Catalog Description: This course covers the applications of algebra and trigonometry to the study of elementary functions and their graphs including polynomial, rational, exponential, logarithmic, and trigonometric functions and may include topics from analytical geometry.
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Semester Credit Hours: 4 Lecture Hours per Week: Contact Hours per Semester: 64 State Approval Code: 2701015800
Perspectives (Those marked with a √ reflect the state-mandated perspectives
taught in this course.)
Establish broad and multiple perspectives
on the individual in relationship to the larger society and world in which
he/she lives, and to understand the responsibilities of living in a culturally
and ethnically diversified world.
Stimulate a capacity to discuss and
reflect upon individual, political, economic, and social aspects of life in
order to understand ways in which to be a responsible member of society.
Recognize the importance
of maintaining health and wellness.
Develop a capacity to use knowledge
of how technology and science affect their lives.
Develop personal values for ethical
behavior.
Develop the ability to make
aesthetic judgments.
Use logical reasoning in problem solving.
Integrate knowledge and understand
the interrelationships of the scholarly disciplines.
Exemplary Objectives (Those marked with a √ reflect state-mandated exemplary
objectives taught in this course.)
Mathematics: The objective of the mathematics component
of the core curriculum is to develop a quantitatively literate college graduate. Every
college graduate should be able to apply basic mathematical tools in the
solution of real-world problems.
To apply arithmetic, algebraic, geometric, higher-order thinking and
statistical methods to modeling and solving real-world situations.
To represent and evaluate basic mathematical information verbally,
numerically, graphically, and symbolically.
To expand mathematical reasoning skills and formal logic to develop
convincing mathematical arguments.
To use appropriate technology to enhance mathematical thinking and
understand and to solve mathematical problems and judge reasonableness
of the results.
To interpret mathematical models such as formulas, graphs, tables
and schematics, and draw inferences from them.
To develop the limitations of mathematical and statistical models.
To develop the view that mathematics is an evolving discipline interrelated
with human culture, and understand its connections to other disciplines.
Instructional Goals and Purposes:
Lee College's instructional goals include 1) creating an academic atmosphere
in which students may develop their intellects and skills and 2) providing
courses so students may receive a certificate/an associate degree or transfer
to a senior institution that offers baccalaureate degrees.
General Course Objectives:
Successful completion of this course will promote the general student learning
outcomes listed below. The student will be able
To improve problem-solving skills through solving application
problems.
To demonstrate at the completion of the course the algebraic
manipulation and problem solving skills that are necessary to be successful
in future coursework.
To develop the vocabulary and methodology necessary for reading
and understanding scientific and mathematical literature.
To construct appropriate mathematical models to solve applications.
To interpret and apply mathematical concepts.
To use multiple approaches - physical, symbolic, and verbal - to
solve application problems.
Specific Course Objectives:
Upon successful completion of the course, the student will be able
To apply coordinate geometry formulas.
To model application problems using functions
To model and solve variation problems.
To perform transformations on functions.
To find real and complex zeros of polynomial functions.
To graph rational, exponential, and logarithmic functions.
To model and solve problems involving exponential and logarithmic
functions.
To model and solve trigonometry problems involving both right
triangles and oblique triangles.
To graph trigonometric functions and their inverses.
To solve trigonometric identities and trigonometric equations.
To write a sum or difference of fractional expressions as
a single fraction.
To model and solve problems involving conic section formulas
for a circle, parabola, ellipse, and hyperbola.
To graph polar and parametric equations.
To model and solve problems involving vectors.
To find limits of functions numerically, algebraically, and
graphically.
To apply the definition of a derivative.
Course Content:
Students will be required to do the following:
Fundamentals and Review
Simplify algebraic expressions, exponents and radicals.
Solve fractional equations and inequalities.
Model and solve problems involving linear equations.
Apply the formulas of coordinate geometry (distance, midpoint).
Write the equation of a circle given its center and radius.
Graph circles, linear functions, and inequalities.
Write equations of linear functions given slope, points, parallel and
perpendicular lines.
Functions
Define a function, domain, and range.
Model and solve problems involving variation functions.
Find the average rate of change, increasing and decreasing intervals,
and extreme values of functions.
Apply transformations to functions.
