introduction differential calculus ulrich rohde [pdf]
Introduction to Differential Calculus by Ulrich Rohde and GC Jain
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About this book :-
Introduction to Differential calculus Calculus (Systematic Studies with Engineering Applications for Beginners) written by
Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh.
This book clarifying prerequisite materials such as algebra, geometry, coordinate geometry, trigonometry, and the concept of limits. Integration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving.
The first six chapters address the prerequisites needed to understand the principles of integral calculus and explore such topics as anti-derivatives, methods of converting integrals into standard form, and the concept of area. It is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.
Book Detail :-
Title: Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners)
Author(s): Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh
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About Author :-
Ulrich L. Rohde, Prof. Dr.-Ing. Dr. h. c. mult., BTU Cottbus, Germany, Synergy Microwave Corporation Peterson, NJ, USA
G. C. Jain (Retd. Scientist) Defense Research and Development Organization, Maharashtra, India
Ajay K. Poddar, Chief Scientist, Synergy Microwave Corporation, Peterson, NJ, USA
A. K. Ghosh, Professor, Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India
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Book Contents :-
Introduction to Differential calculus (Systematic Studies with Engineering Applications for Beginners) written by
Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh
cover the following topics.
1. From Arithmetic to Algebra
2. The Concept of a Function
3. Discovery of Real Numbers: Through Traditional Algebra
4. From Geometry to Coordinate Geometry
5. Trigonometry and Trigonometric Functions
6. More About Functions
7.a The Concept of Limit of a Function
8. The Concept of Continuity of a Function, and Points of Discontinuity
9. The Idea of a Derivative of a Function
10. Algebra of Derivatives: Rules for Computing Derivatives of
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 Number and its Logarithm(s): Pre-Requisite for Understanding Exponential and Logarithmic Functions
13.a Exponential and Logarithmic Functions and Their Derivatives
13.b Methods for Computing Limits of 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 their Applications
22. Extending the Mean Value Theorem to Taylor’s Formula: Taylor Polynomials for Certain Functions
23. 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)
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