This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.
Advanced interdisciplinary introduction to modern scientific computing on parallel supercomputers. Numerical topics include dense and sparse linear algebra, N-body problems, and Fourier transforms. Geometrical topics include partitioning and mesh generation. Other topics include architectures and software systems with hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines.
Linear algebra, vector space methods, and functional analysis are a powerful setting for many topics in engineering, science (including social sciences), and business. This collection starts with the simple idea of a matrix times a vector and develops tools and interpretations for many signal processing and system analysis and design methods.
Exercises for Nerve Fibers and the Strang Quartet
This textbook covers topics such as Trigonometry and Right Angles, Circular Functions, Trigonometric Identities, Inverse Functions, Trigonometric Equations, Triangles and Vectors, as well as Polar Equations and Complex Numbers. It can also be used in conjunction with other directed courses in Mathematical Analysis or Linear Algebra as a full course in Precalculus. This digital textbook was reviewed for its alignment with California content standards.
This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.
This module gives a definition of Cauchy's Integral Formula and describes its use and usefulness.
In this module we begin by discussing integrations of complex functions over complex curves and end with Cauchy's Theorem.
One can look at the operation of a matrix times a vector as changing the basis set for the vector or as changing the vector with the same basis description.
This module defines precisely what a column space is, gives an example of one, and then a method for finding one given an arbitrary matrix.
This module discusses complex differentiation and shows its similarity and differences to real differentiation.
This module discusses complex functions and their relation to systems of linear equations.
This module sets out to instruct about complex numbers: what they are, what they mean, how to manipulate them, and the different ways to describe them (i.e. polar form). The second half of this module proposes to introduce the characteristics of complex vectors and matrices and how they compare to the laws governing standard vectors and matrices.
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. Note: This course was previously called "Mathematical Methods for Engineers I".
This module introduces linear algebra, DFT, FFT, matrix and vector.
The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions. We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.
Elementary Linear Algebra was written and submitted to the Open Textbook Challenge by Dr. Kenneth Kuttler of Brigham Young University. Dr. Kuttler wrote this textbook for use by his students at BYU. According to the introduction of Elementary Linear Algebra, “this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.” A solutions manual for the textbook is included.
This book is an introduction to linear algebra, based on lectures given by me over 17 years, in the (now defunct) first year course MP103 at the University of Queensland.
This is a foundational textbook on abstract algebra with emphasis on linear algebra.
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.
