Introduction to differential calculus : systematic studies with engineering applications for beginners - Rohde, Ulrich L. (Hoboken, N.J. : Wiley, 2012)
"Through the use of examples and graphs, this book maintains a high level of precision in clarifying prerequisite materials such as algebra, geometry, coordinate geometry, trigonometry, and the concept of limits. The book explores concepts of limits of a function, limits of algebraic functions, applications and limitations for limits, and the algebra of limits. It also discusses methods for computing limits of algebraic functions, and explains the concept of continuity and related concepts in depth. This introductory submersion into differential calculus is an essential guide for engineering and the physical sciences students"--
"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"--
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 b3(Bdb4 (Band b3(Bdb4(B: 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.s
Machine generated contents note: Chapter One. From Arithmetic to Algebra. Chapter Two. The Concept of Function. Chapter Three. Discovery of Real Numbers (Through Traditional Algebra). Chapter Four. From Geometry to Co-ordinate Geometry. Chapter Five. Trigonometry and Trigonometric Functions. Chapter Six. More about Functions. Chapter Seven. (a): The Concept of Limit of a Function. Chapter Seven. (b): Methods for Computing Limits of Algebraic Functions. Chapter Eight. The Concept of Continuity of a Function and the Points of Discontinuity. Chapter Nine. The Idea of Derivative of a Function. Chapter Ten. Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions. Chapter Eleven. (a): Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions. Chapter Eleven. (b): Methods of Computing Limits of Trigonometric Functions. Chapter Twelve: Exponential Form(s) of a Positive Real Numbers and its Logarithms. Chapter Thirteen. (a): Exponential and Logarithmic Functions as Their Derivatives. Chapter Thirteen. (b): Methods for Computing Limits and Exponential and Logarithmic Functions. Chapter Fourteen. Inverse Trigonometric Functions and Their Derivatives. Chapter Fifteen. (a): Implicit Functions and Their Differentiation. Chapter Fifteen. (b): Parametric Functions and Their Differentiation. Chapter Sixteen. Differentials 'dy' and 'dx': Meanings and Applications. Chapter Seventeen. Derivatives and Differentials of Higher Order. Chapter Eighteen. Applications of Derivatives in Studying Motion in a Straight Line. Chapter Nineteen. (a): Increasing and Decreasing Functions and the Sign of the First Derivative. Chapter Nineteen. (b): Maximum and Minimum Values of a Function. Chapter Twenty. Rolle's Theorem and the Mean Value Theorem (MVT). Chapter Twenty One. The Generalized Mean Value Theorem (Cauchy's MVT), L'Hospital's Rule, and Its Applications. Chapter Twenty Two. Extending the Mean Value Theorem to Taylor's Formula: Taylor Polynomials for Certain Functions. Chapter Twenty Three. Hyperbolic Functions and Their Properties.
Includes bibliographical references and index.
Print version record.
Keywords: Differential calculus -- Textbooks; MATHEMATICS -- Calculus; MATHEMATICS -- Differential Equations -- General; Differential calculus; Electronic books; Textbooks