(two semester course)
Functions. What is a Function? Domain and Range of a Function. Graphs of Functions. Getting Information from the Graph of a Function. Average Rate of Change of a Function. Transformations of Functions. Combining Functions. One-to-One Functions and Their Inverses. Focus on Modeling, Modeling with Functions.
Polar Coordinates and Parametric Equations. Graphs of Polar Equations. Polar Form of Complex Numbers, De Moivre’s Theorem. Plane Curves and Parametric Equations. Focus on Modeling, the Path of Projectile.
Vectors in Two and Three Dimensions. Vectors in Two dimensions. The Dot Product. Three-Dimensional Coordinate Geometry. Vectors in Three Dimensions. The Cross Product. Equations of Lines and Planes. Focus on Modeling, Vector Fields.
Systems of Equations and inequalities. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Matrices and Systems of Linear Equations. The Algebra of Matrices. Inverses of Matrices and Matrix Equations. Determinants and Cramer’s Rule. Partial Fractions. Systems of Nonlinear Equations. Systems of Inequalities. Focus on Modeling.
Conic Sections. Parabolas. Ellipses. Hyperbolas. Shifted Conics. Rotation of Axes. Polar Equations of Conics. Focus on Modeling, Conics in Architecture.
Sequences and Series. Sequence and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Focus on Modeling, Modeling with Recursive Sequences.
A Preview of Calculus. Finding Limits Numerically and Graphically. Finding Limits Algebraically. Tangent Lines and Derivatives. Limits at Infinity, Limits of Sequences. Areas. Focus on Modeling, Interpretation of Area.