NorthWest Arkansas Community College
Division of Science and Mathematics
Fall 2005
Course Outline
Course:
Math 2043, Survey of Calculus
Catalog Description:
A survey and applications course in calculus designed for students in business, life sciences and social sciences. Topics
include a brief algebra review, differentiation, curve sketching, exponential and logarithmic functions with applications,
integration and, when time permits, multivariable calculus.
Prerequisite: Math 1204 with grade of C or better, or 24 on Math portion of the ACT, or 46 – 100 on the College Algebra
portion of the Compass.
Credit/Contact/Load hours: 3 credit hours/ 3 contact hours/ 3 load hours
Target Audience and Transfer
This course is targeted primarily to students in business and life or social sciences. It is required of some AAS
and AS degrees as well as a variety of four-year programs. It transfers as 3 credit hours of business calculus.
General Course Objectives
Upon successful completion of this course students should exhibit mastery of certain knowledge and basic
skills. These topics will include, but not be limited to:
1) Algebraically and graphically evaluate limits
2) Find basic derivatives using the definition, product, quotient and chain rules
3) Understand and be able to apply derivatives appropriately to real-world problems to optimize functions,
find instantaneous rates of change, marginal cost, marginal profit, etc.
4) Graph functions by hand, including manually finding the extrema using the first derivative test, intervals
where the graph is increasing and decreasing, and finding points of inflection
5) Integrate “basic” integrals including polynomial functions, natural exponential functions, and basic usubstitutions.
6) Relative rates and elasticity of demand
7) Areas between curves
8) Be able to apply integrals appropriately to find the average value, accumulated value, consumer’s surplus and producer’s
surplus
9) Partial Derivatives
10) Optimize functions of several variables, including constrained optimization and Lagrange Multipliers
Required Text: Brief Applied Calculus, 3rd Edition. Berresford, Rockett. Houghton Mifflin, 2004.
Required Content:
Section
Topic
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Limits and Continuity
Slopes, Rates of Change, and Derivatives
Some Differentiation Formulas
The Product and Quotient Rules
Higher-Order Derivatives
The Chain Rule and the Generalized Power Rule
Nondifferentiable Functions
3.1
3.2
3.3
3.4
3.6
Graphing Using the First Derivative
Graphing Using the First and Second Derivatives
Optimization
Further Application of Optimization
Implicit Differentiation and Related Rates
4.1
4.2
4.3
Exponential Functions
Logarithmic Function
Differentiation of Logarithmic and Exponential Functions
4.4
Two Applications to Economics: Relative Rates and Elasticity of
Demand
5.1
5.2
5.3
5.4
5.6
Antiderivatives and Indefinite Integrals
Integrations Using Logarithmic and Exponential Functions
Definite Integrals and Areas
Further Applications of Definite Integrals: Average Value and Area
Between Curves
Two Applications to Economics: Consumers’ Surplus and Income
Distribution
Integration by Substitution
7.1
7.2
7.3
7.5
Functions of Several Variables
Partial Derivatives
Optimizing Functions of Several Variables
Lagrange Multipliers and Constrained Optimization
5.5
Note: A variety of application problems from each required topic should be assigned
Optional Sections
1.1, 1.2, 1.3, 1.4, 3.5, 6.1, 6.2, 6.3, 6.4, 6.5, 6.5, 7.4, 7.6, 7.7
Required Instructional Activities
The content of the course should be taught with graphing calculators as an available tool when appropriate.
Required Forms of Assessment
Each instructor must include a set of 9 departmental final exam questions on his or her final exam.
These questions will be in direct support of the specific objectives stated in the Core Course
Objectives, will be based on material covered in the Required Text Coverage section, and be similar to
the questions on the Departmental Review Sheet for Survey of Calculus. These questions should be
evenly weighted on the final and should compose at least 15% of the students’ overall grade in the
course. The questions will be graded using a departmental grading rubric utilizing a 10-point scale per
question. The results of these questions and overall student performance will be reported when final
grades are turned in. Please note that the only resource other than a graphing calculator allowed
for use by students during the final exam will be a departmental formula sheet for survey of
calculus. It is also a departmental policy that no TI-89 or TI-92 or comparable calculators be
allowed for use during the final exam.
Instructor Resources:
1. Instructor’s Solutions Manual
2. Printed Test Bank
3.
Computerized Test Generator
Student Resources:
1.
Free tutoring at the Math Café and the Learning Lab
2.
Student Solutions Manual
3.
Smarthinking—Live on-line tutoring
4.
Companion Website for students at math.college.hmco.com/students
5.
Videos available through the NWACC library