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7 books match the query 'Calculus'

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A Relatively Painless Guide to Special Relativity

Dave Goldberg

University of Chicago Press, 2023

Serious and accessible—finally the special relativity course book that both physics majors and lifelong learners deserve.

Special relativity challenges one’s physical intuition of space, time, matter, and energy in a way that few other topics in physics do. Yet the subject is often treated as an extra in undergraduate courses—something to be picked up in a few random lectures and presented as a combination of geometric and logical puzzles (seemingly with the premise of getting the novice student to concede that Einstein was a genius and that the universe is weird). But special relativity is absolutely fundamental to modern physics. It is the canvas on which electromagnetism, particle physics, field theory, and ultimately general relativity are based. For physics students, developing a relativistic intuition isn’t just a luxury: it’s a requirement.

Physicist and popular author Dave Goldberg provides a rigorous but conversational introduction to fill this void in spacetime education. Employing the standard calculus a sophomore or junior university student in science, engineering, or computer science will have encountered, Goldberg connects relativity to a student’s work ahead, acquainting them with topics like tensors, the development of new physical theories, and how relativity directly relates to other disciplines. But more than this, Goldberg welcomes lifelong learners who may have encountered special relativity in popular accounts, but are seeking a mathematical challenge to understand an elegant physical theory.

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Calculus for the Modern Engineer

Math and Programming at the Scale of Life

Jessy Grizzle

Michigan Publishing Services, 2026

In the ever-evolving landscape of engineering education, calculus stands as a foundational pillar, yet its teaching methods have remained largely unchanged for decades. This textbook is born out of a deep-seated need for reform. Traditional calculus courses struggle to incorporate relevant, real-world examples. The disconnect between mathematical theory and its real-world uses hinders the learning process and fails to fully engage students in the practical applications of calculus. A second core issue lies not in the examples used but in the selection of material and the overemphasis on lengthy, manual calculations that lack meaningful context. This book represents a radical departure from conventional approaches, inspired by Prof. Grizzle’s experience developing and teaching the first-semester course ROB 101 Computational Linear Algebra. Its goal is to breathe life into mathematics through programming and realistic examples. It begins by placing integration at the beginning of the learning process, starting with sums and progressing to integration, which is not only more intuitive but also lends itself well to programming applications, such as calculating the change in position of mobile robots from velocity curves. Following integration, the book delves into differentiation (both single-variable and multivariable) and its myriad applications. Traditional methods of computing integrals, such as antiderivatives and substitution methods, are then introduced and framed within the context of both manual calculations and modern symbolic tools. The journey continues through improper integrals, ordinary differential equations (ODEs), Laplace Transforms, and Feedback Control, encompassing a breadth of topics rarely seen in a single calculus course.

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Economics and Politics

The Calculus of Support

Helmut Norpoth, Michael S. Lewis-Beck, and Jean-Dominique Lafay, Editors

University of Michigan Press, 1991

How do voters weigh economic concerns in their calculus of partisan choice in voting booths and opinion polls? How do voters arrive at their perceptions of economic conditions and assign responsibility for them to incumbent governments? And when do people go beyond electoral reactions in expressing their sentiments about economic well-being?The contributors to Economics and Politics employ sophisticated methods of analysis to isolate the effects of specific economic conditions such as unemployment and inflation. While some look at the effects of aggregate data on the electorate taken as a whole, others examine individual perceptions of economic conditions gleaned from survey data. The contributors, from several European countries as well as the United States, consider the relationships between economics and politics both cross-nationally and individually in West Germany, the United States, France, Britain, and Italy.Taken together, these contributions present the most comprehensive comparative assessment of economic influence on mass political behavior. The crucial role of strategic politicians, intervening in the economy as well as in public evaluations of the economy, receives considerable attention; so do interventions such as wars and political turnover. In sorting out economic facts and assigning responsibility to politicians amid such uncertainty, the publics of Western democracies display considerable sophistication.

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Fuchsian Groups

Svetlana Katok

University of Chicago Press, 1992

This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry, topology, Lie theory, representation theory, and group theory.

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Several Complex Variables

Raghavan Narasimhan

University of Chicago Press, 1974

Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.

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Systems of Linear Inequalities

A. S. Solodovnikov

University of Chicago Press, 1980

This volume describes the relationship between systems of linear inequalities and the geometry of convex polygons, examines solution sets for systems of linear inequalities in two and three unknowns (extension of the processes introduced to systems in any number of unknowns is quite simple), and examines questions of the consistency or inconsistency of such systems. Finally, it discusses the field of linear programming, one of the principal applications of the theory of systems of linear inequalities. A proof of the duality theorem of linear programming is presented in the last section.

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The Calculus

A Genetic Approach

Otto Toeplitz

University of Chicago Press, 2007

When first published posthumously in 1963, this bookpresented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus.

Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.

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