Differential Calculus: Early Trascendentals - Tapa blanda

Our purpose in this edition of Differential Calculus Early Transcendental is to help the arriving students to the university to face up with exit the topics of calculus. To accomplish this goal, the precalculus material that appeared in the appendixes of the previous edition, was enlarged and presented in the three first chapters of this edition. The third chapter is entirely dedicated to the conics, which are developed thoroughly. The three new chapters were written following the same scheme we use in our texts, balancing the theory and the practice. The theory is illustrated by many examples. A part of each section is dedicated to present, with all the details, solved problems. Most of the theorems are presented with his corresponding proofs. When the proof is complicated, this is presented as a solved problem. CONTENT: Chapter 1. PRELIMINARIES PYTHAGORAS OF SAMOS A short introduction to Logic and Set Theory The Real Number System. Field Axioms Radicals and Rational Exponents Some Topics of Algebra Polinomial Equations Order Axioms for Real Numbers Inequations Absolute Value Chapter 2. THE CARTESIAN PLANE AND THE LINE RENÉ DESCARTES The Cartesian Plane Graphs of Equations of two Variables Symmetry and Translation Criterios The line and the First Degree Equation Chapter 3. THE CONIC APOLONIO OF PERGA Introduction The Parabola The Ellipse La Hipérbola The General Second Degree Equation Rotation of Axes Chapter 4. REAL FUNCTIONS ARCHIMEDES Real Functions and their Graph Trigonometric Functions New functions from old functions Inverse Functions Inverse Trigonometric Functions Exponential Functions Logarithmic Functions Applications of the Exponential and Logarithmic Functions. A Brief history of the Bernoulli family Chapter 5. LIMITS AND CONTINUITY Leonhard Euler Limits, an Informal Introduction Limits, a Rigorous Treatment Trigonometric Limits Continuity Infinite Limits and Verticals Asymptotes Limits at Infinite and Horizontal Asymptotes The Number e as a limit Oblique Asymptotes Chapter 6. THE DERIVATIVE ISAAC NEWTON The Derivative Basic Techniques of Differentiation Derivatives of the Trigonometric Functions Derivatives of the Exponential and Logarithmic Functions The Chain Rule Chapter 7. MORE ON DERIVATIVES GOTTFRIED WILHELD LEIBNIZ Implicit Differentiation and the Derivative of an Inverse Function Logarithmic Differentiation Derivatives of Inverse Trigonometric Functions Higher-order Derivatives, Velocity and Acceleration Hyperbolic and Inverse Hyperbolic Functions Rate of Change Linear Approximations and Differentials Nicholas Bourbaki: The mysterious story of a brilliant Mathematician that never existed Chapter 8. APLICATIONS OF THE DERIVATIVE GUILLAUME F. A. M. DE L’HOSPITAL Maximum and Minimum Values The Mean Value Theorem Monotony, Concavity and Derivative test for extrema Indeterminate Forms. L’Hôspital´s Rule Using Derivatives to Sketch the Graph of a Function Optimization Problems Newton-Raphson Method

Jorge Alfonso Saenz Camacho, born on July 20, 1938, in Cajamarca, Peru, studied Mathematics at UNMSM(Universidad Nacional Mayor de San Marcos, Lima Peru), and at the University of Notre Dame (Indiana, USA), receiving his doctorate (Ph.D). Jorge Saenz although studied Mathematics Education at UNEEGV (Universidad Nacional de Educacion Enrique Guzman y Valle, La Cantuta, Peru) and at the Teachers College, University of Columbia(New York, USA). Jorge Saenz has been teaching and writing about mathematics for more than 30 years, working at universities in several countries, like Puerto Rico, Ecuador, Peru and Venezuela where he became a famous author.