APPLIED MATH I, 2015
SYLLABUS
INSTRUCTOR: Paoti Chang
TEXTBOOK: Gilbert Strang, “LINEAR ALGEBRA AND ITS APPLICATIONS,” Foruth
ED. (2014),
GRADING POLICY: MIDTERM 40%, FINAL 40%, HOMEWORK 20%
EXAM DATES: MIDTERM- APRIL 14, 2009 (IN THE REGULAR MIDTERM WEEK); FINAL-
JUNE 9, 2009 (ONE WEEK EARLIER THAN THE SCHOOL CALENDAR SUGGESTS, WITH A
MAKE-UP CLASS ON JUNE 16)
NO LATE HOMEWORK ACCEPTED!
WE PLAN TO COVER THE FOLLOWING TOPICS:
1. WHAT DOES LINEAR MEAN, AND WHAT IS SO GOOD ABOUT IT?
2. SOLVING SYSTEMS OF LINEAR EQUATIONS
(A) ELIMINATION, THE ALL-AROUND METHOD EVEN IN THIS COMPUTER AGE!
(B) MATRICES
3. VECTOR SPACES
(A) VECTORS
(B) INDEPENDENCE, BASIS AND DIMENSION
(C) LINEAR TRANSFORMATIONS AND THEIR RANKS
(D) LINEAR FUNCTIONALS (NOT IN THE TEXTBOOK)
(E) DUAL SPACE (NOT IN THE TEXTBOOK)
4. DETERMINANTS
(A) FROM ELIMINATION TO DETERMINANTS
(B) CRAMER’S RULE: WHEN TO USE IT, AND WHEN NOT TO
5. EIGENVALUES AND EIGENVECTORS
(A) DIAGONALIZATION: WHAT IS IT GOOD FOR?
(B) WHAT DOES A COMPLEX EIGENVALUE MEAN?
(C) A TASTE OF PERTURBATION THEORY (NOT IN THE TEXTBOOK)
6. ORTHOGONALITY
(A) INNER PRODUCT
(B) PROJECTIONS
(C) GRAM-SCHMIDT PROCESS
(D) FOURIER TRANSFORM
(E) THE PRINCIPAL-AXIS-THEOREM AND NORMAL MODES