Math 383 · Fall 2021 (UNC)

Math 383 Differential Equations, Fall 2021

Thursday August 19

Course Introduction / Syllabus, Overview of Differential Equations, & Section 1.1 (Differential Equations and Mathematical Models)

Tuesday August 24

Section 1.1 (Verifying Solutions & Modeling Falling/Accelerating Bodies) & Section 1.2 (Integrals as Solutions)

Thursday August 26

Section 1.2 (Initial Value Problems & Integration by Parts Review) & Section 1.3 (Slope Fields / Direction Fields)

Tuesday August 31

Section 1.3 (Slope Fields, Solution Curves & Numerical Approximation Intro)

Thursday September 2

Section 1.3 / 1.4 (Simpson's Rule / Numerical Approximation & Intro to Separation of Variables)

Tuesday September 7

Section 1.4 (Separable Equations & Solving the Logistic Equation via Partial Fractions)

Thursday September 9

Section 1.4 / 1.5 (Applications of Separation of Variables, Intro to 1D Heat Equation, & Linear First-Order Equations / Integrating Factors)

Tuesday September 14

Section 1.5 (First-Order Linear Differential Equations & Integrating Factors)

Thursday September 16

Section 1.6 / 2.1 (Substitution Methods, Exact Equations, & Population Models)

Tuesday September 21

Section 2.2 (Autonomous Differential Equations & Stability of Critical / Equilibrium Points)

Thursday September 23

Section 2.2 / 2.3 (Bifurcation Diagrams & Acceleration-Velocity Models)

Thursday September 30

Section 2.3 & Section 2.4 (Newton's Gravitation, Escape Velocity Models, & Numerical Methods / Euler's Method)

Tuesday October 5

Section 3.1 & Section 3.2 (Second-Order Linear Homogeneous Equations, Characteristic Equations, & Distinct/Repeated Roots)

Thursday October 7

Section 3.2 & Section 3.3 (General Linear Homogeneous Equations & Homogeneous Equations with Constant Coefficients)

Thursday October 14

Section 3.3 & Section 3.4 (Complex & Repeated Roots, Euler's Formula, & Mechanical Vibrations / Harmonic Oscillators)

Tuesday October 19

Section 3.5 (Non-Homogeneous Equations & Method of Undetermined Coefficients)

Tuesday October 26

Section 3.5 & Section 3.6 (Rules for Undetermined Coefficients & Intro to Forced Oscillations)

Tuesday November 2

Section 3.6 (Forced Oscillations, Damped vs. Undamped Forcing, & Resonance)

Thursday November 4

Section 5.1 (Introduction to Systems of First-Order Linear Differential Equations & Matrix Review)

Tuesday November 9

Section 5.1 & Section 5.2 (Matrix Representation of Systems & The Eigenvalue Method for Homogeneous Systems)

Thursday November 11

Section 5.2 (The Eigenvalue Method with Distinct Real & Complex Eigenvalues)

Tuesday November 16

Section 5.2 & Section 5.3 (Complex Eigenvalues, Direction Fields / Trajectories, & Phase Plane Classifications)

Thursday November 18

Section 5.3 & Section 5.5 (Classification of 2D Linear Systems & Multiple / Repeated Eigenvalues / Generalized Eigenvectors)

Tuesday November 23

Section 5.5 & Section 5.7 (Defective Eigenvalues / Chains of Generalized Eigenvectors & Intro to Non-Homogeneous Linear Systems)

Tuesday November 30

Section 5.7 & Final Exam Review (Undetermined Coefficients for Linear Systems & Comprehensive Final Review)

Additional Notes
Sec 4.1: First-Order Systems and Applications