Ebook: Computer-Supported Calculus
- Tags: Algorithms, Appl.Mathematics/Computational Methods of Engineering, Symbolic and Algebraic Manipulation
- Series: Texts and Monographs in Symbolic Computation
- Year: 2002
- Publisher: Springer-Verlag Wien
- Edition: 1
- Language: English
- pdf
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of one of the most important mathematical software systems, namely, MACSYMA. This will equip them with the mathematical competence they need for science and engi neering and the competitive workplace. The choice of MACSYMA is not essential for the didactic goal of the book. In fact, any of the other major mathematical software systems, e. g. , AXIOM, MATHEMATICA, MAPLE, DERIVE, or REDUCE, could have been taken for the examples and for acquiring the skill in using these systems for doing mathematics on computers. The symbolic and numerical calcu lations described in this book will be easily performed in any of these systems by slight modification of the syntax as soon as the student understands and masters the MACSYMA examples in this book. What is important, however, is that the student gets all the information necessary to design and execute the calculations in at least one concrete implementation language as this is done in this book and also that the use of the mathematical software system is completely integrated with the text. In these times of globalization, firms which are unable to hire adequately trained technology experts will not prosper. For corporations which depend heavily on sci ence and engineering, remaining competitive in the global economy will require hiring employees having had a traditionally rigorous mathematical education.
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of how to use modern symbolic mathematics software systems for solving problems in calculus. This will equip them with the mathematical competence they need for science and engineering and the competitive workplace. MACSYMA is used as the software in which the example programs and calculations are given. However, by the experience gained in this book, the student will also be able to use any of the other major mathematical software systems, like for example AXIOM, MATHEMATICA, MAPLE, DERIVE or REDUCE, for "doing calculus on computers”.
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of how to use modern symbolic mathematics software systems for solving problems in calculus. This will equip them with the mathematical competence they need for science and engineering and the competitive workplace. MACSYMA is used as the software in which the example programs and calculations are given. However, by the experience gained in this book, the student will also be able to use any of the other major mathematical software systems, like for example AXIOM, MATHEMATICA, MAPLE, DERIVE or REDUCE, for "doing calculus on computers”.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Functions....Pages 2-42
Elementary functions used in calculus....Pages 43-62
Limits and continuity....Pages 63-103
Front Matter....Pages 105-105
Differentiation....Pages 106-147
Differentiation rules....Pages 148-178
Extremum problems....Pages 179-223
Mean value theorem....Pages 224-278
Front Matter....Pages 279-279
Definite integrals....Pages 280-321
Fundamental theorem of calculus....Pages 322-343
Integration techniques....Pages 344-383
Applications of integrals....Pages 384-425
Front Matter....Pages 427-427
Sequences and series....Pages 428-459
Series expansions and approximations....Pages 460-499
Back Matter....Pages 501-612
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of how to use modern symbolic mathematics software systems for solving problems in calculus. This will equip them with the mathematical competence they need for science and engineering and the competitive workplace. MACSYMA is used as the software in which the example programs and calculations are given. However, by the experience gained in this book, the student will also be able to use any of the other major mathematical software systems, like for example AXIOM, MATHEMATICA, MAPLE, DERIVE or REDUCE, for "doing calculus on computers”.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Functions....Pages 2-42
Elementary functions used in calculus....Pages 43-62
Limits and continuity....Pages 63-103
Front Matter....Pages 105-105
Differentiation....Pages 106-147
Differentiation rules....Pages 148-178
Extremum problems....Pages 179-223
Mean value theorem....Pages 224-278
Front Matter....Pages 279-279
Definite integrals....Pages 280-321
Fundamental theorem of calculus....Pages 322-343
Integration techniques....Pages 344-383
Applications of integrals....Pages 384-425
Front Matter....Pages 427-427
Sequences and series....Pages 428-459
Series expansions and approximations....Pages 460-499
Back Matter....Pages 501-612
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