# Mathematical Analysis Functions of One Variable / by Mariano Giaquinta, Giuseppe Modica.

For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics...

Full description

Saved in:
Main Authors: Giaquinta, Mariano (Author), Modica, Giuseppe (Author) eBook English Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2003. 1st ed. 2003. Springer eBook Collection. Click to view e-book Loaded electronically.Electronic access restricted to members of the Holy Cross Community.
• 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 Weierstrass’s 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 Taylor’s 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.