MATH 20580, Introduction to linear algebra and differential
equations
Notre Dame, Spring 2022
Schedule: Monday, Wednesday, Friday 12:50-1:40 (section 05),
2:00-2:50 (section 06), Hayes-Healy 117
Office hours: Monday, Wednesday 4:00-5:00 by Zoom (link)
Digital resources: link
Lecture notes:
1/10 (Poole
2.1, 2.2: Gaussian elimination, row echelon form)
1/12 (Poole 2.2:
Gauss-Jordan elimination, free and leading variables)
1/15 (Poole 2.3, 3.1,
3.3: spans, matrix operations)
1/19 (Poole 3.6:
linear transformations)
1/21 (Poole 2.3, 3.5:
linear independence, subspaces)
1/24 (Poole 3.5: row,
column, null space of a matrix; basis for a subspace)
1/26 (Poole 3.5:
dimension, rank, nullity)
1/28 (Poole 6.3:
coordinate systems)
1/31 (Poole 6.3:
change of basis)
2/4 (Poole 6.1: vector
spaces and subspaces)
2/7 (Poole 6.2: linear
independence, basis, dimension)
2/9 (Poole 6.2, 6.4,
6.5 basis, dimension; linear transformations; kernel and range)
2/11 (Poole 6.5, 6.2:
kernel and range, isomorphisms, coordinates in a vector space)
2/14 (Poole 6.3, 6.6:
change of basis in a vector space; matrix of a linear
transformation)
2/16 (Poole 6.6:
matrix of a linear transformation)
2/18 (Poole 4.2:
determinants)
2/21 (Poole 4.2:
determinants, Cramer's rule)
2/23 (Poole 4.1, 4.3:
eigenvectors and eigenvalues)
2/25 (Poole 4.4:
similarity and diagonalization)
2/28 (Poole 4.4, 4.6:
diagonalization, complex eigenvalues)
3/2 (Poole 4.6: complex
eigenvalues continued)
3/4 (Poole 1.2, 5.1,
5.2: orthogonality, orthogonal complements)
3/14 (Poole 5.1, 5.2:
orthogonal projection, orthonormal sets)
3/16 (Poole 5.1, 5.3:
orthonormal sets, Gram-Schmidt process, QR factorization)
3/18 (Poole 5.3, 7.3:
QR factorization, least squares solutions)
3/21 (Poole 7.3: least
squares solutions)
3/23 (Zill 1.1, 1.2:
types of differential equations, solutions, initial value problems)
3/25 (Zill 2.1, 2.2:
Direction fields, autonomous equations, separable equations)
3/28 (Zill 2.3, 2.4:
linear first order ODEs, exact equations)
3/30 (Zill 2.4, 4.1:
exact equations, existence and uniqueness of solutions of IVPs for
linear ODEs)
4/1 (Zill 4.1, 4.2:
second order linear homogeneous ODEs, Wronskian)
4/4 (Zill 4.2, 4.3:
second order linear homogeneous ODEs - reduction of order, equations
with constant coefficients)
4/6 (Zill 4.3, 4.4:
second order homogeneous equations with constant coefficients,
nonhomogeneous equations -- method of undetermined coefficients)
4/8 (Zill 4.4: method
of undetermined coefficients)
4/11 (Zill 4.6, 4.8.1:
variation of parameters, Green's function)
4/13 - review session, notes: PE3A1, PE3A2, PE3A3, PE3B1, PE3B2, PE3B3, PE3C1, PE3C2, PE3C3 (A,B,C - practice exam variant;
last digit 1 = solutions I wrote for myself, 2= notes from 12:50
section, 3=notes from 2:00 section)
4/20 (Zill 5.1:
Vibrations)
Links to video recordings of classes:
section
5, section
6