Spring 2022
- MATH 311-504: Topics in Applied Mathematics I
Time and venue: TR 12:45–2:00 p.m., BLOC 163
Office hours (BLOC 301b):
- TR 2:10–3:00 p.m.
- by appointment
Office hours (ZOOM meeting):
- Wednesday 5:00–6:00 p.m.
- by appointment
Help sessions for MATH 304 (online at MLC):
Office hours during the finals (ZOOM meeting):
- Wednesday, May 4, 5:00–6:00 p.m.
- Friday, May 6, 3:00–6:00 p.m.
- by appointment
Office hours during the finals (BLOC 301b):
- Monday, May 9, 11:00 a.m.–2:00 p.m.
Final exam: Tuesday, May 10, 8:00-10:00 a.m., BLOC 163
Course outline:
Part I: Elementary linear algebra
- Systems of linear equations
- Gaussian elimination, Gauss-Jordan reduction
- Matrices, matrix algebra
- Determinants
Leon/Colley: Chapters 1-2
Lecture 1: Systems of linear equations.
Lecture 2: Gaussian elimination. Gauss-Jordan reduction.
Lecture 3: Gauss-Jordan reduction (continued). Applications of systems of linear equations.
Lecture 4: Matrix algebra. Diagonal matrices. Inverse matrix.
Lecture 5: Inverse matrix (continued). Transpose of a matrix.
Lecture 6: Determinants.
Part II: Abstract linear algebra
- Vector spaces
- Linear independence
- Basis and dimension
- Coordinates, change of basis
- Linear transformations
Leon/Colley: Chapters 3-4
Lecture 7: Vector spaces. Subspaces.
Lecture 8: Subspaces of vector spaces (continued). Span. Spanning set.
Lecture 9: Linear independence. Basis of a vector space.
Lecture 10: Basis and dimension (continued). Rank and nullity of a matrix.
Lecture 11: Review for Test 1.
- Leon/Colley 1.1-1.5, 2.1-2.2, 3.1-3.4, 3.6
Lecture 12: Basis and coordinates. Change of basis. Linear transformations.
Lecture 13: Linear transformations (continued). General linear equations. Matrix representation of linear maps.
Lecture 14: Matrix of a linear transformation (continued). Similar matrices.
Part III: Advanced linear algebra
- Eigenvalues and eigenvectors
- Diagonalization
- Orthogonality
- Inner products and norms
- The Gram-Schmidt orthogonalization process
Leon/Colley: Chapters 5-7
Lecture 15: Eigenvalues and eigenvectors. Characteristic equation.
Lecture 16: Diagonalization.
Lecture 17: Euclidean structure in Rn. Orthogonal complement. Orthogonal projection.
- Leon/Colley 5.1-5.2, 7.3, 7.6
Lecture 18: Orthogonal projection (continued). Least squares problems. Norm of a vector.
Lecture 19: Inner products. Orthogonality in inner product spaces. The Gram-Schmidt process.
Lecture 20: Review for Test 2.
- Leon/Colley 3.5, 4.1-4.3, 5.1-5.6, 6.1, 6.3
Part IV: Vector analysis
- Main notions of vector analysis
- Review of multiple integrals
- Line and surface integrals
- Green's, Gauss' and Stokes' theorems
Leon/Colley: Chapters 8-11
Lecture 21: Review of differential calculus. Differentiation in normed vector spaces.
- Leon/Colley 7.4, 8.1, 8.3
Lecture 22: Gradient, divergence and curl. Review of integral calculus. Area and volume.
- Leon/Colley 7.4, 8.4, 9.5
Lecture 23: Area and volume (continued). Multiple integrals.
- Leon/Colley 7.4, 7.7, 9.1-9.5
Lecture 24: Line integrals. Conservative vector fields. Surfaces.
- Leon/Colley 8.2, 10.1-10.3, 11.1
Lecture 25: Area of a surface. Surface integrals.
Lecture 26: Review for the final exam.
- Leon/Colley 1.1-1.5, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.6, 6.1, 6.3, 8.1-8.4, 9.1-9.5, 10.1-10.3, 11.1-11.3