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MATH 110: Finite Mathematics for Business and Economics
3.00 Credits
Catholic University of America
This course introduces students to the fundamental ideas of finite mathematics with examples from and emphasis on business and economics. The main topics are (1) linear functions and models, linear systems and solution by geometric and algebraic methods, matrix methods and linear programming problems in two variables. (2) Fundamentals of financial mathematics including simple and compound interest, annuities, amortization. (3) Sets and basic combinatorial methods for counting: permutations and combinations. (4) Elementary probability concepts including sample spaces, probability of events, conditional probability. Prerequisite: Open to majors in Business/Economics by placement. Not open to students who have taken Math 111.
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MATH 110 - Finite Mathematics for Business and Economics
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MATH 111: Calculus for Social-Life Sciences I
3.00 Credits
Catholic University of America
Functions and their graphs; linear functions; functional models; derivative, rate of change and marginal analysis; approximation by differentials; chain rule, implicit differentiation and higher-order derivatives; curve sketching: relative extrema, concavity; absolute extrema; exponential functions and natural logarithms and their derivatives; compound interest. Not open to students who have had 121. Prerequisite: Placement. For majors in Business and Economics, Placement, or a grade of C- or better in Math 110.
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MATH 111 - Calculus for Social-Life Sciences I
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MATH 112: Calculus for Social-Life Sciences II
3.00 Credits
Catholic University of America
The concept of antiderivative; integration by substitution, by parts, and by use of tables; definite integral; area under a curve; applications to business and economics; definite integral as the limit of a sum; improper integrals; probability density; numerical integration; linear and separable differential equations; functions of several variables, partial derivatives, chain rule and total differential; relative extrema; Lagrange multiplier methods; the least square approximation. Not open to students who have had 122. Prerequisite: a grade of C- or better in 111.
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MATH 112 - Calculus for Social-Life Sciences II
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MATH 114: Probability and Statistics
3.00 Credits
Catholic University of America
Designed for students in the social sciences, to acquaint them with the techniques of elementary statistics. Emphasizes computation and interpretation of data. Topics include calculation and graphing methods, measures of central tendency, measures of variation, measures of association and correlation; sampling and hypothesis testing.
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MATH 114 - Probability and Statistics
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MATH 121: Analytic Geometry and Calculus I
4.00 Credits
Catholic University of America
Coordinate systems, functions, graphs, one-to-one and inverse functions; composition of functions; lines and slopes; limits, continuity, maximum and minimum, derivative of a function of one variable; differentiation of polynomials, chain rule; derivatives of trigonometric functions and their inverses; implicit differentiation; antiderivative and definite integral; fundamental theorem of calculus. Not open to students who have had 111. Prerequisite: Placement.
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MATH 121 - Analytic Geometry and Calculus I
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MATH 122: Analytic Geometry & Calculus II
4.00 Credits
Catholic University of America
Antiderivative and definite integral; integration by parts and by substitution; integration of rational functions, powers of trigonometric functions, and rational functions of sin and cos; logarithms and exponential functions and their derivatives: application to computing area, volume; center of gravity and work; polar coordinates, parametric equations; arc length and speed on a curve; area of a surface; curvature; sequences and series; convergence tests; Taylor's formula. Not open to students who have had 112. Prerequisite: a grade of C- or better in 121.
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MATH 122 - Analytic Geometry & Calculus II
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MATH 168: Mathematics in the Modern World
3.00 Credits
Catholic University of America
Intended for liberal arts students. Explores mathematical ideas and current applications of these ideas. Topics include mathematical applications in the management sciences and social sciences and applications of geometry to physics, astronomy, chemistry, and biology.
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MATH 168 - Mathematics in the Modern World
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MATH 187: Introduction to Mathematical Thought
3.00 Credits
Catholic University of America
Intended for liberal arts students. Topics chosen from among: basic logic, number theory, infinite sets and cardinal numbers, symmetry and finite groups, graph theory and polyhedra, Euclidean and non-Euclidean geometry, and others.
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MATH 187 - Introduction to Mathematical Thought
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MATH 221: Analytic Geometry & Calculus III
4.00 Credits
Catholic University of America
Partial derivatives and differential; the chain rule: gradient and directional derivative; derivative of a vector function; tangent planes; critical points and local extrema; Lagrange multipliers; integration over regions in R2; use of polar coordinates; integration over regions in R3; use of cylindrical and spherical coordinates; line integrals; conservative vector fields; Green's theorem; surface integrals and divergence theorem; Stokes' theorem. Prerequisite: 122.
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MATH 221 - Analytic Geometry & Calculus III
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MATH 222: Calculus IV Differential Eqns
4.00 Credits
Catholic University of America
Separable and linear differential equations with one unknown function, method of integrating factors; second order linear differential equations with variable coefficients; Wronski and Cauchy methods; systems of linear differential equations with variable and constant coefficients; Euler and Runge-Kutta methods; Laplace transform methods; series solutions of differential equations and special functions. Prerequisite: 221 or permission of instructor.
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MATH 222 - Calculus IV Differential Eqns
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