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

• Other Authors: Rohde, Ulrich L.
• Format: eBook
• Language: English
• Published: Hoboken, N.J. : Wiley, 2012.
• Edition: 1st ed.
• Subjects: Differential calculus > Textbooks.; MATHEMATICS > Calculus.; MATHEMATICS > Differential Equations > General.; Differential calculus.; Electronic books.; Textbooks.

 "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"--   Provided by publisher. 

 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.