Calculus For The Sciences
MATH 1225-1226
I - Catalogue Description
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Unified calculus course covering techniques of differential and integral calculus
for functions of one variable. This sequence constitutes the standard first-year
mathematics courses for science and engineering. 1225: limits, continuity,
differentiation, transcendental functions, applications of differentiation,
introduction to integration. 1226: techniques and applications of integration,
trapezoidal and Simpson’s rules, improper integrals, sequences and series,
power series, parametric curves and polar coordinates, software-based
techniques. 1225 partially duplicates 1205, 1016 and 1525. 1226 partially
duplicates 1206 and 2015. Pre 1225: 2 units of high school algebra, 1 unit of
geometry, 1/2 unit each of trigonometry and precalculus and placement by Math
Dept.; or a grade of B or better in one of 1015, 1016, or 1536; or a passing grade
on the Calculus Readiness Exam; Pre 1226: 1225. I, II, III (4H,4C)
Course Number:
1225-1226
ADP TITLE: Calc Sci
II - Learning Objectives
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Having successfully completed this sequence, the student will be able to
• Calculate limits, derivatives, and integrals of functions of a single variable
• Employ various techniques to calculate integrals of functions of standard
types
• Produce graphical representations of functions using calculus techniques
• Use polar coordinate representations to plot regions and curves
• Calculate areas of plane regions by means of integration
• Determine the convergence or divergence of infinite series
• Employ these skills in a variety of applied problems
• Use contemporary software to implement calculations
III - Justification
This sequence constitutes the freshman year of a redesigned suite of calculus
courses for science and engineering. The redesign is closely coordinated with
the standard AP curriculum and with courses taken by transfer students at
regional colleges. The redesigned suite reduces the total number of courses
from 6 to 4 and organizes the material in a more natural way.
As the freshman year component of the suite, 1225-6 carries a 1000-level
number. In a transition period courses from both the old and new suites will be
offered simultaneously. To avoid confusion courses from the new suite have
course numbers and titles distinct from the old.
IV - Prerequisites and Corequisites
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Because of the high demand for this course and its critical role for virtually all
technical majors it is important to minimize the failure rate due to students
enrolling without adequate preparation. The prerequisite criteria for the entry
course (1225) have been designed by the Mathematics Department through
years of teaching to identify those circumstances under which students can
expect to succeed. These are the same as the current criteria for 1205; see
http://www.math.vt.edu/courses/math1205/resources/courseinfo.html and
http://www.emporium.vt.edu/Readiness/Test.html .
V - Texts and Special Teaching Aids
Required text:
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Hass, Joel; Weir, Maurice D. and Thomas, George B., Jr. UNIVERSITY
CALCULUS: EARLY TRANSCENDENTALS, I, ii, Addison-Wesley, Boston
Massachusetts MA, 2007, 916.
VI - Syllabus
1225:
1. Limits and continuity
2. Derivatives
Basic theory
Rules of differentiation
Implicit differentiation and inverse functions
Related rates
Linearization and Newton’s method
Extreme and mean value theorems
Curve sketching
Indeterminant forms, L’Hopital’s rule
Applied optimization
3. Integration
Basic concepts
15%
5%
15%
5%
5%
5%
5%
5%
5%
10%
5%
3%
10%
10%
5%
10%
5%
5%
5%
7%
10%
10%
5%
5%
10%
⎯⎯
100%
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1226:
1. Integration
Review
Volume calculations
Work and centers of mass
Integration by parts
Trigonometric integrals
Rational functions
Tables and numerical methods
Improper integrals
2. Sequences and series
Introduction and concepts
Convergence tests
Power series
3. Parametric curves
4. Polar coordinates
5. Labs and software implementation
10%
10%
⎯⎯
100%
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Antidifferentiation and fundamental theorem
Indefinite integrals and substitution
VII - Old (current) Syllabus {in the case of a revised course}
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VIII - Core Curriculum guidelines {if inclusion in the University Core is
desired}
Goals for Area 5
1. Increase basic competence in quantitative reasoning and problem solving,
starting at an appropriate entry level;
2. Understand some fundamental principles of reasoning that are involved in
mathematics or logic;
3. Understand quantitative and symbolic reasoning through the study of
significant applications of mathematical sciences.