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

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)