Introduction to calculus - Mapa, Felina G. (Metro Manila National Book Store, 1984)
Table of Contents: Preface -- Chapter 1. The Real Numbers: 1.1. The Real Numbers and their Numerals -- 1.2. Operations in R -- 1.3. Relations in R -- 1.4. The Real Number Line -- 1.5. The Two Dimensional Real Number Space -- Chapter 2. Functions, Limits, and Continuity: 2.1. Introduction -- 2.2. Relations and Functions -- 2.3. Graphs of Relations and Functions -- 2.4. Sketching the Graphs of Functions -- 2.5. Some Special Types of Functions --_ 2.6. An Arithmetic of Functions -- 2.7. Sequences -- 2.8. Limit of a Function -- 2.9. More on Limits of Functions -- 2.10. Continuity -- Chapter 3. Derivatives: 3.1. Introduction -- 3.2. The Direction of a Straight Line -- 3.3. The Equations of a Straight Line -- 3.4. The Direction of a Curve -- 3.5. The Derivative -- 3.6. More on Evaluating Derivatives -- 3.7. The Chain Rule -- 3.8. Implicit Differentiation -- 3.9. Derivatives of Higher Order -- 3.10. Some Important Theorems -- 3.11. Properties of Functions Deducible from their Derivatives -- Chapter 4. Applications of the Derivative: 4.1. Introduction -- 4.2. Applications of Maxima and Minima -- 4.3. The Derivative as Rate of Change -- 4.4. Derivatives in Problems on Related Rates -- 4.5. The Derivative in Approximations -- Chapter 5. Integration -- 5.1. Introduction -- 5.2. The Area Problem -- 5.3. The Area Theorem -- 5.4. The Antiderivative or Indefinite Integral -- 5.5. The Definite Integral -- 5.6. Application of the Definite Integral to Areas of Plane Figures -- 5.7. Other Applications of the Antiderivative and Models of the Area Problem -- 5.8. The Definite Integral as a Riemann Sum -- Chapter 6. Exponential, Logarithmic and Trigonometric Functions -- 6.1. Introduction -- 6.2. The Exponential -- 6.3. The Derivative of 2X -- 6.4. The Exponential for which f(x)=ex -- 6.5. Logarithms -- 6.6. Some Differential Equations -- 6.7. Trigonometric Functions -- 6.8. The Derivative of the Trigonometric Functions -- 6.9. Antiderivatives Involving Trigonometric Functions -- Answers to Odd-Numbered Exercises. Index.
Includes index.
Keywords: Calculus