Course Outline & Text
MATH 1314, COLLEGE ALGEBRA [3 Hours, 3 Credits] TEXT: Sullivan, College Algebra (Seventh Ed.)
This course continues investigation of the ideas and processes of Intermediate algebra.
We will
1: Review polynomial algebra, showing some special methods useful in treatment of
high degree polynomials;
2: Examine set algebra, and its application to "or" and "and" compound statements;
3: Discuss solutions of linear and polynomial equations (including inconsistent equations
and identities) and apply them to verbal problems;
4: Describe properties of fractions, roots, and absolute values and solution of equations
and inequalities involving these;
5: Look at graphs in rectangular coordinates for linear functions, polynomials, and
rational functions;
6: Discuss "conic sections" and their corresponding equations;
7: Look at techniques for finding or estimating roots of higher degree polynomials
with integer coefficients;
8: Examine different techniques for solving "2x2" and "3x3" systems of linear equations;
and
9: Examine the domains, ranges, and basic properties of exponential and logarithmic
functions.
If you find you are either under prepared for this course or falling behind in it, talk to me immediately about a special study program or other options for catching up with the discussions!
MATH 1316, TRIGONOMETRY [3 Hours, 3 Credits] TEXT: Lial, Hornsby, Schneider, Trigonometry (Eighth Ed.)
This course describes the basic methods and concepts of both "Theoretical" and "Practical"
Trigonometry, with emphasis on knowledge required for the Calculus sequence, Math
2413-2414, and beyond. After a brief review of algebraic methods, we will
1: Describe basic geometric ideas associated with parallel and perpendicular lines
and triangles (especially, right triangles);
2: Define the six Trigonometric Functions for acute angles in terms of sides of right
triangles;
3: Apply these ideas to calculate values of the Trigonometric Functions, prove some
Basic Identities, "solve" right triangles, and compute distances using "remote measurement"
techniques;
4: Extend the definitions of the Trigonometric Functions to "arbitrary" angles (sometimes
the results are called the "Circular Functions") , and show different computational
techniques;
5: Prove the "Basic Identities" for the Trigonometric Functions (these equations must
be memorized);
6: Examine the relationship between different units of angle measurement (degrees,
radians, revolutions); with application to problems involving rotating objects, and
to the American Revolution;
7: Examine features of the Trigonometric Functions (domains, ranges, graphs, ...)
and their Inverse Functions;
8: Use the Fundamental Identities and algebraic trickery to prove other Identities
and to solve Trigonometric Equations;
9: Derive the "Law of Sines" and the "Law of Cosines", and apply to "solving" triangles
of arbitrary shape; and
10: Apply triangle solution methods and "Heron's Formula" to surveying (calculating
land areas).
Many of the problems in this course require the use of calculators ("Scientific",
but not "Graphing"). I will be using a "TI30X IIS", and will be describing "Button
Sequences" in class for this or others identically programmed. Others will be allowed,
but users are responsible for knowing modifications. When a calculator is used on
a Test, written specification of button sequence should be presented.
Trigonometry requires more memorization than most math courses - be prepared for this!
MATH 1325, MATH ANALYSIS FOR BUSINESS ("BUSINESS CALCULUS") [3 Hours, 3 Credits] TEXT: Lial, Greenwell, Ritchey, CALCULUS with Applications (Eighth Ed.)
This is an introductory calculus course for business majors which stresses the functions
and processes of calculus applied to business and economic problems. We shall
1: Briefly review the concepts and procedures of precalculus algebra,
2: Introduce the concept of limit, and learn how to find limits by visual and computational
methods,
3: Define the derivative, look at its geometrical interpretation, and learn how to
compute derivatives of algebraic, exponential, and logarithmic functions,
4: Apply derivatives to problems of curve sketching and extremization (maxima, minima),
5: Do some cost analysis, including marginal cost, revenue, and profit as derivatives,
6: Examine the mathematics of simple and compound interest (including continuous compounding),
accumulation of annuity value, and loan amortization, and
7: Introduce the concept of integral as antiderivative, limit of a sum, and area (with
some basic applications).
This course is intensive, but not as much so as the two-semester "Engineering Calculus" sequence, partially because trigonometric functions are not involved. Further, emphasis here is on applications in business and finance rather than physics, cardiac output, and engineering.
MATH 2413, CALCULUS I [4 Hours, 4 Credits]
This is the first of a two-semester sequence of courses in calculus for students in
science and engineering. We shall
1: Briefly review the concepts and procedures of precalculus algebra and trigonometry,
2: Introduce the concept of limit, and examine its visual and computational properties,
3: Define the concept of derivative and learn how to compute derivatives of all kinds
of functions,
4: Examine applications of derivatives to problems of curve sketching, extremization,
implicit functions, and related rates, and
5: Introduce the concepts of indefinite integral (antiderivative) and definite integral.
This is an intensive course, requiring understanding of fundamental principles, skill in algebraic manipulations, and detailed knowledge of the properties of the functions involved.