Course Description, Outcomes, and Required Materials

Math 2: College Algebra for Calculus

Course Description

Develops the skills and introduces the concepts necessary
for further study in mathematics, and facilitate the
application of those skills and concepts to other fields.
Included is a review of elementary set algebra; the
algebra of functions; the real and complex numbers as a
field; algebraic, exponential, and logarithmic functions;
equations and inequalities of these functions; solution
of linear systems, matrix algebra, and introduction to
sequences and series.

  • CRN: 80332

  • Number of Units: 4

  • Prerequisites: C or better in Math 104 or appropriate multiple measures placement

  • Co-requisites: None

  • Advisories:

Develops the skills and introduces the concepts necessary
for further study in mathematics, and facilitate the
application of those skills and concepts to other fields.
Included is a review of elementary set algebra; the
algebra of functions; the real and complex numbers as a
field; algebraic, exponential, and logarithmic functions;
equations and inequalities of these functions; solution
of linear systems, matrix algebra, and introduction to
sequences and series.

 

Course Objectives

Upon successful completion of the course, a student should be able to demonstrate the following activities:

 Solve systems of equalities and inequalities.
 Solve linear, nonlinear and absolute value inequalities.
 Formulate a mathematical model by interpreting given information and obtain and interpret the solution.
 Prove statements by means of mathematical induction.
 Analyze conic sections algebraically and graphically.
 Use formulas to find the sums of finite and infinite series.
 Apply techniques for finding zeros of polynomials and roots of equations.
 Apply functions and other algebraic techniques to model real-world STEM applications.
 Solve and apply rational, linear, polynomial, radical, absolute value, exponential and logarithmic equations.
 Recognize the relationship between functions and their inverses graphically and algebraically.
 Synthesize results from the graphs and equations of functions.
 Apply transformations to the graphs of equations.
 Apply arithmetic operations on the complex numbers.
 Analyze and investigate properties of functions.
 Interpret, analyze, and formulate a strategy for the solution of a problem.

Student Learning Outcomes

As a result of successful completion of this course, a student will be able to:

  1. Apply functions as a mathematical tool to model the conceptual ideas of algebra.
  2. Determine relevant information to sketch graphs of functions appropriate to the college algebra curriculum.

Required Course Materials and Technology

Students will be required to purchase an access code for MyMathLab and must have access to a scientific calculator

Course Content Outline

I) Introduction to set theory.

II) The real number system.
A) Definitions and notation.
B) Order and absolute value.

III) Functions.
A) Definitions, notation, evaluation and domain and range.
B) Algebra of functions.
C) Functions as mathematical models.
D) Inverses of functions.
E) Functions including linear, polynomial, rational, radical, absolute value, exponential and logarithmic.
1) Graphs and their interpretation including asymptotic behavior, intercepts and vertices.
2) Transformations of graphs of these functions.
3) Solution of equations involving linear, absolute value, polynomial, radical, rational, exponential, and logarithmic functions.
4) Solution of linear, non-linear and absolute value inequalities.
F) Introduction to polynomial functions.
1) Zeroes of a polynomial.
2) Remainder theorem.
3) Factor theorem.

IV) Analytic Geometry.
A) Points and distance.
B) The line.
C) Conic sections and their properties.

V) The complex number system.
A) Definitions.
1) Algebraic operations.
2) Field properties.
3) Rectangular form.
B) Complex zeros of polynomial functions and equations.

VI) Applied linear algebra.
A) Solution of linear system of equations or inequalities.
1) Graphical solutions
2) Substitution and elimination.
3) Gaussian elimination.
B) Matrix algebra.
1) Addition and multiplication.
2) The inverse matrix.
C) Solution of linear systems by matrix methods.
1) The matrix equation.
2) The augmented coefficient matrix.
D) The determinant and its applications.
1) Cramer's rule.
2) Area (optional).
3) Volume (optional).

VII) Introduction to sequences and series.
A) Sequences and series.
1) Definitions.
2) Arithmetic.
3) Geometric.
B) Proof by mathematical induction.

 

 

 

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