{"id":2,"date":"2019-09-11T13:04:41","date_gmt":"2019-09-11T13:04:41","guid":{"rendered":"http:\/\/sites.nd.edu\/math-digital-resources\/?page_id=2"},"modified":"2026-05-12T22:42:46","modified_gmt":"2026-05-13T02:42:46","slug":"20580-2","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/math-digital-resources\/20580-2\/","title":{"rendered":"Introduction to Linear Algebra and Differential Equations (20580)"},"content":{"rendered":"<p>Linear Algebra is a basis on which modern mathematics was built. Almost all solvable problems use the techniques developed in Linear Algebra. Throughout this course, you will<br \/>\nlearn how these techniques are used in a variety of fashions, from standard solving of system of equations to identifying functions that are useful in solving differential equations. It is<br \/>\nappropriate we wrap up the course with an introduction to differential equations, because it is your understanding of linear algebra which will allow you to find or approximate the solutions you need in solving differential equations.<\/p>\n<p>Below are the topics for the Linear Algebra and Differential Equations Course.\u00a0 The links content digital content to help facilitate your understanding of the material.<\/p>\n<p><span style=\"text-decoration: underline\"><strong>Linear Algebra<\/strong><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK00\/Systems_of_equations\/content\/index.html\"><span style=\"font-weight: 400\">Systems of Equations\u00a0<\/span><\/a><\/li>\n<li><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK01\/Meaning-of-Solutions\/content\/index.html\"><span style=\"font-weight: 400\">Meaning of Solutions<\/span><\/a><span style=\"font-weight: 400\">\u00a0 \u00a0<\/span><\/li>\n<li><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK01\/Properties-of-Matrices\/content\/index.html\"><span style=\"font-weight: 400\">Properties of Matrices<\/span><\/a><\/li>\n<li><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK01\/Linear-Transformations\/content\/index.html\"><span style=\"font-weight: 400\">Linear Transformations in Rn<\/span><\/a><span style=\"font-weight: 400\">\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK02\/Subspaces-Euclidean+Spaces\/index.html\"><span style=\"font-weight: 400\">Subspaces<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK02\/Linear+Independence-Euclidean+Spaces\/index.html\"><span style=\"font-weight: 400\">Basis<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK02\/Coordinates-Change+of+Basis\/index.html\"><span style=\"font-weight: 400\">Coordinates in Rn<\/span><\/a><span style=\"font-weight: 400\">\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK03\/Vector+spaces-Subspaces\/index.html\"><span style=\"font-weight: 400\">Abstract Vector Space<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK03\/Linear+transformations\/index.html\"><span style=\"font-weight: 400\">Linear Transformations of Abstract Vector Spaces<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK03\/Coordinates+and+change+of+basis\/index.html\"><span style=\"font-weight: 400\">Coordinates with Abstract Vector Spaces<\/span><\/a><span style=\"font-weight: 400\">\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK04\/Determinants\/index.html\"><span style=\"font-weight: 400\">Determinants<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK04\/Eigenvalues-Eigenvectors\/index.html\"><span style=\"font-weight: 400\">Eigenvectors and Eigenvalues<\/span><\/a><span style=\"font-weight: 400\">\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK05\/Complex+Eigenvalues\/index.html\"><span style=\"font-weight: 400\">Complex Eigenvalues<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK05\/Orthogonality\/index.html\"><span style=\"font-weight: 400\">Orthogonality<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK05\/Least+Squares+Solutions\/index.html\"><span style=\"font-weight: 400\">Least Squares Solution<\/span><\/a><\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline\"><strong>Differential Equations<\/strong><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK06\/Solutions+to+DifEq\/index.html\"><span style=\"font-weight: 400\">Solutions to DifEq<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK06\/1st+Order+Equations\/index.html\"><span style=\"font-weight: 400\">1st Order Equations<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK06\/Modeling\/index.html\"><span style=\"font-weight: 400\">Modeling<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK07\/Linear+Differential+Equations\/index.html\"><span style=\"font-weight: 400\">Linear Differential Equations<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK07\/2nd+Order+Linear+Homogeneous\/index.html\"><span style=\"font-weight: 400\">2nd Order Linear Homogeneous<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK08\/2nd+Order+Linear+Nonhomogenous\/index.html\"><span style=\"font-weight: 400\">2nd Order Linear Nonhomogeneous<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/math24580-linear-algebra-2019.s3.amazonaws.com\/Rise+Pages\/WEEK08\/Vibrations\/index.html\"><span style=\"font-weight: 400\">Vibrations<\/span><\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Linear Algebra is a basis on which modern mathematics was built. Almost all solvable problems use the techniques developed in Linear Algebra. Throughout this course, you will learn how these techniques are used in a variety of fashions, from standard solving of system of equations to identifying functions that are useful in solving differential equations. [&hellip;]<\/p>\n","protected":false},"author":2271,"featured_media":0,"parent":0,"menu_order":3,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-2","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/users\/2271"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/comments?post=2"}],"version-history":[{"count":3,"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":434,"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/pages\/2\/revisions\/434"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/math-digital-resources\/wp-json\/wp\/v2\/media?parent=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}