Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange’s equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange’s equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems.
This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.

Upon successful completion of this course, students will be able to:

Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains
Make quantitative estimates of model parameters from experimental measurements
Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods
Obtain the frequency-domain response of linear systems to sinusoidal inputs
Compensate the transient response of dynamic systems using feedback techniques
Design, implement and test an active control system to achieve a desired performance measure

Mastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.

The DMT Clearinghouse is a registry for online learning resources about research data management. Initial seed funding was provided by the U.S. Geological Survey's Community for Data Integration. Subsequent funding has been granted by an Institute of Museum and Library Services National Leadership Grant (LG-70-18-0092-18). Developed in collaboration with the Earth Sciences Information Partnership (ESIP) Federation, and DataONE, with subsequent support from the University of New Mexico Libraries Research Data Services, the DMT Clearinghouse is available for searching, browsing, and submitting information about learning resources on data management topics. DMT Clearinghouse FeaturesThe Search Interface allows users to find learning resources by entering terms, names of people and organizations, dates, and keywords. The Browse Interface allows users to view the entire list of learning resources, and to filter by educational framework. An educational framework is a plan or set of steps that defines or collects the content using clear, definable standards about what the student should know and understand. For purposes of the DMT Clearinghouse, a given learning resource may be associated with a community-defined standard for data management, for example:USGS Science Support FrameworkDataONE Data Life CycleESIP Data Management Short Course for Scientists The Digital Preservation NetworkInternational Council for Science (ICSU) World Data System (WDS) Training Resource GuideFAIR Data Principles The Submission Form allows users to enter information about learning resources that they would like to see included in the DMT Clearinghouse. A user log in is not required to submit a resource with key, required information. To add more information about a learning resource than just that required, please log in or create an account (click "Log In at the upper right side of the screen.) NOTE: Submissions will be published to the DMT Clearinghouse following an editorial review to ensure the resource meets quality and selection criteria for inclusion.. You may be contacted for more information about your submission, if needed. Your contact information will not be made available publicly without your permission. For questions or feedback, please contact clearinghouseEd@esipfed.org.

Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement.

Game Theory, also known as Multiperson Decision Theory, is the analysis of situations in which the payoff of a decision maker depends not only on his own actions but also on those of others. Game Theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of Game Theory, primarily in economics.

This text is an introductory treatment on the junior level for a two-semester electrical engineering course starting from the Coulomb-Lorentz force law on a point charge. The theory is extended by the continuous superposition of solutions from previously developed simpler problems leading to the general integral and differential field laws. Often the same problem is solved by different methods so that the advantages and limitations of each approach becomes clear. Sample problems and their solutions are presented for each new concept with great emphasis placed on classical models of physical phenomena such as polarization, conduction, and magnetization. A large variety of related problems that reinforce the text material are included at the end of each chapter for exercise and homework.

6.632 is a graduate subject on electromagnetic wave theory, emphasizing mathematical approaches, problem solving, and physical interpretation. Topics covered include: waves in media, equivalence principle, duality and complementarity, Huygens’ principle, Fresnel and Fraunhofer diffraction, dyadic Green’s functions, Lorentz transformation, and Maxwell-Minkowski theory. Examples deal with limiting cases of Maxwell’s theory and diffraction and scattering of electromagnetic waves.

This open course for Elementary Statistics was created through a Round Ten Textbook Transformation Grant:

https://oer.galileo.usg.edu/mathematics-collections/39/

The open course contains ancillary materials for OpenStax Introductory Statistics:

https://openstax.org/details/books/introductory-statistics

Included in the course are introductions to each lesson, lecture slides, videos, and problem questions. Topics include:

Types of Data
Sampling Techniques
Qualitative Data
Frequency Distributions
Descriptive Statistics
Variation and Position
Confidence Intervals
Hypothesis Testing
Chi-Square Goodness of Fit
Linear Regression
Variance ANOVA

This course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. While this is an introductory course, we will (gently) work our way up to some fairly advanced material, including an overview of the proof of Fermat’s last theorem.

This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline.
Acknowledgements
This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of ‘51 Fund for Excellence in Education, Class of ‘55 Fund for Excellence in Teaching, Class of ‘72 Fund for Educational Innovation). The instructors gratefully acknowledge the financial support.
The course was approved by the Undergraduate Committee of the MIT Department of Aeronautics and Astronautics in 2003. The instructors thank Prof. Manuel Martinez-Sanchez and the committee members for their support and suggestions.

This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline.
Acknowledgements
This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of ‘51 Fund for Excellence in Education, Class of ‘55 Fund for Excellence in Teaching, Class of ‘72 Fund for Educational Innovation). The instructors gratefully acknowledge the financial support. The course was approved by the Undergraduate Committee of the MIT Department of Aeronautics and Astronautics in 2003. The instructors thank Prof. Manuel Martinez-Sanchez and the committee members for their support and suggestions.

This intensive micro-subject provides the necessary skills in Microsoft® Excel spreadsheet modeling for ESD.71 Engineering Systems Analysis for Design. Its purpose is to bring entering students up to speed on some of the advanced techniques that we routinely use in analysis. It is motivated by our experience that many students only have an introductory knowledge of Excel, and thus waste a lot of time thrashing about unproductively. Many people think they know Excel, but overlook many efficient tools, such as Data Table and Goal Seek. It is also useful for a variety of other subjects.

This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

ERBA (ESD.72) emphasizes three methodologies - reliability and probabilistic risk assessment (RPRA), decision analysis (DA), and cost-benefit analysis (CBA). In this class, the issues of interest are: the risks associated with large engineering projects such as nuclear power reactors, the International Space Station, and critical infrastructures; the development of new products; the design of processes and operations with environmental externalities; and infrastructure renewal projects.

This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation–the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the decoding of Turbo, LDPC, and Serially-Concatenated codes. The technical portion of the course will conclude with a study of tools for explaining and predicting the behavior of iterative decoding algorithms, including EXIT charts and Density Evolution.

This half-semester course introduces computational methods for solving physical problems, especially in nuclear applications. The course covers ordinary and partial differential equations for particle orbit, and fluid, field, and particle conservation problems; their representation and solution by finite difference numerical approximations; iterative matrix inversion methods; stability, convergence, accuracy and statistics; and particle representations of Boltzmann’s equation and methods of solution such as Monte-Carlo and particle-in-cell techniques.

These are notes prepared for a 7-day course at the QED Verein in Germany. The plan is to explain Feynman diagrams from their origin in quantum field theory to their application in homotopy theory. The course is targeted at a group of bachelor and master students from mixed backgrounds in mathematics, physics or related areas. The course starts with a recap of differential geometry, follows with elementary explanation of perturbative quantum field theory and finishes with the mathematical meaning in differential operators, the IBL-operad and knot theory. The course includes multiple exercises scattered throughout the text. 

The Financial Algebra Course engages students with real-world financial applications while maintaining deep mathematical rigor. The 10 units include: Taxes, Checking, Savings, Budgeting, Intro to Investing, Investing Strategies, Types of Credit, Managing Credit, Paying for College and Insurance.

This course will be heavily collaboration and project based. Students will be required to use google drive, docs and sheets on a regular basis. This course has a distinction of Algebra 1/Integrated 1 or higher. This is a good course for 11th and 12th grade students as an alternative to Integrated 3/Algebra 2.

This course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results.