Differential Calculus and Its Applications

Author: Michael J. Field
Publisher: Courier Corporation
ISBN: 9780486298849
Release Date: 2013-04-10
Genre: Mathematics

Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.

Introduction to Partial Differential Equations with Applications

Author: E. C. Zachmanoglou
Publisher: Courier Corporation
ISBN: 9780486132174
Release Date: 2012-04-20
Genre: Mathematics

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Essential Calculus with Applications

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 9780486318592
Release Date: 2013-04-22
Genre: Mathematics

Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician. The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables. Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

Differential Equations with Applications

Author: Paul D. Ritger
Publisher: Courier Corporation
ISBN: 0486411540
Release Date: 1968
Genre: Mathematics

Coherent, balanced introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and the differences between linear and nonlinear systems. Includes large number of illustrative examples worked out in detail and extensive sets of problems. Answers or hints to most problems appear at end.

An Introduction to Differential Equations and Their Applications

Author: Stanley J. Farlow
Publisher: Courier Corporation
ISBN: 9780486135137
Release Date: 2012-10-23
Genre: Mathematics

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Tensor and Vector Analysis

Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 9780486320915
Release Date: 2013-09-26
Genre: Mathematics

Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Calculus of Variations

Author: Robert Weinstock
Publisher: Courier Corporation
ISBN: 0486630692
Release Date: 1974
Genre: Mathematics

This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.

Kronecker Products and Matrix Calculus with Applications

Author: Alexander Graham
Publisher: Courier Dover Publications
ISBN: 9780486824178
Release Date: 2018-06-13
Genre: Mathematics

Enhanced by many worked examples, problems, and solutions, this in-depth text is suitable for undergraduates and presents a great deal of information previously only available in specialized and hard-to-find texts. 1981 edition.

Lectures on Functional Equations and Their Applications

Author: J. Aczel
Publisher: Courier Corporation
ISBN: 9780486445236
Release Date: 2006-02-01
Genre: Mathematics

Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

An Introduction to the Calculus of Variations

Author: Charles Fox
Publisher: Courier Corporation
ISBN: 0486654990
Release Date: 1950
Genre: Mathematics

In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.

Introduction to Nonlinear Differential and Integral Equations

Author: Harold Thayer Davis
Publisher: Courier Corporation
ISBN: 0486609715
Release Date: 1962
Genre: Mathematics

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Introduction to Differential Calculus

Author: Ulrich L. Rohde
Publisher: John Wiley & Sons
ISBN: 9781118130148
Release Date: 2012-01-12
Genre: Mathematics

Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications. The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including: Concepts of function, continuity, and derivative Properties of exponential and logarithmic function Inverse trigonometric functions and their properties Derivatives of higher order Methods to find maximum and minimum values of a function Hyperbolic functions and their properties Readers are equipped with the necessary tools to quickly learn how to understand 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 Differential Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.

Stochastic Differential Equations and Applications

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486141121
Release Date: 2012-08-28
Genre: Mathematics

Originally published in 2 volumes, this text develops the theory of systems of stochastic differential equations and presents applications in probability, partial differential equations, and stochastic control problems. 1975 edition.

Laplace Transforms and Their Applications to Differential Equations

Author: N.W. McLachlan
Publisher: Courier Corporation
ISBN: 9780486798233
Release Date: 2014-08-20
Genre: Mathematics

Classic graduate-level exposition covers theory and applications to ordinary and partial differential equations. Includes derivation of Laplace transforms of various functions, Laplace transform for a finite interval, and more. 1948 edition.

Integral Equations

Author: F. G. Tricomi
Publisher: Courier Corporation
ISBN: 9780486158303
Release Date: 2012-04-27
Genre: Mathematics

Authoritative, well-written treatment of extremely useful mathematical tool with wide applications. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, more. Advanced undergraduate to graduate level. Exercises. Bibliography.