PENN SUMMER - University of Pennsylvania
PENN SUMMER - University of Pennsylvania
PENN SUMMER - University of Pennsylvania
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sentences, and meanings; language in culture and society; language<br />
change over time; language acquisition and processing; comparison<br />
with non-human communication systems.<br />
MaTheMaTiCS<br />
MaTh 103 910 MTWr 1:00pm–3:10pm staff<br />
Introduction to Calculus<br />
Fulfills Formal Reasoning Course<br />
Introduction to concepts and methods <strong>of</strong> calculus for students with<br />
little or no previous calculus experience. Polynomial and elementary<br />
transcendental functions and their applications, derivatives, extremum<br />
problems, curve-sketching, approximations; integrals and the<br />
fundamental theorem <strong>of</strong> calculus.<br />
MaTh 104 910 MTWr 1:00pm–3:10pm staff<br />
Calculus I<br />
Fulfills Formal Reasoning Course<br />
Brief review <strong>of</strong> High School calculus, applications <strong>of</strong> integrals, transcendental<br />
functions, methods <strong>of</strong> integration, infinite series, Taylor’s<br />
theorem. Use <strong>of</strong> symbolic manipulation and graphics s<strong>of</strong>tware in<br />
calculus.<br />
AdditionAl Section:<br />
MATH 104 911 MTWr 1:00pm–3:10pm staff<br />
MaTh 104 936 MTWr 1:00pm–3:10pm rimmer<br />
Calculus, Part I<br />
This course is delivered in a fully online format in order to allow more<br />
flexibility for LPS students. Class sessions are <strong>of</strong>fered through a course<br />
website and include live lectures and interactive discussions through both<br />
direct messaging and voice over internet. Between classes, the learning<br />
experience is extended through assignments, threaded discussions and<br />
<strong>of</strong>fice hours. For additional information, please visit www.sas.upenn.edu/<br />
lps/online. Online course fee: $60.<br />
Fulfills Formal Reasoning Course<br />
Brief review <strong>of</strong> high school calculus, applications <strong>of</strong> integrals, transcendental<br />
functions, methods <strong>of</strong> integration, infinite series, Taylor’s<br />
theorem. Use <strong>of</strong> symbolic manipulation and graphics s<strong>of</strong>tware in<br />
calculus.<br />
MaTh 114 910 MTWr 1:00pm–3:10pm staff<br />
Calculus II<br />
Fulfills Formal Reasoning Course / Prerequisite(s): MATH 104<br />
Functions <strong>of</strong> several variables, vector-valued functions, partial derivatives<br />
and applications, double and triple integrals, conic sections,<br />
polar coordinates, vectors and analytic geometry, first and second order<br />
ordinary differential equations. Applications to physical sciences.<br />
Use <strong>of</strong> symbolic manipulation and graphics s<strong>of</strong>tware in calculus.<br />
MaTh 115 910 MTWr 4:00pm–6:10pm staff<br />
Calculus, Part II with Probability and Matrices<br />
Fulfills Formal Reasoning Course / Prerequisite(s): MATH 104<br />
Functions <strong>of</strong> several variables, partial derivatives, multiple integrals,<br />
differential equations; introduction to linear algebra and matrices with<br />
applications to linear programming and Markov processes. Elements <strong>of</strong><br />
probability and statistics. Applications to social and biological sciences.<br />
Use <strong>of</strong> symbolic manipulation and graphics s<strong>of</strong>tware in calculus.<br />
MaTh 170 910 MTWr 4:00pm–6:10pm staff<br />
Ideas in Mathematics<br />
Fulfills Formal Reasoning Course / May also be counted toward the General<br />
Requirement in Natural Science & Mathematics<br />
Topics from among the following: logic, sets, calculus, probability,<br />
history and philosophy <strong>of</strong> mathematics, game theory, geometry, and<br />
their relevance to contemporary science and society.<br />
MaTh 240 910 MTWr 1:00pm–3:10pm staff<br />
Calculus III<br />
Prerequisite(s): Calculus II<br />
Linear algebra: vectors, matrices, systems <strong>of</strong> linear equations, eigenvalues<br />
and eigenvectors. Vector calculus: functions <strong>of</strong> several variables,<br />
vector fields, line and surface integrals, Green’s, Stokes’ and<br />
divergence theorems. Series solutions <strong>of</strong> ordinary differential equations,<br />
Laplace transforms and systems <strong>of</strong> ordinary differential equations.<br />
Use <strong>of</strong> symbolic manipulation and graphics s<strong>of</strong>tware.<br />
MaTh 241 910 MTWr 1:00pm–3:10pm staff<br />
Calculus IV<br />
Prerequisite(s): MATH 240<br />
Sturm-Liouville problems, orthogonal functions, Fourier series, and<br />
partial differential equations including solutions <strong>of</strong> the wave, heat<br />
and Laplace equations, Fourier transforms. Introduction to complex<br />
analysis. Use <strong>of</strong> symbolic manipulation and graphics s<strong>of</strong>tware.<br />
MaTh 361 910 MTWr 10:00am–12:10pm staff<br />
Advanced Calculus<br />
Prerequisite(s): MATH 360<br />
Continuation <strong>of</strong> MATH 360.<br />
MaTh 371 910 MTWr 1:00pm–3:10pm staff<br />
Algebra<br />
Prerequisite(s): MATH 370 / Students who have already received credit for<br />
either MATH 370, 371, 502 or 503 cannot receive further credit for MATH<br />
312 or MATH 313/513. Students can receive credit for at most one <strong>of</strong> MATH<br />
312 and MATH 313/513.<br />
Continuation <strong>of</strong> MATH 370.<br />
MaTh 420 910 MTWr 1:00pm–3:10pm staff<br />
Ordinary Differential Equations<br />
Prerequisite(s): MATH 241 or permission <strong>of</strong> instructor<br />
After a rapid review <strong>of</strong> the basic techniques for solving equations, the<br />
course will discuss one or more <strong>of</strong> the following topics: stability <strong>of</strong><br />
linear and nonlinear systems, boundary value problems and orthogonal<br />
functions, numerical techniques, Laplace transform methods.<br />
MUSiC<br />
MusC 021 910 Tr 5:30pm–8:40pm Frank<br />
1000 Years <strong>of</strong> Musical Listening<br />
Fulfills Arts & Letters Sector<br />
In this historical survey, students learn to listen analytically, historically,<br />
and creatively to music from the Middle Ages to the present<br />
day. A wide range <strong>of</strong> musical repertories including plainchant, opera,<br />
orchestral music, and chamber music is covered. Composers studied<br />
include Bach, Mozart, Beethoven, Verdi, and Wagner. No prior musical<br />
knowledge is required.<br />
<strong>SUMMER</strong> SESSIOn I • MAY 24–JULY 2, 2010 21