This is a four unit module. The first two units cover the basic concepts of the differential and integral calculus of functions of a single variable. The third unit is devoted to sequences of real numbers and infinite series of both real numbers and of some special functions. The fourth unit is on the differential and integral calculus of functions of several variables.
Analysis I in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.
Introduction to Sociology 2e adheres to the scope and sequence of a typical, one-semester introductory sociology course. It offers comprehensive coverage of core concepts, foundational scholars, and emerging theories, which are supported by a wealth of engaging learning materials. The textbook presents detailed section reviews with rich questions, discussions that help students apply their knowledge, and features that draw learners into the discipline in meaningful ways. The second edition retains the book’s conceptual organization, aligning to most courses, and has been significantly updated to reflect the latest research and provide examples most relevant to today’s students. In order to help instructors transition to the revised version, the 2e changes are described within the preface.
Understand types of economic systems and their historical development
Describe capitalism and socialism both in theory and in practice
Discussion how functionalists, conflict theorists, and symbolic interactionists view the economy and work
" This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods."
Examines the relationship between popular and high culture and the problem of evaluating texts that tell stories. Treats a range of narrative and dramatic works as well as films. May be repeated for credit, with permission of instructor. Topic for Fall: Masterminds. Topic for Spring: Popular Culture in the Age of Media Convergence. Our purpose is to consider some of the most elaborate and thoughtful efforts to define and delineate "all-mastering," and to consider some of the delineations of "all-mastering the intellect" in various guises - from magicians to master spies to detectives to scientists (mad and otherwise). The major written work of the term will be an ongoing reading journal, which you will circulate to your classmates using an e-mail mailing list. The use of that list is fundamental - it is my intention to generate a sort of ongoing cyberconversation.
Principles of Macroeconomics 2e covers the scope and sequence of most introductory economics courses. The text includes many current examples, which are handled in a politically equitable way. The outcome is a balanced approach to the theory and application of economics concepts. The second edition has been thoroughly revised to increase clarity, update data and current event impacts, and incorporate the feedback from many reviewers and adopters. Changes made in Principles of Macroeconomics 2e are described in the preface and the transition guide to help instructors transition to the second edition. The first edition of Principles of Macroeconomics by OpenStax is available in web view here.
By the end of this section, you will be able to:
Explain economic convergence
Analyze various arguments for and against economic convergence
Evaluate the speed of economic convergence between high-income countries and the rest of the world
This course is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. Upon successful completion of this course, students will be able to: Define and describe the indefinite integral; Compute elementary definite and indefinite integrals; Explain the relationship between the area problem and the indefinite integral; Use the midpoint, trapezoidal, and Simpson's rule to approximate the area under a curve; State the fundamental theorem of calculus; Use change of variables to compute more complicated integrals; Integrate transcendental, logarithmic, hyperbolic, and trigonometric functions; Find the area between two curves; Find the volumes of solids using ideas from geometry; Find the volumes of solids of revolution using disks, washers, and shells; Find the surface area of a solid of revolution; Compute the average value of a function; Use integrals to compute displacement, total distance traveled, moments, centers of mass, and work; Use integration by parts to compute definite integrals; Use trigonometric substitution to compute definite and indefinite integrals; Use the natural logarithm in substitutions to compute integrals; Integrate rational functions using the method of partial fractions; Compute improper integrals of both types; Graph and differentiate parametric equations; Convert between Cartesian and polar coordinates; Graph and differentiate equations in polar coordinates; Write and interpret a parameterization for a curve; Find the length of a curve described in Cartesian coordinates, described in polar coordinates, or described by a parameterization; Compute areas under curves described by polar coordinates; Define convergence and limits in the context of sequences and series; Find the limits of sequences and series; Discuss the convergence of the geometric and binomial series; Show the convergence of positive series using the comparison, integral, limit comparison, ratio, and root tests; Show the divergence of a positive series using the divergence test; Show the convergence of alternating series; Define absolute and conditional convergence; Show the absolute convergence of a series using the comparison, integral, limit comparison, ratio, and root tests; Manipulate power series algebraically; Differentiate and integrate power series; Compute Taylor and MacLaurin series; Recognize a first order differential equation; Recognize an initial value problem; Solve a first order ODE/IVP using separation of variables; Draw a slope field given an ODE; Use Euler's method to approximate solutions to basic ODE; Apply basic solution techniques for linear, first order ODE to problems involving exponential growth and decay, logistic growth, radioactive decay, compound interest, epidemiology, and Newton's Law of Cooling. (Mathematics 102; See also: Chemistry 004, Computer Science 104, Mechanical Engineering 002)