Basic calculus /
Zenon R. Abao
- viii, 268 pages ; 26 cm.
Limits ? Lesson 1.1: Intuitive Concept: Limit of a Function Using a Table of Values ? Lesson 1.2 Definition of Limit Lesson 1.3: Theorems on Limit ? Lesson 1.4: One Sided Limits ? Lesson 1.5: Continuity of Function at a Number ? Lesson 1.6: Infinite Limits ? Lesson 1.7: Limits at Infinity ? Lesson 1.8: Types of Discontinuity ? The Derivatives ? Lesson 1.2: The Derivative ? Lesson 2.2: Theorems on Differentiation ? Lesson 2.3: Derivative of a Composite Function ?The Chain Rules ? Lesson 2.4: The Derivative of a Power Function with Rational Exponents ? Lesson 2.5: Implicit Differentiation ? Lesson 2.6: Differentiability and Continuity: One-Sided Derivatives ? Lesson 2.7: Applications of the Derivatives ? Lesson 2.7.1: The Tangent and Normal Lines ? Lesson 2.8: Tools for the Applications of Derivatives ? Lesson 2.9: Rolle?s Theorem and Decreasing Functions and Relative Extrema ? Lesson 2.10: Increasing and Decreasing Functions and Relative Etrema ? 2.11: Applications Using the Second Derivative ? 2.12: Applications of the Maximum and Minimum Values ? Lesson 2.14: The Differential Function ? Lesson 2.14.1: The Differential and Approximations ? Lesson 2.15: The Differential Notation ? Lesson 2.16: Related Rates ? Lesson 2.17: Newton?s Method of Approximation ? 2.18: Trigonometric Functions and Their Application ? Lesson 2.18.1: Some Special Limits ? Lesson 2.19: The Differentiation of Trigonometric Functions ? Lesson 2.20: Application of Differentiation of Trigonometric Functions ? Lesson 2.21: Inverse Trigonometric Functions and Their Curves ? Lesson 2.21.1: Inverse Trigonometric Functions and Their Curves ? Lesson 2.21.2: Differentiation of Differentiation of Inverse Trigonometric Functions ? Indefinite Integrals ? Lesson 3.1: Definition and Properties ? Lesson 3.2: Basic Integration Formulas ? Techniques of Integration ? Lesson 4.1: Integration by Parts ? Lesson 4.2: Algebraic Substitution ? Lesson 4.3: Trigonometric Substitution ? Lesson 4.4: Integration of Rational Fractions ? Definite Integrals ? Lesson 5.1: Definition and Properties ? Lesson 5.2: Evaluation of Definite Integrals ? Lesson 5.3: Improper Integrals ? Plane Areas by Integration ? Lesson 6.1: Plane Areas in Rectangular Coordinates ? Lesson 6.2: Plane Areas in Polar Coordinates ? About The Author..