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.

Describes the physical, plasma and chemical processes controlling ionospheres, upper atmospheres and exospheres, for researchers and graduates.

Today, early-stage investors and entrepreneurs find themselves in a dilemma in which they must choose between profit and impact; between traditional, for-profit-only models on the one hand, and multiple-bottom-line structures with a positive social or environmental impact on the other. At a time in which climate change, exponentially growing technologies, social polarization, and looming pandemics are calling into question humanity’s priorities, this Report to the Club of Rome and the World Academy of Art and Science dissolves this dilemma by proposing a new investment paradigm, namely Integral Investing. Integral Investing incorporates and transcends the best practices of both traditional venture capital and impact investing. It provides a seamless integration and shows how technological progress need not be our rival, but can instead be our ally in ensuring the prosperous society we all want. Drawing on her own investments and stellar track record since 1995, the author reveals the mechanism of Integral Investing. At the heart of it is a powerful, 360-degree de-risking tool called the Theta Model, which reveals how to make smart investment decisions based on the comprehensive integration of traditional due-diligence criteria, sustainability metrics, and assessments of the founders’ and team culture. But it doesn’t stop there. In turn, this handbook demonstrates how to use human-centered AI to scale and digitalize the investment process. The goal here is to accelerate the use of exponential tech, capital, and consciousness leadership to transition to a sustainable global society: a process the author refers to as the Investment Turnaround. The 21 principles of Integral Investing, which she defines using Ken Wilber’s Integral Theory, lead to her manifesto on how to implement the UN Sustainable Development Goals within Planetary Boundaries by 2050 through early-stage investing and entrepreneurship. Similar to the 15th century, when the Medicis inspired the Renaissance, today humanity is once again at a crucial turning point where pioneering public and private financiers, investors, entrepreneurs, and other committed individuals have the opportunity to leave behind the legacy of a prosperous society. This handbook provides a source of inspiration, and shows how self-actualization, a positive mindset, and a consciousness that is backed by a world-centric desire can become the driving force for solving the global grand challenges.

This text begins with simple examples of a variety of integral equations and the methods of their solution, and progresses to become gradually more abstract and encompass discussions of Hilbert space. 1977 edition.