{"id":1425,"date":"2023-02-15T11:58:43","date_gmt":"2023-02-15T19:58:43","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=1425"},"modified":"2023-08-05T13:19:10","modified_gmt":"2023-08-05T20:19:10","slug":"math-126-calculus-2","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/math-126-calculus-2\/","title":{"rendered":"MATH 126\/129 – Calculus II"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

Math 126 is a coordinated course<\/a> and a common final exam is offered at the end of each semester.<\/span>
\nYou can find past common finals here<\/a>.<\/span><\/p>\n

Math 129 is not<\/em> coordinated and will take its own final exam.\u00a0 Math 129 has the same basic requirements as Math 126 but typically includes additional topics and applications from Physics and Engineering.<\/span><\/p>\n

 <\/p>\n

REQUIRED TEXTBOOK<\/strong><\/p>\n

Stewart, Essential Calculus (2nd ed.)<\/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.\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
Sections<\/strong><\/td>\nTopics<\/strong><\/td>\nLectures<\/strong><\/td>\n<\/tr>\n
5.6 – 5.8<\/td>\nInverse Functions, L\u2019Hopital\u2019s Rule<\/td>\n4<\/td>\n<\/tr>\n
6.1-6.3, 6.5, 6.6<\/td>\nTechniques of Integration<\/td>\n8<\/td>\n<\/tr>\n
7.1 – 7.6<\/td>\nApplications of Integration<\/td>\n9<\/td>\n<\/tr>\n
8.1 – 8.8<\/td>\nSequences and Infinite Series<\/td>\n14<\/td>\n<\/tr>\n
9.3 – 9.4<\/td>\nPolar Coordinates<\/td>\n3<\/td>\n<\/tr>\n
<\/td>\nTotal<\/td>\n38<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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

    \n
  • Section 6.4 on Integration with Tables or CAS<\/li>\n
  • Section 7.7 on Differential Equations<\/li>\n
  • Proof by Induction as it relates to Chapter 8<\/li>\n
  • Section 9.1 on Parametric Curves<\/li>\n
  • Section 9.2 with more on Parametric Curves<\/li>\n
  • Other outside topics, readings, videos, or materials the Instructor deems relevant<\/li>\n<\/ul>\n

    If all<\/em> course instructors in a given semester cover a particular topic, they may choose to include that topic in the common final exam.<\/p>\n

     <\/p>\n

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

    By the end of this course, students should be able to:<\/p>\n

     <\/p>\n

      \n
    1. Understand and apply advanced techniques of integration, including integration by parts, trigonometric substitutions, and partial fraction decomposition.<\/li>\n
    2. Compute integrals via inverse trig functions and hyperbolic functions.<\/li>\n
    3. Evaluate improper integrals and understand their convergence properties.<\/li>\n
    4. Use l’H\u00f4pital’s rule to determine limits of functions.<\/li>\n
    5. Compute the length of curves, surface areas of revolution, and volumes of solids of revolution using integration.<\/li>\n
    6. Apply numerical integration techniques, such as Simpson’s rule and the trapezoidal rule, to approximate definite integrals.<\/li>\n
    7. Explore sequences and series, including the concepts of convergence, divergence, and the relationship between sequences and functions.<\/li>\n
    8. Determine the convergence and divergence of infinite series using various tests, such as the comparison test, ratio test, and integral test.<\/li>\n
    9. Apply power series representations to approximate functions and\/or solve differential equations.<\/li>\n
    10. Analyze Taylor and Maclaurin series expansions and use them to approximate functions to a desired degree of accuracy.<\/li>\n
    11. Understand polar coordinates in R<\/strong>2<\/sup> and apply them to graph curves and evaluate integrals.<\/li>\n<\/ol>\n

       <\/p>\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-1425","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nMATH 126\/129 - Calculus II - Department of Mathematics<\/title>\n<meta name=\"description\" content=\"Syllabus and Learning Objectives\" \/>\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-126-calculus-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MATH 126\/129 - Calculus II - Department of Mathematics\" \/>\n<meta property=\"og:description\" content=\"Syllabus and Learning Objectives\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/mathematics\/math-126-calculus-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Department of Mathematics\" \/>\n<meta property=\"article:modified_time\" content=\"2023-08-05T20:19:10+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-126-calculus-2\/\",\"url\":\"https:\/\/dornsife.usc.edu\/mathematics\/math-126-calculus-2\/\",\"name\":\"MATH 126\/129 - 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