Rohde: Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

• 1 From Arithmetic to Algebra.
• 2 The Concept of Function.
• 3 Discovery of Real Numbers (Through Traditional Algebra).
• 4 From Geometry to Co-ordinate Geometry.
• 5 Trigonometry and Trigonometric Functions.
• 6 More about Functions.
• 7 (a): The Concept of Limit of a Function.
• 7 (b): Methods for Computing Limits of Algebraic Functions.
• 8 The Concept of Continuity of a Function and the Points of Discontinuity.
• 9 The Idea of Derivative of a Function.
• 10. Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions.
• 11 (a): Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions.
• 11 (b): Methods of Computing Limits of Trigonometric Functions.
• 12 Exponential Form(s) of a Positive Real Numbers and its Logarithms.
• 13 (a): Exponential and Logarithmic Functions as Their Derivatives.
• 13 (b): Methods for Computing Limits and Exponential and Logarithmic Functions.
• 14 Inverse Trigonometric Functions and Their Derivatives.
• 15 (a): Implicit Functions and Their Differentiation.
• 15 (b): Parametric Functions and Their Differentiation.
• 16 Differentials ‘dy’ and ‘dx’: Meanings and Applications.
• 17 Derivatives and Differentials of Higher Order.
• 18 Applications of Derivatives in Studying Motion in a Straight Line.
• 19 (a): Increasing and Decreasing Functions and the Sign of the First Derivative.
• 19 (b): Maximum and Minimum Values of a Function.
• 20 Rolle’s Theorem and the Mean Value Theorem (MVT).
• 21 The Generalized Mean Value Theorem (Cauchy’s MVT), L’Hospital’s Rule, and Its Applications.
• 22 Extending the Mean Value Theorem to taylor’s Formula: Taylor Polynomials for Certain Functions.
• 23 Hyperbolic Functions and Their Properties.

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners 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. Also, applications and limitations of this definition, along with the algebra of limits (i.e. limit theorems) are discussed. Finally, Sandwich theorem, which is useful for evaluating limit(s) of trigonometric functions, is proved, and the concept of onesided limits is introduced.

The methods for computing limits of algebraic functions are discussed, and the concept of continuity and related concepts are also featured at length. Suitable examples of functions and their graphs are selected carefully to prevent reader confusion. Classification of the points of discontinuity is explained, and the methods for checking continuity of functions involving trigonometric, exponential, and logarithmic functions are discussed through solved examples. Theorems on continuity of functions (i.e. algebra of continuous functions) are stated without proof. Also, very important theorems on continuity (without proof) are provided.

About the Author

• Ulrich L. Rohde, PhD, ScD, Dr-Ing, is Chairman of Synergy Microwave Corporation, President of Communications Consulting Corporation, and a Partner of Rohde & Schwarz. A Fellow of the IEEE, Professor Rohde holds several patents and has published more than 200 scientific papers.
• G. C. Jain, BSc, is a retired scientist from the Defense Research and Development Organization in India.
• Ajay K. Poddar, PhD, is Chief Scientist at Synergy Microwave Corporation. A Senior Member of the IEEE, Dr. Poddar holds several dozen patents and has published more than 180 scientific papers.
• A. K. Ghosh, PhD, is Professor in the Department of Aerospace Engineering at IIT Kanpur, India. He has published more than 120 scientific papers.

Book Details

• Hardcover: 784 pages
• Publisher: Wiley; 1 edition (December, 2011)
• Language: English
• ISBN-10: 1118117751
• ISBN-13: 978-1118117750

List Price: $140.00 

 

Tags: Engineering Mathematics, General Engineering, Wiley