Differential Calculus: The Limits and The Derivative

This book is designed as an advanced guide to Differential Calculus. This covers the following topics: introduction and strict definition of limits, properties of limits, limits of trigonometric functions, infinite limits and limits to infinity, continuity of functions, derivatives, the slope of the secant line and tangent line, the derivative and continuity, derivative rules, derivative of trigonometric functions, chain rule, higher-order derivatives, velocity and acceleration, implicit derivation, rates of change, differentials and approximations, applications of the derivative, maximum and minimum, monotony and concavity, local extremes, maximum and minimum exercises, graphing functions, the mean value theorem for derivatives, miscellaneous of exercises. This is including the deduction of many formulas to clarify concepts and fill all the needs of the students to achieve the fundamentals of differential calculus. Finally, another objective of the book is to achieve the interest and motivation of the students to the real nature of differential calculus.