Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

This book explores the differential calculus and its plentiful applications in engineering and the physical sciences.  The first six chapters offer a refresher of algebra, geometry, coordinate geometry, trigonometry, the concept of function, etc. since these topics are vital to the complete understanding of calculus.  The book then moves on to the concept of limit of a function.  Suitable examples of algebraic functions are selected, and their limits are discussed to visualize all possible situations that may occur in evaluating limit of a function, other than algebraic functions. Also, applications and limitations of this definition, along with the algebra of limits (i.e. limit theorems) are discussed. Finally, Sandwich theorem, which is useful for evaluating limit(s) of trigonometric functions, is proved, and the concept of onesided limits is introduced. The methods for computing limits of algebraic functions are discussed, and the concept of continuity and related concepts are also featured at length. Suitable examples of functions and their graphs are selected carefully to prevent reader confusion. Classification of the points of discontinuity is explained, and the methods for checking continuity of functions involving trigonometric, exponential, and logarithmic functions are discussed through solved examples.  Theorems on continuity of functions (i.e. algebra of continuous functions) are stated without proof. Also, very important theorems on continuity (without proof) are provided.

Keywords: Calculus, Differential Calculus, Calculus made easy, Ulrich Rohde, Differential Calculus help, Calculus for engineering, Introduction to differential calculus