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Keywords: differential equations
(Complete Item Description)
- Abstract: Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.
Note: this is a 57 MB PDF Document.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
Individual Authors
(Complete Item Description)
- Abstract: This book introduces differentiability as a local property without using limits. The philosophy behind this idea is that limits are the a big stumbling block for most students who see calculus for the first time, and they take up a substantial part of the first semester.
(Complete Item Description)
- Abstract: The module discusses how to represent linear, time-invariant systems.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Fact-sheet outlining the method of solution of differential equations. Includes an illustrative example on first order variables separable differential equation.
- Subject:
Mathematics and Statistics
- Grade Level:
Secondary
- Collection:
Scoilnet
(Complete Item Description)
- Abstract: Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.
This digital textbook was reviewed for its alignment with California content standards.
(Complete Item Description)
- Abstract: This book grew out of a two-quarter sequence of undergraduate courses offered at the University of California (UCSB), for science majors, engineers and mathematicians. These courses along with a two-quarter sequence on ordinary differential equations (ODEs) and dynamical systems constitute the applied mathematics courses for the Program in Scientific Computations, a joint program between the mathematics department and the College of Engineering at UCSB.
(Complete Item Description)
- Abstract: This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from Calculus and Differential Equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.
(Complete Item Description)
- Abstract: Presents and solves chemical engineering problems in an industrial context, with applications varying by semester. Emphasis on the integration of fundamental concepts with approaches of process design. Emphasis on problems that demand synthesis, economic analysis, and process design .This course introduces students to methods and background needed for the conceptual design of continuously operating chemical plants. Particular attention is paid to the use of process modeling tools such as Aspen that are used in industry and to problems of current interest. Each student team is assigned to evaluate and design a different technology and prepare a final design report. For spring 2006, the theme of the course is to design technologies for lowering the emissions of climatically active gases from processes that use coal as the primary fuel.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: Introduction to Groups, Invariants & Particles is a book for Seniors and advanced Juniors who are majoring in the Physical Sciences or Mathematics. The book places the subject matter in its historical context with discussions of Galois groups, algebraic invariants, Lie groups and differential equations, presented at a level that is not the standard fare for students majoring in the Physical Sciences. A sound mathematical basis is thereby provided for the study of special unitary groups and their applications to Particle Physics.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Yale University
(Complete Item Description)
- Abstract: An introduction to the formulation, methodology, and techniques for numerical solution of engineering problems. Fundamental principles of digital computing and the implications for algorithm accuracy and stability. Error propagation and stability. The solution of systems of linear equations, including direct and iterative techniques. Roots of equations and systems of equations. Numerical interpolation, differentiation and integration. Fundamentals of finite-difference solutions to ordinary differential equations. Error and convergence analysis. Subject taught first half of term.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This class was originally listed in Course 13 (Ocean Engineering) as 13.002J.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: This course analyzes the basic techniques for the efficient numerical solution of problems in science and engineering.
- Subject:
Mathematics and Statistics
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: Introduction to computational techniques for the simulation of a large variety of engineering and engineered systems. Applications drawn from aerospace, mechanical, electrical, and chemical engineering, materials science, and operations research. Topics: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary and partial differential equations; methods for the solution of integral equations; model-order reduction; and Monte Carlo techniques. An introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: The class will cover 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 3.012 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, fourier analysis and random walks.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: 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.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
(Complete Item Description)
- Abstract: This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.
(Complete Item Description)
- Abstract: This unit is intended to further develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in solving systems of differential equations, this unit assumes that you have some understanding of eigenvalues and eigenvectors.
(Complete Item Description)
- Abstract: This course introduces students to MATLAB. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
MIT OpenCourseWare
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