Introduction to Integral Calculus – Systematic Studies with Engineering Applications for Beginners Systematic Studies with Engineering Applications for Beginners

An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences

I ntegration 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.

This book explores the integral calculus and its plentiful applications in engineering and the physical sciences.  The authors aim to develop a basic understanding of integral calculus combined with scientific problems, and throughout, the book details the numerous applications of calculus as well as presents the topic as a deep, rich, intellectual achievement.  The needed fundamental information is presented in addition to plentiful references, exercises, and examples.  The definition of an integral is motivated by the familiar notion of area.  Although the methods of plane geometry allow for the areas of polygons to be calculated, they do not provide ways of finding the area of plane regions whose boundaries are curves other than circles.  By means of the integral, the areas of many such regions can be found. The authors also use this definition to calculate volumes and length of curves etc.  Topical coverage includes anti-differentiation; integration of trigonometric functions; integration by substitution; methods of substitution; the definite integral; methods for evaluating definite integrals; differential equations and their solutions; and ordinary differential equations of first order and first degree.

This book explores the integral calculus and its plentiful applications in engineering and the physical sciences.  The authors aim to develop a basic understanding of integral calculus combined with scientific problems, and throughout, the book details the numerous applications of calculus as well as presents the topic as a deep, rich, intellectual achievement.  The needed fundamental information is presented in addition to plentiful references, exercises, and examples.  The definition of an integral is motivated by the familiar notion of area.  Although the methods of plane geometry allow for the areas of polygons to be calculated, they do not provide ways of finding the area of plane regions whose boundaries are curves other than circles.  By means of the integral, the areas of many such regions can be found. The authors also use this definition to calculate volumes and length of curves etc.  Topical coverage includes anti-differentiation; integration of trigonometric functions; integration by substitution; methods of substitution; the definite integral; methods for evaluating definite integrals; differential equations and their solutions; and ordinary differential equations of first order and first degree.