{"id":1403,"date":"2023-02-15T11:48:50","date_gmt":"2023-02-15T19:48:50","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=1403"},"modified":"2024-06-20T09:01:27","modified_gmt":"2024-06-20T16:01:27","slug":"math-108-precalculus","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/math-108-precalculus\/","title":{"rendered":"MATH 108 – Precalculus"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

RECOMMENDED TEXTBOOKS<\/strong><\/p>\n

Hungerford & Shaw, Contemporary Precalculus (5th ed.)<\/a><\/p>\n

OpenStax Precalculus (2nd ed.)<\/a>
\nMAA Precalculus: An Investigation of Functions (open source)<\/a><\/p>\n

 <\/p>\n

SECTION COVERAGE<\/strong><\/p>\n

The following table lists the minimum<\/em> set of topics to be included in this course, based on the textbook by Hungerford & Shaw above.\u00a0 The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.<\/p>\n

There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Sections<\/strong><\/td>\nTopics<\/strong><\/td>\nLectures<\/strong><\/td>\n<\/tr>\n
1.1 – 1.4<\/td>\nBasics (Review)<\/td>\n3<\/td>\n<\/tr>\n
3.1 – 3.7<\/td>\nFunctions and Graphs<\/td>\n6<\/td>\n<\/tr>\n
4.1 – 4.7<\/td>\nPolynomial and Rational\u00a0Functions<\/td>\n8<\/td>\n<\/tr>\n
5.1 – 5.5<\/td>\nExponential and Logarithmic Functions<\/td>\n6<\/td>\n<\/tr>\n
6.1 – 6.6<\/td>\nTrigonometric Functions<\/td>\n5<\/td>\n<\/tr>\n
7.1 – 7.5<\/td>\nTrigonometric Identities and Equations<\/td>\n3<\/td>\n<\/tr>\n
8.1 – 8.2<\/td>\nTriangle Trigonometry<\/td>\n4<\/td>\n<\/tr>\n
9.1<\/td>\nPolar Form of Complex Numbers<\/td>\n2<\/td>\n<\/tr>\n
10.1 – 10.3<\/td>\nAnalytic Geometry<\/td>\n3<\/td>\n<\/tr>\n
<\/td>\nTotal<\/td>\n40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

OPTIONAL TOPICS (time permitting)<\/strong><\/p>\n

    \n
  • All lettered sections (e.g. Section 1.2A<\/strong>) are considered optional, but all are good topics and we should consider covering the majority of them.<\/li>\n
  • The graphs<\/em> of sec\/csc\/cot (in H\/S, Section 6.5A<\/strong>).<\/li>\n
  • Sections 8.3\/8.4 on the Laws of Sines and Cosines, which are traditional but not used in Calculus.<\/li>\n
  • Section 9.2 on DeMoivre\u2019s Theorem and the roots of complex numbers.<\/li>\n
  • Section 10.6 on polar coordinates is natural when discussing the Unit Circle.<\/li>\n
  • Other outside topics, readings, videos, or materials the Instructor deems relevant.<\/li>\n<\/ul>\n

     <\/p>\n

    MEASURABLE OBJECTIVES<\/strong><\/p>\n

      \n
    1. Students can interpret and use mathematical notation and vocabulary related to the concepts of a function and the graph of a function.<\/li>\n
    2. Students can identify shifts, stretches, compressions, and reflections of a function via its graph and its defining formula.<\/li>\n
    3. Students can compose functions, invert functions, and interpret relationships between inverse functions via composition.<\/li>\n
    4. Students can compute, compare, and interpret average and instantaneous rates of change of a function.<\/li>\n
    5. Students can write equations describing ellipses, hyperbolas, and parabolas, and graph them, identifying their important features.<\/li>\n
    6. Students can write and graph quadratic functions, and find and interpret their vertices in a given context.<\/li>\n
    7. Students can write and graph polynomial functions, and solve polynomial equations and inequalities.<\/li>\n
    8. Students can identify features of rational functions from formulas and graphs, and solve rational equations and inequalities.<\/li>\n
    9. Students can write and graph functions representing both exponential growth and exponential decay.<\/li>\n
    10. Students can define a logarithm, graph logarithmic functions, and use the properties of logarithms to solve exponential equations.<\/li>\n
    11. Students can evaluate trigonometric functions at acute angles in right triangles and solve applied problems involving right triangles.<\/li>\n
    12. Students can use the unit circle to find the values of trigonometric functions at special angles measured in degrees or radians.<\/li>\n
    13. Students can graph the three basic trigonometric functions and their transformations by hand.<\/li>\n
    14. Students can use trigonometric identities to simplify expressions, evaluate trigonometric functions, and solve trigonometric equations.<\/li>\n
    15. Students can efficiently find products, quotients, and powers of complex numbers using their polar forms.<\/li>\n<\/ol>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":328,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1403","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nMATH 108 - Precalculus - Department of Mathematics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/mathematics\/math-108-precalculus\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MATH 108 - Precalculus - Department of Mathematics\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/mathematics\/math-108-precalculus\/\" \/>\n<meta property=\"og:site_name\" content=\"Department of Mathematics\" \/>\n<meta property=\"article:modified_time\" content=\"2024-06-20T16:01:27+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/mathematics\/math-108-precalculus\/\",\"url\":\"https:\/\/dornsife.usc.edu\/mathematics\/math-108-precalculus\/\",\"name\":\"MATH 108 - 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