{"id":3758,"date":"2021-05-12T20:24:05","date_gmt":"2021-05-12T20:24:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus1\/chapter\/course-contents-at-a-glance\/"},"modified":"2021-06-15T20:24:25","modified_gmt":"2021-06-15T20:24:25","slug":"course-contents-at-a-glance","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus1\/chapter\/course-contents-at-a-glance\/","title":{"raw":"Course Contents at a Glance","rendered":"Course Contents at a Glance"},"content":{"raw":"<img class=\"aligncenter wp-image-220\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/01212659\/binoculars2.png\" alt=\"an icon of a pair of binoculars\" width=\"250\" height=\"142\" \/>\r\n\r\nThe following list shows a summary of the topics covered in this course. To see all of the course pages, visit the\u00a0<a href=\"https:\/\/courses.lumenlearning.com\/calculus1\/\" target=\"_blank\" rel=\"noopener\">Table of Contents<\/a>.\r\n<h2>Module 1: Functions and Graphs<\/h2>\r\n<ul>\r\n \t<li>Review of Functions<\/li>\r\n \t<li>Basic Classes of Functions<\/li>\r\n \t<li>Trigonometric Functions<\/li>\r\n \t<li>Inverse Functions<\/li>\r\n \t<li>Exponential and Logarithmic Functions<\/li>\r\n<\/ul>\r\n<h2>Module 2: Limits<\/h2>\r\n<ul>\r\n \t<li class=\"chapter standard\">A Preview of Calculus<\/li>\r\n \t<li class=\"chapter standard\">The Limit of a Function<\/li>\r\n \t<li class=\"chapter standard\">The Limit Laws<\/li>\r\n \t<li class=\"chapter standard\">Continuity<\/li>\r\n \t<li class=\"chapter standard\">The Precise Definition of a Limit<\/li>\r\n<\/ul>\r\n<h2>Module 3: Derivatives<\/h2>\r\n<ul>\r\n \t<li>Defining the Derivative<\/li>\r\n \t<li>The Derivative as a Function<\/li>\r\n \t<li>Differentiation Rules<\/li>\r\n \t<li>Derivatives as Rates of Change<\/li>\r\n \t<li>Derivatives of Trigonometric Functions<\/li>\r\n \t<li>The Chain Rule<\/li>\r\n \t<li>Derivatives of Inverse Functions<\/li>\r\n \t<li>Implicit Differentiation<\/li>\r\n \t<li>Derivatives of Exponential and Logarithmic Functions<\/li>\r\n<\/ul>\r\n<h2>Module 4: Applications of Derivatives<\/h2>\r\n<ul>\r\n \t<li>Related Rates<\/li>\r\n \t<li>Linear Approximations and Differentials<\/li>\r\n \t<li>Maxima and Minima<\/li>\r\n \t<li>The Mean Value Theorem<\/li>\r\n \t<li>Derivatives and the Shape of a Graph<\/li>\r\n \t<li>Limits at Infinity and Asymptotes<\/li>\r\n \t<li>Applied Optimization Problems<\/li>\r\n \t<li>L\u2019H\u00f4pital\u2019s Rule<\/li>\r\n \t<li>Newton\u2019s Method<\/li>\r\n \t<li>Antiderivatives<\/li>\r\n<\/ul>\r\n<h2>Module 5: Integration<\/h2>\r\n<ul>\r\n \t<li class=\"chapter standard\">Approximating Areas<\/li>\r\n \t<li class=\"chapter standard\">The Definite Integral<\/li>\r\n \t<li class=\"chapter standard\">The Fundamental Theorem of Calculus<\/li>\r\n \t<li class=\"chapter standard\">Integration Formulas and the Net Change Theorem<\/li>\r\n \t<li class=\"chapter standard\">Substitution<\/li>\r\n \t<li class=\"chapter standard\">Integrals Involving Exponential and Logarithmic Functions<\/li>\r\n \t<li class=\"chapter standard\">Integrals Resulting in Inverse Trigonometric Functions<\/li>\r\n \t<li>Approximating Integrals<\/li>\r\n<\/ul>\r\n<h2>Module 6: Applications of Integration<\/h2>\r\n<ul>\r\n \t<li class=\"chapter standard\">Areas Between Curves<\/li>\r\n \t<li class=\"chapter standard\">Determining Volumes by Slicing<\/li>\r\n \t<li class=\"chapter standard\">Volumes of Revolution: Cylindrical Shells<\/li>\r\n \t<li class=\"chapter standard\">Arc Length of a Curve and Surface Area<\/li>\r\n \t<li class=\"chapter standard\">Physical Applications<\/li>\r\n \t<li class=\"chapter standard\">Moments and Centers of Mass<\/li>\r\n \t<li class=\"chapter standard\">Integrals, Exponential Functions, and Logarithms<\/li>\r\n \t<li class=\"chapter standard\">Exponential Growth and Decay<\/li>\r\n \t<li class=\"chapter standard\">Calculus of the Hyperbolic Functions<\/li>\r\n<\/ul>","rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-220\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/01212659\/binoculars2.png\" alt=\"an icon of a pair of binoculars\" width=\"250\" height=\"142\" \/><\/p>\n<p>The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the\u00a0<a href=\"https:\/\/courses.lumenlearning.com\/calculus1\/\" target=\"_blank\" rel=\"noopener\">Table of Contents<\/a>.