:Systematic Studies with Engineering Applications for Beginners
/ Ulrich L. Rohde... [et al.]
1st edition
Hoboken, N.J.
: Wiley
, 2012.
xxix, 747 p.
: , ill
Print
Bibliography
Index
Machine generated contents note: From Arithmetic to Algebra.- The Concept of Function.- Discovery of Real Numbers (Through Traditional Algebra).- From Geometry to Co-ordinate Geometry.-. Trigonometry and Trigonometric Functions.- More about Functions.-. (a): The Concept of Limit of a Function.- (b): Methods for Computing Limits of Algebraic Functions.- The Concept of Continuity of a Function and the Points of Discontinuity.- The Idea of Derivative of a Function.- Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions.- (a): Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions.- (b): Methods of Computing Limits of Trigonometric Functions.- Exponential Form(s) of a Positive Real Numbers and its Logarithms.- (a): Exponential and Logarithmic Functions as Their Derivatives.- (b): Methods for Computing Limits and Exponential and Logarithmic Functions.- Inverse Trigonometric Functions and Their Derivatives.- (a): Implicit Functions and Their Differentiation.- (b): Parametric Functions and Their Differentiation.- Differentials 'dy' and 'dx': Meanings and Applications.- Derivatives and Differentials of Higher Order.Chapter Eighteen. Applications of Derivatives in Studying Motion in a Straight Line.- (a): Increasing and Decreasing Functions and the Sign of the First Derivative.- (b): 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 Its Applications.- Extending the Mean Value Theorem to taylor's Formula: Taylor Polynomials for Certain Functions.- Hyperbolic Functions and Their Properties