability and Continuity 2 26
3.3 Some Theorems on Differentiation of Algebraic Functions 222
3.4 Marginal Cost, Elasticity of Cost, and Marginal Revenue 228
3.5 The Derivative as a Rate of Change 236
3.6 The Derivative of a Composite Function 240
3.7 Implicit Differentiation and Related Rates 244
4 APPLICATIONS OF THE DERIVATIVE 252
4.1 Maximum and Minimum Values of a Function 252
4.2 Applications Involving an Absolute Extremum on a Closed
Interval 259
4.3 Increasing and Decreasing Functions and the First derivative
Test 263
4.4 Derivatives of Higher Order and the Second derivative Test for
Relative Extrema 268
4.5 Additional Problems Involving Absolute Extrema 2 74
4.6 Concavity and Points of Inflection 282
4.7 Applications to Drawing a Sketch of the Graph of a Function 288
4.8 Marginal Analysis in Economics 292
4.9 Price Elasticity of Demand 296
4.10 Profit 202
4.11 Rolle s Theorem and the Mean Value Theorem (Optional) 209
5 THE DIFFERENTIAL AND ANTIDIFFERENTIATION 227
5.1 The Differential 22 7
5.2 Antidifferentiation 227
5.3 Differential Equations with Variables Separable 234
5.4 Applications of Antidifferentiation in Economics 239
CONTENTS ix
6 THE DEFINITE INTEGRAL 245
6.1 Area 245
6.2 The Definite Integral 256
6.3 The Fundamental Theorem of the Calculus 263
6.4 Area of a Region in a Plane 272
6.5 Consumers Surplus and Producers Surplus 278
7 LOGARITHMIC AND EXPONENTIAL FUNCTIONS 289
7.1 The Natural Logarithmic Function 289
7.2 Logarithmic Differentiation and Integrals Yielding the Natural
Logarithmic Function 300
7.3 The Exponential Function 303
7.4 Other Exponential and Logarithmic Functions 312
7.5 Laws of Growth and Decay 318
7.6 Interest: Simple, Compound, and Compounded Continuously 324
7.7 Annuities 333
8 TECHNIQUES OF INTEGRATION 343
8.1 Introduction 343
8.2 Integration by Parts 344
8.3 Integration of Rational Functions by Partial Fractions 349
8.4 Approximate Integration 359
8.5 Improper Integrals 369
9 DIFFERENTIAL CALCULUS OF FUNCTIONS OF SEVERAL
VARIABLES 377
9.1 R3, the Three Dimensional Number Space 377
9.2 Functions of More Than One Variable 387
9.3 Limits and Continuity of Functions of More Than One
Variable 398
S14 Partial Derivatives 407
9.5 Extrema of Functions of Two Variables 417
9.6 Some Applications of Partial Derivatives to Economics 427
9.7 Lagrange Multipliers 437
APPENDIX A l
Table 1 Powers and Roots A 3
Table 2 Common Logarithms A 4
x CONTENTS
Table 3 Natural Logarithms A 6
Table 4 Exponential Functions A 8
Table 5 Amount of $1 n Periods hence at Compound Interest at Rate / per
Period: (1 + /) A 15
Table 6 Present Value of $1 to Be Received n Periods hence at Compound
Interest at Rate / per Period: (1 + /) A 16
Table 7 Amount of an Annuity of $1 per Period, n Periods hence, at Rate
/ per Period: [(1 + /) 1]// A 17
Table 8 Present Value of an Annuity of $1 per Period for n Periods at
Interest Rate / per Period: [1 — (1 + ;)~n]/; A 18
ANSWERS TO ODD—NUMBERED EXERCISES A 19
INDEX A 33
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:45:51Z |
| institution | BVB |
| isbn | 0060439475 |
| language | English |
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| owner_facet | DE-706 DE-188 |
| physical | XIV, 442, 37 S. graph. Darst. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Harper & Row |
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| spelling | Leithold, Louis Verfasser aut Essentials of calculus for business and economics Louis Leithold New York Harper & Row 1978 XIV, 442, 37 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calcul infinitésimal Mathématiques financières Mathématiques économiques Business mathematics Calculus Economics, Mathematical Analysis (DE-588)4001865-9 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Analysis (DE-588)4001865-9 s Anwendung (DE-588)4196864-5 s DE-604 Infinitesimalrechnung (DE-588)4072798-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004070644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leithold, Louis Essentials of calculus for business and economics Calcul infinitésimal Mathématiques financières Mathématiques économiques Business mathematics Calculus Economics, Mathematical Analysis (DE-588)4001865-9 gnd Anwendung (DE-588)4196864-5 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4196864-5 (DE-588)4072798-1 |
| title | Essentials of calculus for business and economics |
| title_auth | Essentials of calculus for business and economics |
| title_exact_search | Essentials of calculus for business and economics |
| title_full | Essentials of calculus for business and economics Louis Leithold |
| title_fullStr | Essentials of calculus for business and economics Louis Leithold |
| title_full_unstemmed | Essentials of calculus for business and economics Louis Leithold |
| title_short | Essentials of calculus for business and economics |
| title_sort | essentials of calculus for business and economics |
| topic | Calcul infinitésimal Mathématiques financières Mathématiques économiques Business mathematics Calculus Economics, Mathematical Analysis (DE-588)4001865-9 gnd Anwendung (DE-588)4196864-5 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Calcul infinitésimal Mathématiques financières Mathématiques économiques Business mathematics Calculus Economics, Mathematical Analysis Anwendung Infinitesimalrechnung |
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