<\/p>\n<h2>Module 1: Functions and Graphs<\/h2>\n<ul>\n<li>Review of Functions<\/li>\n<li>Basic Classes of Functions<\/li>\n<li>Trigonometric Functions<\/li>\n<li>Inverse Functions<\/li>\n<li>Exponential and Logarithmic Functions<\/li>\n<\/ul>\n<h2>Module 2: Limits<\/h2>\n<ul>\n<li class=\"chapter standard\">A Preview of Calculus<\/li>\n<li class=\"chapter standard\">The Limit of a Function<\/li>\n<li class=\"chapter standard\">The Limit Laws<\/li>\n<li class=\"chapter standard\">Continuity<\/li>\n<li class=\"chapter standard\">The Precise Definition of a Limit<\/li>\n<\/ul>\n<h2>Module 3: Derivatives<\/h2>\n<ul>\n<li>Defining the Derivative<\/li>\n<li>The Derivative as a Function<\/li>\n<li>Differentiation Rules<\/li>\n<li>Derivatives as Rates of Change<\/li>\n<li>Derivatives of Trigonometric Functions<\/li>\n<li>The Chain Rule<\/li>\n<li>Derivatives of Inverse Functions<\/li>\n<li>Implicit Differentiation<\/li>\n<li>Derivatives of Exponential and Logarithmic Functions<\/li>\n<\/ul>\n<h2>Module 4: Applications of Derivatives<\/h2>\n<ul>\n<li>Related Rates<\/li>\n<li>Linear Approximations and Differentials<\/li>\n<li>Maxima and Minima<\/li>\n<li>The Mean Value Theorem<\/li>\n<li>Derivatives and the Shape of a Graph<\/li>\n<li>Limits at Infinity and Asymptotes<\/li>\n<li>Applied Optimization Problems<\/li>\n<li>L\u2019H\u00f4pital\u2019s Rule<\/li>\n<li>Newton\u2019s Method<\/li>\n<li>Antiderivatives<\/li>\n<\/ul>\n<h2>Module 5: Integration<\/h2>\n<ul>\n<li class=\"chapter standard\">Approximating Areas<\/li>\n<li class=\"chapter standard\">The Definite Integral<\/li>\n<li class=\"chapter standard\">The Fundamental Theorem of Calculus<\/li>\n<li class=\"chapter standard\">Integration Formulas and the Net Change Theorem<\/li>\n<li class=\"chapter standard\">Substitution<\/li>\n<li class=\"chapter standard\">Integrals Involving Exponential and Logarithmic Functions<\/li>\n<li class=\"chapter standard\">Integrals Resulting in Inverse Trigonometric Functions<\/li>\n<li>Approximating Integrals<\/li>\n<\/ul>\n<h2>Module 6: Applications of Integration<\/h2>\n<ul>\n<li class=\"chapter standard\">Areas Between Curves<\/li>\n<li class=\"chapter standard\">Determining Volumes by Slicing<\/li>\n<li class=\"chapter standard\">Volumes of Revolution: Cylindrical Shells<\/li>\n<li class=\"chapter standard\">Arc Length of a Curve and Surface Area<\/li>\n<li class=\"chapter standard\">Physical Applications<\/li>\n<li class=\"chapter standard\">Moments and Centers of Mass<\/li>\n<li class=\"chapter standard\">Integrals, Exponential Functions, and Logarithms<\/li>\n<li class=\"chapter standard\">Exponential Growth and Decay<\/li>\n<li class=\"chapter standard\">Calculus of the Hyperbolic Functions<\/li>\n<\/ul>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-3758\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Course Contents at a Glance. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Binoculars Icon. <strong>Authored by<\/strong>: Musmellow. <strong>Provided by<\/strong>: Noun Project. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/thenounproject.com\/term\/binoculars\/1234056\/\">https:\/\/thenounproject.com\/term\/binoculars\/1234056\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Binoculars Icon\",\"author\":\"Musmellow\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/binoculars\/1234056\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Course Contents at a Glance\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3758","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3758","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3758\/revisions"}],"predecessor-version":[{"id":4302,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3758\/revisions\/4302"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3758\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3758"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3758"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3758"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}