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21 112: Calculus II
10.00 Credits
Carnegie Mellon University
Indefinite integral, definite integral and applications, techniques of integration, trigonometric functions, functions of several variables, partial derivatives, maximum-minimum problems, Lagrange multipliers, geometric series, Newton's method, applications. Successful completion of 21-111 and 21-112 entitles a student to enroll in any mathematics course for which 21-120 is a prerequisite. 3 hrs. lec., 2 hrs. rec.
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21 112 - Calculus II
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21 120: Differential and Integral Calculus
10.00 Credits
Carnegie Mellon University
Functions, limits, derivatives, logarithmic, exponential, and trigonometric functions, inverse functions; L'Hospital's Rule, curve sketching, Mean Value Theorem, related rates, linear and quadratic approximations, maximum-minimum problems, inverse functions, definite and indefinite integrals, and hyperbolic functions; applications of integration, integration by substitution and by parts. 3 hrs lec., 2 hrs. rec.
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21 120 - Differential and Integral Calculus
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21 122: Integration, Differential Equations and Approximation
10.00 Credits
Carnegie Mellon University
Integration by trigonometric substitution and partial fractions; arclength; improper integrals; Simpson's and Trapezoidal Rules for numerical integration; separable differential equations, first order linear differential equations, homogeneous second order linear differential equations with constant coefficients, series solution, Newton's method, Taylor's Theorem including a discussion of the remainder, sequences, series, power series. 3 hrs lec., 2 hrs. rec.
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21 122 - Integration, Differential Equations and Approximation
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21 123: Calculus of Approximation
5.00 Credits
Carnegie Mellon University
Newton's method, Taylor's Theorem including a discussion of the remainder, sequences, series, power series. 3 hrs. lec., 2 hrs. rec.
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21 123 - Calculus of Approximation
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21 126: Introduction to Mathematical Software
3.00 Credits
Carnegie Mellon University
This course provides an introduction to the use of several software packages, which are useful to mathematics students. Among the packages are Maple and Mathematica for symbolic computing, TeX and LaTeX for mathematical documents, and Matlab for numerical computing. The course will also introduce the mathematical facilities built into spreadsheets such as Excel. The aim of the course is to provide the student with some basic skills in the use of this software without attempting complete coverage. A deeper knowledge of the software will be easy to obtain after completing this course. There are no prerequisites for the course, other than basic computer literacy and a knowledge of elementary mathematics. It is suggested that the course should be taken during the first two years of undergraduate studies.
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21 126 - Introduction to Mathematical Software
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21 127: Concepts of Mathematics
9.00 Credits
Carnegie Mellon University
This course introduces the basic concepts, ideas and tools involved in doing mathematics. As such, its main focus is on presenting informal logic, and the methods of mathematical proof. These subjects are closely related to the application of mathematics in many areas, particularly computer science. Topics discussed include a basic introduction to elementary number theory, induction, the algebra of sets, relations, equivalence relations, congruences, partitions, and functions, including injections, surjections, and bijections. A prerequisite for 15-211. 3 hrs. lec., 2 hrs. rec.
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21 127 - Concepts of Mathematics
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21 132: Analysis II
10.00 Credits
Carnegie Mellon University
A continuation of Analysis I. L'Hospital's rule; trigonometric, logarithmic, and exponential functions; techniques of integration; approximation by polynomials, Taylor's theorem; sequences, series, power series; introduction to linear differential equations. 3 hrs. lec., 2 hrs. rec.
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21 132 - Analysis II
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21 200: Undergraduate Seminar
6.00 Credits
Carnegie Mellon University
No course description available.
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21 200 - Undergraduate Seminar
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21 201: Undergrad Colloquium
1.00 Credits
Carnegie Mellon University
All mathematics majors meet for one hour each week to hear discussions on current research by faculty or students, presentations on mathematics from mathematicians outside academia, and expository talks on selected mathematical topics not part of the usual curricula. Also will include topics of special interest to undergraduates such as preparation for graduate school.
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21 201 - Undergrad Colloquium
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21 228: Discrete Mathematics
9.00 Credits
Carnegie Mellon University
The techniques of discrete mathematics arise in every application of mathematics, which is not purely continuous, for example in computer science, economics, and general problems of optimization. This course introduces two of the fundamental areas of discrete mathematics: enumeration and graph theory. The introduction to enumeration includes permutations, combinations, and topics such as discrete probability, combinatorial distributions, recurrence relations, generating functions, Ramsey's Theorem, and the principle of inclusion and exclusion. The introduction to graph theory includes topics such as paths, walks, connectivity, Eulerian and Hamilton cycles, planar graphs, Euler's Theorem, graph coloring, matchings, networks, and trees. 3 hrs. lec, 1 hr. rec.
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21 228 - Discrete Mathematics
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