Math 54, Summer 2019
Syllabus
Office Hours: MWF 10-11, 1087 Evans

Homework:
Homework 1 Due June 27 Solutions
Homework 2 Due July 2 Solutions
Homework 3 Due July 5 Solutions
No homework due July 9.
No homework due July 11.
Homework 4 Due July 16 (An alternate version was accidently posted on Monday morning--also fine if you did that one instead. Sorry for the mixup.) Solutions
Homework 5 Due July 18 Solutions
Homework 6 Due July 23 Solutions
Homework 7 Due July 25 Solutions
No homework due July 30.
Homework 8 Due August 6 Solutions
Homework 9 Due Tuesday August 13 Solutions
Homework 10 Due Tuesday August 13 Solutions

Class Summary
June 24: Review
June 25: Lines and planes in R^2 and R^3, row reduction (Lay 1.1, 1.2)
June 26: More row reduction, parametrizing solutions to linear equations (Lay 1.1, 1.2)
June 27: Visualizing parametrized solutions, span, linear independence (Lay 1.3, 1.5, 1.7)
June 28: Examples of span and linear independence, definition of subspaces and bases (Lay 1.3, 1.7, 4.1, 4.3)
July 1: More bases, matrix multiplication (Lay 4.3, 2.1)
July 2: Injectivity, surjectivity, image (reference); Linear transformations (Lay 1.8)
July 3: Kernel of a linear map, more on injectivity and surjectivity (Lay 4.2)
July 5: The matrix of a linear map (Lay 1.9)
July 9: Midterm 1. 8:10-9 AM. The midterm will cover material through July 5. There will be no lecture 9-10 AM. Practice 1 Solutions Practice 2 Solutions Midterm Solutions
July 10: Invertible Matrices (Lay 2.2, 2.3)
July 11: Determinants (Lay 3.1, 3.2)
July 12: More Determinants (Lay 3.1, 3.2)
July 15: Change of Basis (notes), Eigenvectors/Eigenvalues/Eigenspaces (Lay 5.1)
July 16: Solving for eigenvectors and eigenvalues, diagonalization (Lay 5.2, 5.3)
July 17: More diagonalization, computing Fibonacci numbers
July 18: Solution to the Fibonacci problem
July 19: Complex Numbers, Matrices with complex eigenvalues (Lay 5.5)
July 22: The dot product (Lay 6.1)
July 23: Orthogonal sets and Gram-Schmidt (Lay 6.2, 6.4)
July 24: Orthogonal Complements and Orthogonal Projections (Lay 6.3)
July 25: Orthogonal Projections in Statistics (not on midterm) (Lay 6.5, 6.6), SVD (Lay 7.4)
July 26: More SVD
July 29: Midterm 2 Review
July 30: Midterm 2. 8:10-9 AM. There will be no lecture 9:00-10 AM. The midterm will cover the material from July 10-July 26. To be more precise, it will cover the material from 2.2 (not the part about elementary matrices), 2.3, 2.9 (not the part about coordinate systems), 3.1, 3.2, 5.1, 5.2, 5.3, 5.5, 6.1 (not theorem 3), 6.2, 6.3, 6.4 (not QR factorization), 7.4 (not applications of SVD). I won't ask you to compute a singular value decomposition but I might ask you to do something with a singular value decomposition that I give you. Practice 1 Solutions Practice 2 Solutions Midterm Solutions
July 31: Various kinds of differential equations
August 1: First-order differential equations; homogeneous and inhomogeneous equations
August 2: Second-order differential equations (Nagle 4.2, 4.3, 4.4)
August 5-9: Fourier Series and Partial Differential Equations
August 12-14: Final Review Practice Final 1 Solutions Practice Final 2 Solutions
August 15: Final (usual classroom, 8:10-10 AM)