All but the most straightforward proofs are worked out in detail before being presented formally in this book. Thus most of the ideas are expressed in two different ways: the first encourages and develops the intuition and the second gives a feeling for what constitutes a proof. In this way, intuition and rigour appear as partners rather than competitors. The informal discussions, the examples and the exercises may assume some familiarity with calculus, but the definitions, theorems and formal proofs are presented in the correct logical order and assume no prior knowledge of calculus. Thus some basic knowledge of calculus is blended into the presentation rather than being completely excluded.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Broschur/Paperback
Klebebindung
ISBN-13
978-981-02-4163-6 (9789810241636)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Univ Of Canterbury, New Zealand
Part 1 The Real Numbers: The Real Number System; Upper and Lower Bounds. Part 2 Sequences and Series: Algebraic Operations on Limits; Monotone Sequences; Infinite Series. Part 3 Continuous Functions: Functions, Limits and Continuity; The Intermediate Value Property for Continuous Functions; Uniform Continuity; Increasing Functions. Part 4 Differentiable Functions: Repeated Differentiation; Mean Value Theorems; Local Maxima and Minima; Taylor's Theorem. Part 5 Further Results on Infinite Series: Tests for Convergence; Series of Complex Terms; Power Series; Multiplication of Series. Part 6 Special Functions: The Exponential Function; The Logarithm; Trigonometric Functions; Inverse Trigonometric Functions. Part 7 The Riemann Integral: Integral Forms of the Mean Value Theorems; Integration Over Unbounded Intervals; Integration of Unbounded Functions. Part 8 The Number Pi.
