{"id":57,"date":"2020-04-22T23:53:04","date_gmt":"2020-04-23T04:53:04","guid":{"rendered":"https:\/\/mathtalker.org\/blog\/?page_id=57"},"modified":"2026-04-16T16:14:53","modified_gmt":"2026-04-16T21:14:53","slug":"linear-algebra-and-differential-equations-class-notes","status":"publish","type":"page","link":"https:\/\/mathtalker.org\/blog\/linear-algebra-and-differential-equations-class-notes\/","title":{"rendered":"Linear Algebra and Differential Equations"},"content":{"rendered":"<p><script type=\"application\/ld+json\"><br \/>\n{<br \/>\n  \"@context\": \"https:\/\/schema.org\",<br \/>\n  \"@type\": \"CollectionPage\",<br \/>\n  \"name\": \"Differential Equations and Linear Algebra Class Notes\",<br \/>\n  \"headline\": \"Differential Equations and Linear Algebra Class Notes\",<br \/>\n  \"description\": \"Free differential equations and linear algebra class notes based on Edwards and Penney, with worked examples, in-class exercises, and solutions.\",<br \/>\n  \"url\": \"https:\/\/mathtalker.org\/www\/Class_Notes.php\",<br \/>\n  \"author\": {<br \/>\n    \"@type\": \"Person\",<br \/>\n    \"name\": \"Jodin Morey\",<br \/>\n    \"url\": \"https:\/\/mathtalker.org\/www\/\"<br \/>\n  },<br \/>\n  \"publisher\": {<br \/>\n    \"@type\": \"Person\",<br \/>\n    \"name\": \"Jodin Morey\"<br \/>\n  },<br \/>\n  \"about\": [<br \/>\n    \"Differential equations\",<br \/>\n    \"Linear algebra\",<br \/>\n    \"Euler's method\",<br \/>\n    \"Matrix algebra\",<br \/>\n    \"Vector spaces\",<br \/>\n    \"Eigenvalues\",<br \/>\n    \"Linear systems\",<br \/>\n    \"Laplace transforms\",<br \/>\n    \"Power series\"<br \/>\n  ]<br \/>\n}<br \/>\n<\/script><\/p>\n<h2>Differential Equations and Linear Algebra Class Notes<\/h2>\n<p><strong>Keywords:<\/strong> differential equations notes, linear algebra notes, Edwards and Penney, Euler method, eigenvalues, vector spaces, Laplace transform, linear systems, power series.<\/p>\n<p>As an instructor for linear algebra and differential equations, I prepared these class notes as a review of the sections in <a href=\"https:\/\/www.pearson.com\/us\/higher-education\/program\/Edwards-Differential-Equations-and-Linear-Algebra-3rd-Edition\/PGM146246.html\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Differential Equations and Linear Algebra<\/em> by Edwards and Penney<\/a>. They include example problems which have been worked out in some detail. I hope you find these useful.<\/p>\n<style>\n.notes-table {<br \/>\n    width: 100%;<br \/>\n    border-collapse: collapse;<br \/>\n    margin-top: 20px;<br \/>\n}<\/p>\n<p>.notes-table th,<br \/>\n.notes-table td {<br \/>\n    border: 1px solid #999;<br \/>\n    padding: 10px;<br \/>\n    text-align: left;<br \/>\n    vertical-align: top;<br \/>\n}<\/p>\n<p>.notes-table th {<br \/>\n    background-color: #f2f2f2;<br \/>\n}<\/p>\n<p>.notes-table tr:nth-child(even) {<br \/>\n    background-color: #fafafa;<br \/>\n}<br \/>\n<\/style>\n<table class=\"notes-table\">\n<thead>\n<tr>\n<th>Class Notes<\/th>\n<th>In-Class Exercises<\/th>\n<th>Solutions<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_01p1_Differential_Equations_and_Mathematical_Models.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.1 Differential Equations and Mathematical Models<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 1.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_01p2_Integrals_as_General_and_Particular_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.2 Integrals as General and Particular Solutions<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 1.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_01p3_Slope_Fields_and_Solution_Curves.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.3 Slope Fields and Solution Curves<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 1.3<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p3_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.3<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_01p4_Separable_DEQs_and_Applications.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.4 Separable Equations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 1.4<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p4_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.4<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_01p5_Linear_First_Order_DEQs.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.5 Linear First-Order Equations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 1.5<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p5_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.5<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_01p6_Substitution_Method_Exact_Equations.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.6 Substitution Method, Exact Equations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p6.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 1.6<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_01p6_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.6<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_02p1_Mathematical_Models_and_Numerical_Methods.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.1 Mathematical Models and Numerical Methods<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_02p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 2.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_02p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 2.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_02p2_Equilibrium_Solutions_and_Stability.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.2 Equilibrium Solutions and Stability<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_02p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 2.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_02p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 2.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_02p3_Acceleration_Velocity_Models.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.3 Acceleration Velocity Models<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_02p4_Euler_Method.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.4 Euler Method<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_02p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 2.4<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_02p4_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 2.4<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_02p5_Advanced_Euler_Method.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.5 Advanced Euler Method<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_03p1_and_03p2_Intro_to_Linear_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.1 &amp; 3.2 Linear Systems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 3.1<\/a><br \/>\n<a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 3.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.1<\/a><br \/>\n<a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_03p3_Reduced_Echelon_Matrices.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.3 Reduced Echelon Matrices<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 3.3<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p3_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.3<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_03p4_Matrix_Operations.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.4 Matrix Operations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 3.4<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p4_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.4<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_03p5_Inverses_of_Matrices.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.5 Inverses of Matrices<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 3.5<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p5_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.5<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_03p6_Determinants.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.6 Determinants<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p6.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 3.6<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_03p6_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.6<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_03p7_Linear_Equations_and_Curve_Fitting.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.7 Linear Equations and Curve Fitting<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_04p1_Vector_Space.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.1 Vector Space<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 4.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 4.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_04p2_Vector_Space_and_Subspaces.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.2 Subspaces<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 4.