This book is a scientific curriculum for the course Calculus (1), taught to first-year students in the faculties of Science, Engineering, Computer Science, and Education. The topics are presented in a simplified, scientific manner, similar to lectures, suitable for this academic level. It includes a very large collection of solved exercises to help students gain a deeper understanding of the subject matter. This is preceded by clear definitions and the governing theories, almost all of which are provided with proofs.

This book includes six chapters:

• Chapter One: Dedicated to presenting some algebraic principles needed in subsequent chapters, such as: Sets, Numbers, Intervals, Equations, Inequalities, Absolute Value, Mathematical Induction, Binomial Expansion, and Sequences.
• Chapter Two: Provides basics of analytical geometry, concepts crucial for many topics in calculus, through the study of: Straight Lines, The Circle, The Parabola, The Ellipse, The Hyperbola, and eliminating the xy term from a second-degree equation using axis rotation.
• Chapter Three: Focuses on the study of functions, covering: Definition of a function, Domain and Codomain, and various types of functions such as: Constant Function, Identity Function, Polynomial Function, Rational Function, Step Function, Trigonometric Functions, Inverse Trigonometric Functions, Exponential Function, Logarithmic Function, Hyperbolic Functions, and Inverse Hyperbolic Functions.
• Chapter Four: Covers the study of the limit of a function, resolving some forms of indeterminacy, the basic theorems for calculating limits, and the continuity of a function.
• Chapter Five: Addresses the study of derivatives using the definition, basic rules of differentiation, derivatives of trigonometric functions, inverse trigonometric functions, exponential functions, logarithmic functions, hyperbolic functions, and inverse hyperbolic functions, the chain rule, higher-order derivatives, Leibniz's rule, implicit differentiation, and parametric differentiation.
• Chapter Six: Deals with the applications of differentiation in various fields, such as: calculating the equations of the tangent and normal lines, calculating the actual and approximate rate of change of functions, Taylor and Maclaurin series expansions and their use in calculating some limits, Mean Value Theorems including Rolle's Theorem and Cauchy's Mean Value Theorem, calculating limits using L'Hôpital's rule, studying the intervals of increase and decrease of a function, finding maximum and minimum points using the first and second derivative tests, and sketching the behavior of a function.

Book Details:

• Number of Pages: 472
• Year of Publication: 2014
• Binding Type: Paperback
• Edition: 2
• Printing Color: Black
• Dimensions (cm): 17x24
• Weight (kg): 0.850
• Barcode: 9789957068707