The calendar below provides information on the course’s lecture (L), recitation (R) and exam (E) sessions.

L0 Terminology and implicit solutions  
Unit I: First-order differential equations  
L1 Integration and solutions  
R1 Recitation 1  
L2 Fundamental principles  
L3 First-order linear equations  
R2 Recitation 2  
L4 Separable equations  
R3 Recitation 3  
L5 Linear fractional equations Problem set 1 due
Unit II: Second-order linear equations  
L6 Second-order linear equations  
L7 Mechanical oscillation  
R4 Recitation 4  
L8 Uniqueness and the wronskian Problem set 2 due
L9 Separation and comparison theorems  
R5 Practice midterm 1  
E1 Midterm 1  
R6 Recitation 6  
L10 The maximum principle  
Unit III: Higher-order linear equations  
L11 Higher-order linear equations  
R7 Recitation 7  
L12 Solution bases  
R8 Recitation 8  
L13 Inhomogeneous equations Problem set 3 due
L14 Stability  
R9 Recitation 9  
L15 Wellposedness; introduction  
R10 Recitation 10  
L16 Uniform convergence Problem set 4 due
L17 Uniqueness and continuity  
R11 Practice midterm 2  
E2 Midterm 2  
L18 Remarks on wellposedness  
Unit V: The Laplace transform  
L19 Laplace transform  
L20 Transform and differential equations: generalized solutions, application to ODEs  
R12 Recitation 12  
L21 Step functions Problem set 5 due
L22 Convolution  
R13 Recitation 13  
L23 The dirac distribution  
R14 Recitation 14  
L24 The transfer function and the pole diagram Problem set 6 due
Unit VI: The linear systems  
L25 Linear systems  
R15 Recitation 15  
L26 Eigenvalues and eigenvectors  
R16 Recitation 16 Problem set 7 due
L27 Complex solutions and the fundamental matrix  
R17 Practice midterm 3  
E3 Midterm 3  
L28 Repeated eigenvalues and the matrix exponential  
L29 Phase planes I  
L30 Phase planes II  
L31 Plane autonomous system Problem set 8 due
L32 Stability and almost linear systems  
L33 Problems from ecology  
L34 Methods of Lyapunov Problem set 9 due
L35 Nonlinear oscillations  
L36 The Poincare-Bendixson theorem  
R18 Recitation 18  
E4 Final exam  

Course Info

Learning Resource Types

assignment_turned_in Problem Sets with Solutions
notes Lecture Notes
group_work Projects with Examples