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.

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Seminar focuses on core issues and approaches in anthropological theory and method. Studies theoretical frameworks for the analysis and integration of material from other subjects in cultural anthropology. Subject provides instruction and practice in writing and revision whereby students produce one paper that is appropriate for publication or as a proposal for funding. This course introduces students to some of the major social theories and debates that inspire and inform anthropological analysis. Over the course of the semester, we will investigate a range of theoretical propositions concerning such topics as agency, structure, subjectivity, history, social change, power, culture, and the politics of representation. Ultimately, all theories can be read as statements about human beings and the worlds they create and inhabit. We will approach each theoretical perspective or proposition on three levels: (1) in terms of its analytical or explanatory power for understanding human behavior and the social world; (2) in the context of the social and historical circumstances in which they were produced; and (3) as contributions to ongoing dialogues and debate.

CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

In this module we begin by discussing integrations of complex functions over complex curves and end with Cauchy's Theorem.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

A short introduction to writing Content MathML by hand. It covers tokens, prefix notation, and applying functions and operators. In addition it introduces writing derivatives, integrals, vectors, and matrices.

This book covers the following topics: Sequences, limits, and difference equations; functions and their properties; best affine approximations; integration; polynomial approximations and Taylor series; transcendental functions; the complex plane; differential equations.

This graduate course is in three Parts. Together they are intended to provide theoretical, empirical, and policy perspectives on source and consequences of globalization, focusing on emergent structures and processes, and on the implications of flows of goods and services across national boundaries - with special attention to the issue of migration, on the assumption that people matter and matter a lot. An important concern addressed pertains to the dilemmas of international policies that are shaped by the macro-level consequences of micro-level behavior.

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.

This course analyzes the basic techniques for the efficient numerical solution of problems in science and engineering.

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.

This course will introduce the student to United States history from the end of the Civil War to the present era. The student will learn about the major political, economic, and social changes that took place in America during this 150-year period. By the end of the course, the student will understand how the United States grew from a relatively weak and divided agricultural nation into a cohesive military and industrial superpower by the beginning of the twenty-first century. Upon completion of this course, the student will be able to: Identify the objectives of presidential and congressional Reconstruction following the Civil War and assess the impact of Reconstruction on Caucasian and African-American residents of the American South; Identify the origins of industrialization in the United States and assess its impact on native-born Americans and immigrants in the post-Civil War era; Compare and contrast American settlement of the trans-Mississippi West in the post-Civil War era with American economic expansion into Latin America and the Pacific Ocean in the late nineteenth century; Identify the origins of political and social reform movements in the United States in the late nineteenth century and assess how these movements altered political, economic, and social life throughout the United States in the early twentieth century; Describe how and why America became involved in World War I and assess the impact of American involvement on the postwar peace settlement; Explain how the Great Depression and World War II reshaped American society and politics; Explain how the Cold War and the Civil Rights Movement altered America's standing in the global community and reshaped political and social institutions at home; Identify the origins of American military involvement in Vietnam and assess how the war led to social, political, and economic turmoil throughout the United States in the 1960s and 1970s; Explain America's place within the global community and evaluate how political and social trends in the 1980s and 1990s have shaped contemporary life in the United States; Analyze and interpret primary source documents from the nineteenth through the twenty-first centuries, using historical research methods. (History 212)

Presents an overview of major issues related to the design, function, management, regulation, and evaluation of health insurance and managed care plans. Provides a firm foundation in basic concepts pertaining to private and public sector health insurance/benefit plans, both as provided by employers and government agencies such as Medicaid and Medicare. Key topics include population care management techniques, provider payment, organizational integration, quality and accountability, cost-containment, and public policy. The course makes extensive use of outside experts Course is relevant for management- or policy-oriented students who will be working in, or interrelating with, public and private (both for-profit and not-for-profit) health insurance plans and organized delivery systems such as HMOs and hospital/physician "integrated" delivery systems. Course is also relevant to students who will be researching and analyzing these systems. Although the emphasis is placed on the US, the material is applicable to international students who are interested in financing and organization of highly developed medical care delivery systems in other nations.

A basic introduction to Calculus and Linear Algebra. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline. The first week covers differential calculus: graphing functions, limits, derivatives, and applying differentiation to real-world problems, such as maximization and rates of change. The second week covers integral calculus: sums, integration, areas under curves and computing volumes. This is not meant to be a comprehensive calculus course, but rather an introduction to the fundamental concepts. The third and fourth weeks introduce some basic linear algebra: vector spaces, linear transformations, matrices, matrix operations, and diagonalization. The emphasis will be on using the results, not on their proofs.

looks at the 1968 Supreme Court ruling that ended a decade of resistance to school desegregation in the South (1955-1964) and triggered massive integration of schools (1968-1973). The New Kent and George W. Watkins schools illustrated typical characteristics of a southern rural school system that achieved token desegregation following the Brown decision.

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.

Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.

Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.

This course examines how numerical methods are used by engineers to translate the language of mathematics and physics into information that may be used to make engineering decisions. Often, this translation is implemented so that calculations may be done by machines (computers). Upon successful completion of this course, the student will be able to: Quantify absolute and relative errors; Distinguish between round-off and truncation errors; Interconvert binary and base-10 number representations; Define and use floating-point representations; Quantify how errors propagate through arithmetic operations; Derive difference equations for first and second order derivatives; Evaluate first and second order derivatives from numerical evaluations of continuous functions or table lookup of discrete data; Describe situations in which numerical solutions to nonlinear equations are needed; Implement the bisection method for solving equations; List advantages and disadvantages of the bisection method; Implement both Newton-Raphson and secant methods; Describe the difference between Newton-Raphson and secant methods; Demonstrate the relative performance of bisection, Newton-Raphson, and secant methods; Define and identify special types of matrices; Perform basic matrix operations; Define and perform Gaussian elimination to solve a linear system; Identify pitfalls of Gaussian elimination; Define and perform Gauss-Seidel method for solving a linear system; Use LU decomposition to find the inverse of a matrix; Define and perform singular value decomposition; explain the significance of singular value decomposition; Define interpolation; Define and use direct interpolation to approximate data and find derivatives; Define and use NewtonŐs divided difference method of interpolation; Define and use Lagrange and spline interpolation; Define regression; Perform linear least-squares regression and nonlinear regression; Derive and apply the trapezoidal rule and Simpson's rule of integration; Distinguish Simpson's method from the trapezoidal rule; Estimate errors in trapezoidal and Simpson integration; Derive and apply Romberg and Gaussian quadrature for integration; Define and distinguish between ordinary and partial differential equations; Implement Euler's methods for solving ordinary differential equations; Investigate how step size affects accuracy in Euler's method; Implement and use the Runge-Kutta 2nd order method for solving ordinary differential equations; Apply the shooting method to solve boundary-value problems; Define Fourier series and the Fourier transform; Find Fourier coefficients for a given data set or function and domain; Describe the finite element method for one-dimensional problems. (Mechanical Engineering 205)