# Math 370- PreCalculus

Description: |
This course provides foundational mathematics and problems that require critical thinking in preparation for the calculus sequence for science, technology, engineering, and mathematics (STEM) majors. Topics include rigorous treatment of polynomial, rational, logarithmic, exponential and trigonometric functions, including graphing and applications, as well as systems of linear and non-linear equations and inequalities. The course also covers analytic geometry, conic sections, vectors, parametric equations, and polar equations. |

**Learning Outcomes and Objectives Upon completion of this course, the student will be able to:**

- apply the basic concepts of the complex and real number systems to solve equations and inequalities
- perform operations of arithmetic and composition on various functions
- use analytic methods to determine roots, domain, and range, both with and without a graphing utility
- solve equations involving polynomial, rational, exponential, logarithmic, and trigonometric functions
- state and apply the Remainder Theorem, Factor Theorem, Rational Root Theorem, and the Fundamental Theorem of Algebra
- use analytic methods to graph polynomial, rational, exponential, logarithmic, and trigonometric functions without the aid of a graphing utility
- state basic trig identities including Pythagorean, double angle, half-angle, and sum of angle, and use these identities to find the exact solutions of trigonometric equations, solve various applications, and simplify expressions
- state and appropriately apply the Law of Sines and the Law of Cosines to solve triangles in various applications
- analyze the geometry of lines and conic sections
- solve word problems using methods from algebra, analytical geometry and trigonometry
- solve linear and nonlinear systems of equations and inequalities

**Course Topics The topics for this course are typically allocated as follows:**

Lec |
Topic |

4 | Algebra review Basic rules of algebra Exponents Radicals Cartesian plane |

6 | Adding, subtracting polynomials Multiplying polynomials, special products Factoring polynomials |

5 | Functions Definition Graphs of functions Shifting Stretching Reflecting of graphs |

5 | Operations on functions Inverse functions |

5 | Graphs of polynomial functions of degree greater than 2 Graphing rational functions using asymptotes Dividing polynomials |

5 | Complex and rational zeros of polynomials Fundamental Theorem of Algebra |

3 | Exponential functions, e, bases other than e, applications |

4 | Logarithmic functions, natural logarithms, properties of logarithms |

5 | Trigonometric functions Right triangle circular function and real number function Graphing Right triangle applications |

5 | Analytic trigonometry Verifying trigonometric identities Trigonometric equations Sum and difference formulas Multiple-angle product-to-sum formulas Inverse trigonometric functions |

4 | Applications of trigonometry Laws of Sines and Cosines |

6 | Trigonometric form of complex numbers DeMoivre's Theorem Roots of complex numbers Vectors Dot product |

5 | Sequences, series Summation notation Arithmetic and geometric sequences |

5 | Mathematical induction Binomial Theorem |

5 | Topics from analytic geometry Parabolas Ellipses Hyperbolas |

6 | Parametric equations Polar coordinates Polar equations of conics |

4 | Systems of equations Systems of inequalities |

6 | Partial fractions Algebra of matrices Cramer's Rule |

2 | Final exam |