Written for beginners, this well organized introduction promotes a solid understanding of differential equations that is flexible enough to meet the needs of many different disciplines. With less emphasis on formal calculation than found in other books all the basic methods are covered—first order equations, separation, exact form, and linear equations—as well as higher order cases, linear equation with constant and variable coefficients, Laplace transform methods, and boundary value problems. The book's systems focus induces an intuitive understanding of the concept of a solution of an initial value problem in order to resolve potential confusion about what is being approximated when a numerical method is used. The author outlines first order equations including linear and nonlinear equations and systems of differential equations, as well as linear differential equations including the Laplace transform, and variable coefficients, nonlinear differential equations, and boundary problems and PDEs. For those looking for a solid introduction to differential equations.
With this revised edition, students can gain a more comprehensive understanding of differential equations. The book exploits students' access to computers by including many new problems and examples that incorporate computer technology.
"The solution to quasilinear first order hyperbolic systems of equations may be interpretated in terms of waves, which belong to a certain function class and propagate in some suitable space,...
University of Strathclyde Seminars in Applied Mathematical Analysis: Multiparameter Problems
Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed...
This text is designed for engineers, scientists, and mathematicians with a background in elementary ordinary differential equations and calculus.
Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year. The main prerequisite is a working...
This book strikes a balance between the traditional and the modern—combining the traditional material with a modern systems emphasis. Chapter topics cover an introduction to differential equations, first-order equations, modeling...
Differential Equations and Boundary Value Problems: Computing and Modeling
Elementary Differential Equations and Boundary Value Problems
本书主要内容包括:糖水的秘密——糖水不等式、木桶盛水有学问——木桶不等式、绝对值函数与绝对值不等式、耐克函数与耐克不等式、万丈高楼平地起——基本不等式、各种平均数,究竟谁最大——均值不等式等十三章。