Introduction to integral calculus : systematic studies with engineering applications for beginners / Ulrich L. Rohde, G.C. Jain, Ajay K. Poddar, A.K. Ghosh.
Contributor(s): Rohde, Ulrich L [editor.].Material type: BookPublisher: Hoboken, New Jersey : John Wiley & Sons, Inc., Copyright date: ©2012Description: 1 online resource (xxv, 402 pages) : illustrations.Content type: text Media type: computer Carrier type: online resourceISBN: 9781118130346; 1118130340; 9781118130315; 1118130316; 9781118130339; 1118130332.Subject(s): Calculus, Integral -- Textbooks | MATHEMATICS -- Calculus | MATHEMATICS -- Mathematical Analysis | Calculus, IntegralGenre/Form: Electronic books. | TextbooksAdditional physical formats: Print version:: Introduction to integral calculus.DDC classification: 515/.43 Online resources: Wiley Online Library
Includes bibliographical references and index.
Frontmatter -- Antiderivative(s) [or Indefinite Integral(s)] -- Integration Using Trigonometric Identities -- Integration by Substitution: Change of Variable of Integration -- Further Integration by Substitution: Additional Standard Integrals -- Integration by Parts -- Further Integration by Parts: Where the given Integral Reappears on Right-Hand Side -- Preparation for the Definite Integral: The Concept of Area -- The Fundamental Theorems of Calculus -- The Integral Function Identified as ln or log -- Methods for Evaluating Definite Integrals -- Some Important Properties of Definite Integrals -- Applying the Definite Integral to Compute the Area of a Plane Figure -- To Find Length(s) of Arc(s) of Curve(s), the Volume(s) of Solid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s) of Revolution -- Differential Equations: Related Concepts and Terminology -- Methods of Solving Ordinary Differential Equations of the First Order and of the First Degree -- Index.
"An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences. 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. Next, the authors review numerous methods and applications of integral calculus, including: Mastering and applying the first and second fundamental theorems of calculus to compute definite integrals ; Defining the natural logarithmic function using calculus ; Evaluating definite integrals ; Calculating plane areas bounded by curves ; Applying basic concepts of differential equations to solve ordinary differential equations. With this book as their guide, readers quickly learn to solve a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Integral Calculus 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"--Provided by publisher.
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