Course Title: Calculus and Analytic
Geometry II
Course No.: MAT 222 No. of Credits:
5 Associate Degree Designation:
MS
Contact hrs/wk: Lecture 5 Lecture/Discussion
Lab
Course Prerequisites: A grade of C or better in MAT 221, or placement
based on the department Calculus Proficiency Test, or AP Exam.
Catalog description: Continuation of 221. Techniques of
integration, polar coordinates, conic sections, infinite series and vectors of
two and three dimensions. Note: The order of topics covered in
MAT 221 and MAT 222 may depend on the text used and the instructor.
Course Content (list of topics normally covered):
Note: Some topics may be omitted if covered in
previous courses.
· Techniques
of Integration
Integration
by Parts
Trigonometric
Integrals
Trigonometric
Substitution
Partial
Fractions
Improper
Integrals
· Polar
Coordinates
Graphing
Finding
Lengths
Finding
Areas
· Conic
Sections
Parabola
Ellipse
Hyperbola
Conic
Sections in Polar Coordinates
· Vectors
of Two and Three Dimensions
Vector
Algebra
Representations
of Lines and Planes
Tangent
and
Curvature
· Infinite
Series
Arithmetic
Series
Geometric
Series
p Series
Ratio
Test
Root
Test
Comparison
Test
Integral
Test
Alternating
Series
Power
Series
Taylor
and Maclaurin Series
Binomial
Series
· Parametric
Curves
Graphing
Derivatives
Finding
Lengths
Finding
Areas
· Other
Applications
Arc
Length
Surface
Area of a Solid of Revolution
Centroids
· Differential
Equations (optional)
Direction
Fields
Separable
Equations
Linear
Equations
Content-based department proficiencies:
·
Be able to find
anti-derivatives of various functions, choosing appropriate methods, including
integration by parts, trigonometric substitution, and partial fractions.
·
Be able to
evaluate improper integrals using appropriate methods.
·
Be able to solve
first order differential equations using the techniques of separation of
variables or integrating factors
·
Be able to switch
freely between a conic section's description, equation, and graph
·
Be able to find
areas and tangent lines of curves described by polar or parametric equations
·
Be able to
determine convergence or diverge of various series, choosing appropriate
methods including ratio test, root test, alternating series test, and integral
test.
·
Be able to
generate
Colleges-wide
proficiencies assigned to course:
Students should be able to demonstrate the
following:
A. Analytical skills Performance Indicators: Students should be
able to:
1. Interpret and synthesize information
and ideas.
4. Select and apply scientific and other
appropriate methodologies.
B. Quantitative skills Performance Indicators: Students should be
able to:
1. Solve quantitative and mathematical
problems.
2. Interpret graphs, tables, and diagrams.
Representative textbooks used for the
courses:
· Calculus: One and Several Variables, 6th ed., Ellis/Gulick
·
Calculus:
Concepts and Contexts, 2nd ed.,
Stewart
·
Single
Variable Calculus, 5th ed., Stewart
·
Calculus with
Analytic Geometry, 4th ed.,
Edwards/Penney
·
Thomas'
Calculus, 10th ed.,
Finney/Weir/Giordano
Approved April 22, 2006