Topical Outline with Specific Course Objectives
- Introduction of Functions, the Properties, Graphs, and Inverses
- Analyze and interpret functions using graphs, tables, and equations.
- Determine domain and range both algebraically and graphically.
- Demonstrate an understanding of both composition and decomposition of functions.
- Construct the inverse of a function, both graphically and algebraically when feasible.
- Demonstrate an intuitive understanding of functions including limits, continuity, increasing, decreasing, maximum and minimum values, symmetry and concavity.
- Demonstrate an understanding of transformations graphically, symbolically, and numerically.
- Graph and write equations for piecewise-defined functions.
- Polynomial and Rational Functions
- Identify multiplicities of zeros and their effect on the graph.
- Create graphs and write equations given sufficient information.
- Use formal limit definitions and limit notation to define the end behavior and vertical and horizontal asymptotes for functions given in numerical, graphical, and symbolic forms.
- Determine when a rational function has a hole and the point at which it occurs.
- Exponential and Logarithmic Functions
- Create graphs and write equations for exponential and logarithmic functions given sufficient information.
- Use formal limit definitions and limit notation to define the end behavior and vertical and horizontal asymptotes for functions given in numerical, graphical, and symbolic forms.
- Demonstrate mastery of the logarithmic properties by applying them in a variety of settings.
- Understand the inverse relationship and use it to solve exponential and logarithmic equations.
- Use exponential, logarithmic, and related functions in science based applications.
- Solving Equations and Inequalities
- Solve non-linear equations and inequalities numerically, graphically, and symbolically.
- Recognize when a solution is approximate and have a rough idea of its accuracy.
- State exact solutions in proper mathematical form.
- Conic Sections
- Identify and graph a conic section from its equation.
- Find the equation of a conic section from its description.
- Identify the attributes of a conic section.
- Matrices
- Perform basic matrix algebra and demonstrate knowledge of the commutative properties.
- Use expansion by cofactors to compute the determinant of matrices up to dimension
- Construct the inverse of a matrix using row operations.
- Use matrices and determinants to solve linear systems of equations.
- Sequences and Series
- Recognize arithmetic and geometric sequences and series in summation or iterative notation.
- Demonstrate an understanding of sequences and series notation by expanding a given formula and by creating a formula for a given expansion.
- Find the sum of a finite series.
- Special Topics
- Apply the Binomial Theorem.
- Demonstrate an understanding of Proof by Induction.
- Department Policies
- Graphing Calculator not allowed on proctored tests or final exam
- Comprehensive Final