Instructor Key

DF = Prof. Dan Frey
GS = Prof. Gilbert Strang

Session Key

L = Lecture
R = Recitation
E = Quiz or Exam

L1 Course introduction: What are differential equations and linear algebra? How do engineers use them? Four examples of first order differential equations. DF Problem Set 1
L2 First-order equations: Constant source, step function (Heaviside), delta (Dirac), exponentials, real and complex sinusoids. GS  
R1 Recitation    
L3 First-order equations (continued): Separable equations, exact equations. GS

Problem Set 1 Due

Problem Set 2 Assigned

L4 Second-order equations: Second derivatives in engineering, complex numbers, constant coefficient equations. GS  
E1 Quiz 1
L5 Second-order equations (continued): Forced oscillations, examples in electrical and mechanical systems, Laplace transforms. GS Problem Set 3 Assigned
L6 Laplace transforms (continued): Graphical Methods: Direction fields, nonlinear equations, sources, sinks, saddles, and spirals. DF Problem Set 2 Due
R2 Recitation    
L7 Graphical and numerical methods: Linearization, stability, Euler's method. DF  
L8 Linear systems of equations: Gaussian elimination, matrix multiplication. DF  
R3 Recitation    
L9 Linear systems of equations: Matrix inverse. Existence and uniqueness of solutions. Column, row, null space. DF

Problem Set 3 Due

Problem Set 4 Assigned

L10 Linear systems of equations (continued): Mechanical engineering examples. DF  
R4 Recitation    
E2 Quiz 2: Oral exams scheduled throughout the week.
L11 Eigenvalues and eigenvectors: The eigenvalue problem. Diagonalization, exponentiation of a matrix. DF

Problem Set 4 Due

Problem Set 5 Assigned

L12 Least squares and projection: Positive definite matrices. Singular value decomposition. DF Problem Set 5 Due
L13 Review session for the final exam. DF  
R5 Review session for the final exam (continued).    
E3 Final Exam