Introduction to differential calculus : systematic studies with engineering applications for beginners

Content: Frontmatter --
From Arithmetic to Algebra --
The Concept of a Function --
Discovery of Real Numbers: Through Traditional Algebra --
From Geometry to Coordinate Geometry --
Trigonometry and Trigonometric Functions --
More About Functions --
The Concept of Limit of a Function --
Methods for Computing Limits of Algebraic Functions --
The Concept of Continuity of a Function, and Points of Discontinuity --
The Idea of a Derivative of a Function --
Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions --
Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions --
Methods of Computing Limits of Trigonometric Functions --
Exponential Form(s) of a Positive Real Number and its Logarithm(s): Pre-Requisite for Understanding Exponential and Logarithmic Functions --
Exponential and Logarithmic Functions and Their Derivatives --
Methods for Computing Limits of Exponential and Logarithmic Functions --
Inverse Trigonometric Functions and Their Derivatives --
Implicit Functions and Their Differentiation --
Parametric Functions and Their Differentiation --
Differentials ₃d₄ and ₃d₄: Meanings and Applications --
Derivatives and Differentials of Higher Order --
Applications of Derivatives in Studying Motion in a Straight Line --
Increasing and Decreasing Functions and the Sign of the First Derivative --
Maximum and Minimum Values of a Function --
Rolle\'s Theorem and the Mean Value Theorem (MVT) --
The Generalized Mean Value Theorem (Cauchy\'s MVT), L\' Hospital\'s Rule, and their Applications --
Extending the Mean Value Theorem to Taylor\'s Formula: Taylor Polynomials for Certain Functions --
Hyperbolic Functions and Their Properties --
Appendix A (Related To Chapter-2): Elementary Set Theory --
Appendix B (Related To Chapter-4) --
Appendix C (Related To Chapter-20) --
Index.