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"Edmund Landau is a great mathematician and a great expositor of whom the whole mathematical world may be justly proud. His writings perpetuate brilliantly the traditions of Gauss and Weierstrass. This latest book [is] in its crystalline beauty, an inspiration to students of all nations." /. F. Ritt, American Math. Monthly
". . . should be required reading for writers of text-books in the calculus ... it shows that rigorous proofs are simple proofs."
W. A. Wilson, Bulletin of the A. M. S.
Introduction: Residue Systems, The Decimal System, Finite and Infinite Sets. Chap. I. Limits. Chap. II. Logarithms, Powers and Roots. Chap. III. Functions and Continuity. Chap. IV. Limits jor n->t. Chap. V. Definition of the Derivative. Chap. VL General Theorems on the Formation of the Derivative. Chap. VII. Increase, Decrease, Maximum, Minimum. Chap. VIII. General Properties of a Continuous Function in a Closed Interval. Chap. IX. Rolle's Theorem and the Theorem of the Mean. Chap. X. Higher Order Derivatives^ Taylor's Theorem. Chap. XI. "0/0" and Similar Topics. Chap. XII. Infinite Series (including double series, rearrangement of series, etc.} Chap. XIII. Uniform Convergence (.series of functions'). Chap. XIV. Power Series. Chap. XV. The Exponential Series and the Binomial Series. Chap. XVI. The Trigonometric Functions. Chap. XVII. Functions of Two Variables; Partial Derivatives. Chap. XVIII. Inverse Functions; Implicit Functions. Chap. XIX. The Inverse Trigonometric Functions. Chap. XX. Some Algebraic Theorems (The Fundamental Theorem of Algebra, Decomposition of Rational Functions into Partial Fractions} . Chap. XXI. The Integral. Chap. XXII. Basic Formulas of the Integral Calculus. Chap. XXIII. The Integration of Rational Functions. Chap. XXIV. The Integration of Certain Non-Rational Functions. Chap. XXV. The Definite Integral. Chap. XXVI. Theorems on the Definite Integral (properties of the integral, second Mean-value Theorem, etc.) Chap. XXVII. The Integration of Infinite Series. Chap. XXVIIL The Improper Integral. CHap. XXIX. Improper Integral (Infinite Limits of Integration). Chap. XXX. The Gamma Function. Chap. XXXI. Fourier Series.
1951                     374 pages                      6x9