Abstract: Continues 18.014. Parallel to 18.02, but at a deeper level, emphasizing careful reasoning and understanding of proofs. Considerable emphasis on linear algebra and vector integral calculus. This course is a continuation of 18.014. Covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. Considerable emphasis on linear algebra and vector integral calculus. Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.
Abstract: Introduces and examines the basic principles which guide growth and development and the health of individuals across the lifespan, from the prenatal period through senescence. Presents methodological, conceptual and substantive issues necessary for understanding and evaluating empirically based information about growth, development and health at different stages of life and from different academic perspectives. Course covers several themes, including contributions of biological and environmental factors to health and human development, measuring the health of individuals in communities, understanding determinants and consequences of health and development across the lifespan, measuring population health and assessing the implications of health disparities.
Abstract: Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB. Compared with 18.700, more emphasis on matrix algorithms and many applications.
Abstract: This course covers differentiation and integration of functions of one variable, with applications. Topics in differentiation include the definition of differentiation, rules, application to graphing, rates, approximations, and extremum problems. Topics in indefinite integration include separable first-order differential equations and the fundamental theorem of calculus. Other topics covered include applications of integration to geometry and science, elementary functions, techniques of integration, polar coordinates, L'Hôpital's rule, improper integrals, and infinite series: geometric, p-harmonic, simple comparison tests, and formal power series for some elementary functions. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.
Abstract: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.
Abstract: This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.