SANTA BARBARA CITY COLLEGE
ASSOCIATE
DEGREE CREDIT COURSE OUTLINE
Department: Mathematics
Subject
Area and Course Number: Mathematics 131
Course
Title: Calculus for Biological Sciences, Social Sciences and
Business II
Discipline:
Mathematics
Units: 3
Repeatability: None
Catalog
Course Description: Techniques of integration for single
and multivariable calculus, functions of several variables, partial
differentiation, maxima/minima problems, differential equations, and
probability. Optional topics:
infinite series, TaylorÕs Theorem and the calculus of trigonometric functions.
Description
for Schedule of Classes: Calculus of single and several
variables, partial differentiation, multiple integration, extrema problems and
differential equations, and probability.
Optional: infinite series, TaylorÕs Theorem and the calculus of
trigonometric functions.
Lecture
Hours per Week: 3.3 (48-54 Total Semester Hours)
Laboratory
Hours per Week: None
Plus
hours: None
Prerequisites: Math 130, with a minimum grade of a ÒC.Ó
Co-Requisites: None
Skills
Advisories: Eligibility for English 100 or English
103
Course
Advisories: None
Limitation
on Enrollment: None
Course
Objectives: By the end of the course, students will be able to:
1. Demonstrate
an understanding of multivariable functions and their applications in business,
economics, and life sciences.
2. Demonstrate
an understanding of single and multiple definite integrals.
3. Demonstrate
an understanding of differential equations in the modeling of physical phenomena.
4. Demonstrate
the ability to find exact solutions to differential equations using analytical
methods.
5. Demonstrate
the ability to estimate solutions to differential equations using numerical
approximation techniques.
6. Discriminate
between those differential equations with solutions that need to be
approximated and those that do not.
7. Use
the above concepts to solve problems in business, economics, and life sciences
Course Content and Scope:
I. Multivariable
Calculus
A. Functions
of Several Variables
B. Level
Curves and Contour Diagrams
C. Partial
Derivatives
D. Maxima and Minima
E. The Method
of Least Squares (Optional)
F. Double
Integrals
G. Applications
II. Calculus
and Probability
A. Basic
Concepts: Finite Random Variables
B. Continuous
Random Variables
C. Exponential
and Normal Random Variables
III. Sequences and Series
A. Sequences
B. Series
C. Taylor
Series
D. NewtonÕs Method
(Optional)
IV. Differential
Equations
A. Separable
Differential Equations
B. Applications
of Differential Equations
C. Slope
Fields and Euler's Method
Methods of Instruction: Lecture is the primary activity in class with student problem
solving. Students are also
expected to work outside of class on assigned exercises, reading from the text
and supplemental reading as determined by the instructor.
Required Assignments:
A. Appropriate
Readings: Students are
required to read assigned sections in text or supplements. Outside readings are generally not
required.
B. Writing
Assignments: Students must
work assigned mathematical problems requiring the manipulation of abstract
symbols.
C. Appropriate
Outside Assignments: Students
are expected to spend a sufficient amount of time outside of class to practice
techniques presented during class time, read assigned materials, and complete
frequent homework assignments.
D. Appropriate
Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills which involve
analyzing information, recognizing concepts in new contexts, and drawing
analogies.
Methods of Evaluation: A
studentÕs grade will be based on multiple measures of performance in the
solving of algebraic problems, preparation and analysis of graphs, and analysis
of logical arguments. Such
measures may include at least three exams and a comprehensive final examination
requiring demonstration of problem- solving skills. In addition, instructors may make use of quizzes, written
homework assignments, or other appropriate means to judge a studentÕs dexterity
with algebra skills, and familiarity with mathematical vocabulary. Calculator
(or computer use) is incorporated in the courses. Students should be able to perform differentiation and some
basic integration "by hand."
Appropriate Texts and Supplies:
Hoffman,
Bradley, Applied Calculus, 9th Ed., 2007
TI-84
Graphing Calculator
Student Learning Outcomes:
1.
Determine
extreme values of functions of several variables.
2.
Set
up and evaluate double integrals that represent areas and volumes.
3.
Solve
separable and linear differential equations.
4.
Set
up, evaluate, and interpret integrals of probability density functions.
CO/mej/FRC
(WPC)
April
21, 2003; 8/24/09