Mar 03, 2024  
2016-2017 Catalog 
    
2016-2017 Catalog [PAST CATALOG]

MAT 151 - Introductory Analysis (Pre-Calculus Mathematics)

4 credit hours - Four hours weekly; one term.
This course meets the Mathematics General Education Requirement.

Strengthen algebra and mathematical modeling skills to prepare for further studies in mathematics, engineering, and the sciences. Study equations and graphs including polynomial, rational, exponential, logarithmic, and trigonometric functions. Use trigonometric identities to simplify expressions and solve equations. Explore plane analytic geometry.

Prerequisite(s): Achieve an appropriate score on the mathematics part of the ACT or SAT, or score at an appropriate level on the Mathematics Placement Test, or completion of MAT 012  or MAT 012E  with a grade of at least B.

Note: MAT 151 is open to all qualified students planning to take calculus. Credit is not given for both MAT 151 and MAT 121 or MAT 151 and MAT 141  (formerly MAT 131) or MAT 151 and MAT 142 .

Course Outcomes
Upon successful completion of this course, students will be able to:
 

  • Solves equations involving polynomial, rational, exponential, logarithmic and trigonometric expressions.
    • Determines when an expression of one of these types becomes zero, or when two such expressions are equal, using graphical, numerical, and symbolic manipulation methods.
  • Solves inequalities involving polynomial and rational expressions.
    • Determines when an expression of one of these types is positive or negative, or when one such expression is larger or smaller than another, using graphical, numerical, and symbolic manipulation methods.
  • Graphs polynomial, piece-wise defined, rational, exponential, logarithmic and trigonometric relations, and conic sections.
    • Produces the graph of a relation both by hand and with appropriate technology.
    • Produces the graph of a shifted, reflected, stretched or compressed function given the graph of the original function.
  • Analyzes graphs of linear, polynomial, piece-wise defined, rational, exponential, logarithmic and trigonometric relations.
    • Given a relation or a graph, identifies the analytical characteristics of the relation (e.g. the symmetries, the domain and range of a function, intervals on which a function is increasing or decreasing, extrema).
    • Identifies the analytical characteristics of conic sections.
    • Identifies the transformations that produce a given graph.
    • Uses technology to assist in visualizing graphs.
    • Determines if a graph represents a function and if it is one-to-one.
    • For periodic functions, identifies the amplitude, period and phase shift.
  • Models problems from the social and natural sciences with the appropriate polynomial, exponential, logarithmic and trigonometric functions.
    • Uses the provided data to determine an equation in one variable that can be solved, optimized or evaluated to find an unknown quantity.
  • Performs algebraic operations on functions.
    • Evaluates and simplifies sums, differences, products and quotients of functions.
    • Forms and evaluates the compositions of functions.
    • Finds, where possible, the inverse of a function.
    • Verifies trigonometric identities and uses them to simplify trigonometric expressions.
Core Competencies
Core 1 Communication Core 2 Technology Fluency Core 7 Quantitative Reasoning Core 10 Innovative and Critical Thinking