{"id":1420,"date":"2023-02-15T11:57:30","date_gmt":"2023-02-15T19:57:30","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=1420"},"modified":"2023-08-05T13:09:49","modified_gmt":"2023-08-05T20:09:49","slug":"math-125-calculus-1","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/math-125-calculus-1\/","title":{"rendered":"MATH 125 – Calculus I"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

Math 125 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

 <\/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
1.1 – 1.6<\/td>\nLimits and Continuity<\/td>\n10<\/td>\n<\/tr>\n
2.1 – 2.8<\/td>\nDerivatives<\/td>\n8<\/td>\n<\/tr>\n
3.1-3.5, 3.7<\/td>\nApplications of Derivatives<\/td>\n8<\/td>\n<\/tr>\n
4.1 – 4.5<\/td>\nIntegrals<\/td>\n8<\/td>\n<\/tr>\n
5.1 – 5.5<\/td>\nLog and Exp<\/td>\n6<\/td>\n<\/tr>\n
<\/td>\nTotal<\/td>\n40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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

    \n
  • The epsilon\/delta definition of limits from early Ch 1<\/li>\n
  • Section 3.6 on Newton’s Method of approximation<\/li>\n
  • Section 5.6 on Inverse Trig Functions<\/li>\n
  • Section 5.7 on Hyperbolic Functions<\/li>\n
  • Section 6.4 on Integration with Tables or CAS<\/li>\n
  • Section 7.7 on Differential Equations<\/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 the fundamental concepts of calculus, including limits, continuity, and the definition of derivatives.<\/li>\n
    2. Compute limits algebraically and graphically to evaluate indeterminate forms and understand the behavior of functions at specific points.<\/li>\n
    3. Differentiate algebraic, trigonometric, exponential, and logarithmic functions using various differentiation rules.<\/li>\n
    4. Apply the chain rule, product rule, and quotient rule to find derivatives of composite functions and functions involving products and quotients.<\/li>\n
    5. Use derivatives to analyze the behavior of functions, including identifying critical points, extrema, and points of inflection.<\/li>\n
    6. Apply the first derivative test and the second derivative test to determine the intervals of increase, decrease, and concavity of functions.<\/li>\n
    7. Solve optimization problems using derivatives to find maximum and minimum values of functions.<\/li>\n
    8. Understand the concept of antiderivatives and find them for simple functions and apply the power rule and integration by substitution.<\/li>\n
    9. Calculate definite integrals using the concept of Riemann sums and interpret the integral as the area under a curve.<\/li>\n
    10. Apply the fundamental theorem of calculus to evaluate definite integrals and compute areas between curves.<\/li>\n
    11. Use integration to find the total change, average value, and displacement of a function over a specified interval.<\/li>\n
    12. Apply the concept of integration to solve real-world problems, such as problems in physics, engineering, and economics.<\/li>\n
    13. Utilize computational tools and software (e.g., MATLAB, Python) to perform calculus calculations and visualize functions and their derivatives.<\/li>\n
    14. Understand the application of calculus in various fields and appreciate its significance in modeling and analyzing real-world phenomena.<\/li>\n<\/ol>\n

       <\/p>\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-1420","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nMATH 125 - Calculus I - 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-125-calculus-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MATH 125 - Calculus I - 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-125-calculus-1\/\" \/>\n<meta property=\"og:site_name\" content=\"Department of Mathematics\" \/>\n<meta property=\"article:modified_time\" content=\"2023-08-05T20:09:49+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-125-calculus-1\/\",\"url\":\"https:\/\/dornsife.usc.edu\/mathematics\/math-125-calculus-1\/\",\"name\":\"MATH 125 - 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