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Catalin Zara
Text Only Version
Last updated:
August 22, 2008
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Teaching
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Classes taught at UMass Boston
Classes taught at Penn State Altoona
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Math 140 - Calculus with Analytic Geometry, I (Spring 04, Fall 04)
- Description: Functions, limits; analytic geometry; derivatives,
differentials, applications; integrals, applications.
- Text: Stewart, Calculus Early Transcendentals, 5th
Edition.
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Math 141 - Calculus with Analytic Geometry, II (Fall 03, Spring 05)
- Description: Derivatives, integrals, applications; sequences and
series; analytic geometry; polar coordinates.
- Text: Stewart, Calculus Early Transcendentals, 5th
Edition.
Classes taught at Yale University
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Math 115 - Calculus of Functions of One Variable (Fall 00, Summer 01)
- Description: Applications of integration, with some formal
techniques and numerical methods. Calculus of further transcendental functions
(inverse trigonometric functions, exponentials, logarithms). Improper
integrals, approximation of functions by polynomials, infinite series.
- Text: Stewart, Single Variable Calculus, 4th Ed.
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Math 118 - Introduction to Functions of Several Variables (Spring 01, Fall 02)
- Description: Calculus of several variables and some linear algebra. Intended for
students in the social sciences, especially Economics.
- Text : Barnett, Ziegler, and Byleen, Applied Mathematics. For
Business, Economics, Life Sciences, and Social Sciences.
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Math 118S - Mathematics for Economists (Summer 02, Summer 03)
- Description: After a brief review of univariate calculus
(sequences, differentiation, chain rule, Taylor series) and an introduction to
linear algebra (linear independence, systems of equations, operation on
matrices, determinants, eigenvectors), the course covers functions of many
variables, partial differentiation, the implicit function theorem and the
inverse function theorem. This allows a study of optimization theory;
unconstrained and constrained optimization are considered.
- Text: Simon and Blume, Mathematics for Economists.
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Math 225 - Linear Algebra and Matrix Theory (Spring 02)
- Description: An introduction to the theory of vector spaces, matrix
theory and linear transformations, determinants, eigenvalues, and quadratic
forms. Some relations to calculus and geometry will also be included.
- Text: Serge Lang, Linear Algebra.
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Math 246 - Ordinary Differential Equations (Fall 01)
- Description: First-order equations, second-order equations, linear
systems with constant coefficients. Numerical solution methods. Geometric and
algebraic properties of differential equations.
- Text: Bruce and DiPrima, Introduction to Differential Equations
and Boundary Value Problems, 7th Ed.
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Math 435 - Differential Geometry (Spring 03)
- Description: Applications of calculus to the study of the geometry
of curves and surfaces in Euclidean space, intrinsic differential geometric
properties of manifolds, and connections with non-Euclidean geometries and
topology. Emphasis on use of computer graphics to enhance ability to visualize
geometric objects. Use of Mathematica.
- Text: M.P. do Carmo, Differential Geometry.
Classes taught at MIT
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Calculus,
Project
Interphase
- Description: Project Interphase is a rigorous seven and half week
residential, academic enrichment, confidence and community building program for
admitted freshmen who will benefit from support in their transition to MIT.
In addition, Project Interphase is designed to provide academic support,
as well as community building opportunities, in order to enhance matriculation,
promote higher retention and greater excellence in participants, both under-represented
minorities (African American, Mexican American, Hispanic/Latino and Native American)
and other students.
- Text: G.F. Simmons, Calculus with Analytic Geometry (in
1998) and C.H. Edwards & D.E. Penney, Calculus with Analytic Geometry
(in 1999).
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18.022 Multivariable Calculus
- Description: 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. Additional material, relevant to
physical theory and applications, in geometry, vector fields, and linear
algebra.
- Text: H.Rogers, Multivariable Calculus with Vectors.
- Recitation instructor. Lectures by H. Rogers.
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18.02A Multivariable Calculus, Intensive
- Description: First half is taught during the last six weeks of the
fall term; covers material in the first half of 18.02 (through double integrals). Second half of 18.02A can be taken
either during IAP (daily lectures) or during the first half of the Spring
term; it covers the remaining material in 18.02.
- Text: Edwards & Penney, Calculus with Analytic Geometry.
- Recitation instructor. Lectures by E. Ionel.
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18.01 Calculus
- Description: Differentiation and integration of functions of one
variable, with applications. Concepts of function, limits, and continuity.
Differentiation rules, application to graphing, rates, approximations, and
extremum problems. Definite and indefinite integration. Fundamental theorem of
calculus. Applications of integration to geometry and science. Elementary
functions. Techniques of integration. Approximation of definite integrals,
improper integrals, and l'Hôpital's rule.
- Text: G.F.Simmons, Calculus with Analytical Geometry.
- Recitation instructor. Lectures by F. Diamond.
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18.095 Mathematics Lecture Series
- Description: Ten lectures by mathematics faculty members on
interesting topics from both classical and modern mathematics. All lectures
accessible to students with calculus background and an interest in
mathematics. At each lecture, reading and exercises are assigned. Students
prepare these for discussion in a weekly problem session.
- Conducted weekly problem sessions
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Coordinator for the Mathematics Tutoring Center, Fall 1998.
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Research Science Institute (RSI), Summer 1998,1999,2000.
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Summer Program for Undergraduate Research (SPUR), Summer 2000
Classes taught at the University of Bucharest
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