Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra.
For the vectors b for which Ax = b is indeed a consistent equation, how many solution vectors x does each equation have? Why? Suppose that A is a 3×4 matrix for which the homogeneous equation Ax = 0 has exactly one free variable present ...
The contents of the book have been made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological.
Elementary Differential Equations with Linear Algebra, Third Edition provides an introduction to differential equation and linear algebra. This book includes topics on numerical methods and Laplace transforms.
This volume offers an exploration of both ordinary differential equations and linear algebra - motivated throughout by applications to science and engineering.
Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more.
... for in this case [yp](s)=s[yp](s), [yp](s)=s2[yp](s). As we will see in the examples, this assumption also makes it possible to deal with the initial ...
This book caters to the needs of Engineering students in general and in particular, to students of Computer Science & Engineering, Artificial Intelligence, Machine Learning and Robotics.
Differential Equations with Linear Algebra
Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization.