Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.

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.

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, ĺÎĺ_ĺĚĄ_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.ĺÎĺ_ĺĚĺÎĺ A solutions manual for the textbook is included.

Fundamental methods used for exploring the information content of observations related to kinematical and dynamical models. Basic statistics and linear algebra for inverse methods including singular value decompositions, control theory, sequential estimation (Kalman filters and smoothing algorithms), adjoint/Pontryagin principle methods, model testing, etc. Second part focuses on stationary processes, including Fourier methods, z-transforms, sampling theorems, spectra including multi-taper methods, coherences, filtering, etc. Directed at the quantitative combinations of models, with realistic, i.e. sparse and noisy observations.

These notes are intended to provide a brief, noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.

We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.

Linear Algebra is a text for a first US undergraduate Linear Algebra course. It is Free. You can use it as a main text, as a supplement, or for independent study.

The Linear Algebra course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in November 2018. The course is part of the Ohio Transfer Module and is also named OMT019. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadAnna Davis                                         Ohio Dominican UniversityContent ContributorsPaul Bender                                       Ohio Dominican UniversityRosemarie Emanuele                        Ursuline CollegePaul Zachlin                                       Lakeland Community CollegeLibrarianDaniel Dotson                                    Ohio State University                     Review TeamJim Fowler                                         Ohio State UniversityJim Cottrill                                          Ohio Dominican University

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

Mathematics explained: Here you find videos on various math topics:

Pre-university Calculus (functions, equations, differentiation and integration)
Vector calculus (preparation for mechanics and dynamics courses)
Differential equations, Calculus
Functions of several variables, Calculus
Linear Algebra
Probability and Statistics

Topics vary from year to year. Topic for Fall: Eigenvalues of random matrices. How many are real? Why are the spacings so important? Subject covers the mathematics and applications in physics, engineering, computation, and computer science. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB programming.

This is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers. It has a hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines. We will make prominent use of the Julia Language software project.

Introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory and optimization techniques. Emphasis on basic ideas and on applications in mechanical engineering. Selection will change every year. This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.