Author | Giaquinta, Mariano. author |
---|---|
Title | Mathematical Analysis [electronic resource] : Functions of One Variable / by Mariano Giaquinta, Giuseppe Modica |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0007-9 |
Descript | XIII, 353 p. online resource |
1. Numbers, Functions and their Graphs -- 1.1 Real Numbers: a Description -- 1.2 The Cartesian Plane -- 1.3 Elementary Functions -- 1.4 Remarks on Common Language and the Language of Mathematics -- 1.5 Exercises -- 2. Limits and Continuity -- 2.1 Limits -- 2.2. Continuous Functions -- 2.3. Continuous functions on an interval -- 2.4 Weierstrassโs Theorem -- 2.5 Summing Up -- 2.6 Exercises -- 3. The Fundamental Ideas of the Differential and Integral Calculus -- 3.1 Differential Calculus -- 3.2 Integral Calculus -- 3.3 The Fundamental Theorem of Calculus -- 3.4 Calculus: Some Historical Remarks -- 3.5 Summing Up -- 3.6 Exercises -- 4. The Calculus of Derivatives and of Integrals -- 4.1 Computation of Derivatives -- 4.2 Integrals and Primitives -- 4.3 A Definition of the Trigonometric, Logarithmic and Exponential Functions -- 4.4 Some Differential Equations -- 4.5 Generalized Integrals -- 4.6 Summing Up -- 4.7 Exercises -- 5. Further Developments in Calculus -- 5.1 Taylorโs Formula -- 5.2 The Calculus of Limits -- 5.3 Convex Functions -- 5.4 Some Inequalities -- 5.5 Graphing a Function -- 5.6 Summing Up -- 5.7 Exercises -- 6. Toward Differential Equations and Minimum Principles -- 6.1 Linear Ordinary Differential Equations -- 6.2 First Order ODEs -- 6.3 One-Dimensional Motions -- 6.4 Optimization Problems -- 6.5 Summing Up -- 6.6 Exercises -- A. Matematicians and Other Scientists -- B. Bibliographical Notes -- C. Index