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 4.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_04p3_Linear_Combinations_and_Independence_of_Vectors.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.3 Linear Combinations and Independence of Vectors<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 4.3<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p3_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 4.3<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_04p4_Bases_and_Dimensions_for_Vector_Spaces.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.4 Bases and Dimension for Vector Spaces<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 4.4<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_04p4_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 4.4<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_04p5_Row_and_Column_Spaces.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.5 Row and Column Spaces<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_04p7_General_Vector_Spaces.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.7 General Vector Spaces<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_05p1_Second_Order_Linear_DEQs.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.1 Second-Order Linear Equations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 5.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 5.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_05p2_General_Solutions_of_Linear_DEQs.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.2 General Solutions of Linear Equations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 5.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 5.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_05p3_Homogeneous_DEQs_with_Constant_Coefficients.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.3 Homogeneous Equations with Constant Coefficients<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 5.3<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p3_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 5.3<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_05p4_Mechanical_Vibrations.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.4 Mechanical Vibrations<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_05p5_NonHomogeneous_DEQs_and_Undetermined_Coefficients.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.5 Nonhomogeneous Equations, Undetermined Coefficients<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 5.5<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_05p5_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 5.5<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_05p6_Forced_Oscillations_and_Resonance.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.6 Forced Oscillations and Resonance<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_06p1_Eigenvalues.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">6.1 Eigenvalues<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_06p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 6.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_06p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 6.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_06p2_Diagonals_of_Matrices.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">6.2 Diagonals of Matrices<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_06p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 6.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_06p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 6.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_06p3_Applications_Involving_Powers_of_Matrices.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">6.3 Powers of Matrices<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_06p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 6.3<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_06p3_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 6.3<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p1_First_Order_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.1 First-Order Systems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 7.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p2_Matrices_and_Linear_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.2 Matrices and Linear Systems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 7.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p3_Eigenvalue_Method_for_Linear_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.3 Eigenvalue Method for Linear Systems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 7.3<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p3_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.3<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p4_Solution_Curves_of_Linear_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.4 Solution Curves of Linear Systems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 7.4<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_07p4_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.4<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p5_Second_Order_Systems_and_Mechanical_Applications.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.5 Second Order Systems and Mechanical Applications<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p6_Multiple_Eigenvalue.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.6 Multiple Eigenvalue<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_07p7_Numerical_Methods_for_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.7 Numerical Methods for Systems<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_08p2_Nonhomogeneous_Linear_DEQs.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">8.2 Nonhomogeneous Linear Differential Equations<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_08p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 8.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_08p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 8.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_09p1_Stability_and_the_Phase_Plane.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">9.1 Stability and the Phase Plane<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_09p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 9.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_09p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 9.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_09p2_Linear_and_Almost_Linear_Systems.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">9.2 Linear and Almost Linear Systems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_09p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 9.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_09p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 9.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_09p3_Ecological_Models.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">9.3 Ecological Models<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_10p1_Laplace_Transform_Methods.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">10.1 Laplace Transform<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_10p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 10.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_10p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 10.1<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_10p2_Laplace_Transformation_of_IVPs.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">10.2 Laplace Transformation of Initial Value Problems<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_10p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 10.2<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_10p2_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 10.2<\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_10p3_Translation_and_Partial_Fractions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">10.3 Translation and Partial Fractions<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/ClassNotes_11p1_Power_Series_Method.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">11.1 Power Series Method<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_11p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Exercises 11.1<\/a><\/td>\n<td><a href=\"https:\/\/mathtalker.org\/www\/pdfs\/Linear_Algebra_Differential_Equations_Penney_Edwards\/exercises\/Exercise_11p1_Solutions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 11.1<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Differential Equations and Linear Algebra Class Notes Keywords: differential equations notes, linear algebra notes, Edwards and Penney, Euler method, eigenvalues, vector spaces, Laplace transform, linear systems, power series. 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