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

• Άλλοι συγγραφείς: Rohde, Ulrich L.
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Hoboken, N.J. : Wiley, 2012.
• Έκδοση: 1st ed.
• Θέματα: 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,...

Πίνακας περιεχομένων:

• 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.