Model problems using functions.
Combine functions by adding, subtracting, multiplying, dividing, and
composition.
Define one-to-one functions and find their inverses.
Polynomial and Rational Functions
Define a polynomial function and sketch its graph using end behavior,
zeros, local extrema, and test points.
Divide polynomials by using synthetic division.
Define and apply the remainder and the factor theorems.
Find the rational zeros of a polynomial by use of the rational zeros
theorem, Descartes' rule of signs, and the upper/lower bound theorem.
Add, subtract, multiply, and divide complex numbers.
Find the complex roots of quadratic equations.
Apply the Fundamental Theorem of Algebra and the Complete Factorization
Theorem to find the complex roots of a polynomial function.
Write a polynomial function give its complex and real roots.
Find the vertical and horizontal asymptotes of a rational function.
Sketch the graph of a rational function.
Exponential and Logarithmic Functions
Sketch the graph of an exponential and logarithmic function and find
the domain and range.
Model and solve problems involving compound interest.
Define the natural logarithm and its properties.
Apply the Laws of Logarithms to simplify and solve logarithmic equations.
Solve exponential equations.
Model and solve problems involving exponential and logarithmic functions.
Trigonometric Functions of Real Numbers
Define the unit circle and use reference numbers to find terminal points.
Define the trigonometric functions, their even-odd properties, their
signs in different quadrants, and the domains and ranges of each.
Sketch the graphs of the trigonometric functions.
Find the period and amplitude of trigonometric functions.
Graph transformations of the trigonometric functions.
Trigonometric Functions of Angles
Convert between radians and degrees.
Model and solve problems involving the formulas for length of a circular
arc, area of a sector of a circle, and linear and angular speed.
Model and solve problems involving trigonometry of right triangles.
Use reference numbers (unit circle) or reference triangles to evaluate
trigonometric functions.
Apply the Law of Sines and the Law of Cosines to solve oblique
triangle problems.
Analytic Trigonometry
Prove Trigonometric Identities.
Apply the Addition and Subtraction Formulas to problems and identities.
Apply the Sum of Sines and Cosines Formulas.
Apply the Double-Angle and Half-Angle Formulas to problems and identities.
Apply the Product-to-Sum and Sum-to-Product Formulas.
Define and sketch the inverse trigonometric functions.
Solve trigonometric equations involving single and multiple angles.
Vectors
Understand the geometric and the analytic description of vectors.
Find the magnitude, horizontal and vertical components of a vector.
Find the resultant force of two or more vectors.
Apply vectors to model and solve problems involving velocity and force.
Find the dot product of two vectors and use it to find the angle between
the two vectors.
Find the component vector of u along v.
Find the projection of u onto v.
Apply vectors to solve problems involving work.
Partial Fractions
Write a sum or difference of fractional expressions as a single fraction..
Topics in Analytic Geometry
Write the formulas (in standard form) for a parabola, ellipse, and
hyperbola, with a vertical (major) axis and with a horizontal (major)
axis.
Sketch the graphs of shifted conic sections.
Complete the square of a conic equation and sketch its graph.
Write the polar and rectangular forms of a point.
Apply symmetry to sketch the graph of a polar equation.
Convert a polar equation to a rectangular coordinate equation.
Convert a rectangular coordinate equation to a polar equation.
Sketch a parametric equation.
Eliminate the parameter in a parametric equation.
Find the parametric equations for a graph.
Limits: A Preview of Calculus
Find the limit of a function numerically, algebraically, and graphically.
Define a one-sided limit.
Write the definition of a limit.
Apply the Limit Laws.
Find and prove limits by applying right- and left-hand limits.
Write the definition of a derivative.
Find the equation of a line tangent to a curve at a given point.
Find the instantaneous velocity of a falling object.
Find the limit of a function at infinity.
Find the horizontal asymptote of a rational function by applying limits
at infinity.
Methods of Instruction/Course Format/Delivery:
Faculty may choose from but are not limited to the following methods of instruction: lecture,
discussion, Internet, video, television, demonstrations, field trips, collaboration,
readings.
Assessment:
Faculty may assign both in- and out-of-class activities to evaluate students'
knowledge and abilities. Faculty may choose from the following methods:
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