Ebook: Introduction to Calculus and Analysis I

From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)

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From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)

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From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)
Content:
Front Matter....Pages N1-xxiii
Introduction....Pages 1-118
The Fundamental Ideas of the Integral and Differential Calculus....Pages 119-200
The Techniques of Calculus....Pages 201-323
Applications in Physics and Geometry....Pages 324-439
Taylor’s Expansion....Pages 440-480
Numerical Methods....Pages 481-509
Infinite Sums and Products....Pages 510-570
Trigonometric Series....Pages 571-632
Differential Equations for the Simplest Types of Vibration....Pages 633-649
Back Matter....Pages 650-661

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From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)
Content:
Front Matter....Pages N1-xxiii
Introduction....Pages 1-118
The Fundamental Ideas of the Integral and Differential Calculus....Pages 119-200
The Techniques of Calculus....Pages 201-323
Applications in Physics and Geometry....Pages 324-439
Taylor’s Expansion....Pages 440-480
Numerical Methods....Pages 481-509
Infinite Sums and Products....Pages 510-570
Trigonometric Series....Pages 571-632
Differential Equations for the Simplest Types of Vibration....Pages 633-649
Back Matter....Pages 650-661
....