Ebook: Calculus of One Variable
Author: Keith E. Hirst BSc PhD (auth.)
- Tags: Real Functions
- Series: Springer Undergraduate Mathematics Series
- Year: 2006
- Publisher: Springer-Verlag London
- Edition: 1
- Language: English
- pdf
Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering;
algebraic techniques
functions and graphs
an informal discussion of limits
techniques of differentiation and integration
Maclaurin and Taylor expansions
geometrical applications
Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.
The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.
Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering;
algebraic techniques
functions and graphs
an informal discussion of limits
techniques of differentiation and integration
Maclaurin and Taylor expansions
geometrical applications
Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.
The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.
Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering;
algebraic techniques
functions and graphs
an informal discussion of limits
techniques of differentiation and integration
Maclaurin and Taylor expansions
geometrical applications
Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.
The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.
Content:
Front Matter....Pages i-xi
Functions and Graphs....Pages 1-45
Limits of Functions....Pages 47-77
Differentiation....Pages 79-92
Techniques of Differentiation....Pages 93-109
Applications of Differentiation....Pages 111-132
Maclaurin and Taylor Expansions....Pages 133-151
Integration....Pages 153-171
Integration by Parts....Pages 173-183
Integration by Substitution....Pages 185-199
Integration of Rational Functions....Pages 201-216
Geometrical Applications of Integration....Pages 217-239
Back Matter....Pages 241-267
Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering;
algebraic techniques
functions and graphs
an informal discussion of limits
techniques of differentiation and integration
Maclaurin and Taylor expansions
geometrical applications
Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.
The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.
Content:
Front Matter....Pages i-xi
Functions and Graphs....Pages 1-45
Limits of Functions....Pages 47-77
Differentiation....Pages 79-92
Techniques of Differentiation....Pages 93-109
Applications of Differentiation....Pages 111-132
Maclaurin and Taylor Expansions....Pages 133-151
Integration....Pages 153-171
Integration by Parts....Pages 173-183
Integration by Substitution....Pages 185-199
Integration of Rational Functions....Pages 201-216
Geometrical Applications of Integration....Pages 217-239
Back Matter....Pages 241-267
....