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. Language: English