Worked example involving angles of friction using a past LC question.

These modules capture the broad array of activities conducted by vertically integrated research groups comprised of member of the Mathematics, Statistics, and Computational and Applied Mathematics departments at Rice University and supported by a VIGRE (Vertically Integrated Grants for Research and Education in the Mathematical Sciences) award from the National Science Foundation. VIGRE working groups are known as PFUGs. Pronounced like "fugue," the acronym derives from the groups' composition of Postdocs, Faculty, Undergraduates and Graduate students. The name derives from the musical meaning for fugue, "an idea that is introduced by one voice and developed by others."

Fact-sheet outlining a method of approach for finding the distance (h) of the center of gravity of compound bodies from an axis.

Worked example illustrating the concepts involved in the use of a velocity-time graph.

Worked example using a past LC question to illustrate the use of equations in solving a consecutive motion problem.

Fact-sheet covering the derivation of the equations of motion for linear motion under constant acceleration using differential equation theory.

Fact-sheet outlining the method of solution of differential equations. Includes an illustrative example on first order variables separable differential equation.

Worked example illustrating the use of equations of motion.

Worksheet with exercises requiring students to determine an approximate value for "g", the acceleration due to gravity.

Fact-sheet on the topic of friction -- it covers limiting friction and angle of friction.

Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute.

Information about the derivation of the equations of motion for linear motion under constant acceleration. Good for revision.

Printable worksheet with four exercises for students on linear motion under constant acceleration. Answers are not included.

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.

Fact-sheet that examines the theory of bodies falling freely under gravity using a worked example.

Numerical Computing with MATLAB is a textbook for an introductory course in numerical methods, MATLAB, and technical computing. It emphasizes the informed use of mathematical software. Topics include matrix computation, interpolation and zero finding, differential equations, random numbers, and Fourier analysis.

Fact-sheet that examines overtaking. Three questions are presented and explained.

Fact-sheet with a worked example on the use of the parallel axes theorem.