Math 54

Math 54 - Linear Algebra & Differential Equations -- [4 units]

Prerequisites: 1A-1B or equivalent. Note: calculus courses at most institutions either have no differential equations, or less than Berkeley's Math 1B. Transfer students who have taken such a course need to learn that differential equations material (Stewart, Calculus: Early Transcendentals, 5th Ed., Ch.s 9 and 17) on their own, by approximately the 10th week of Math 54. The instructor and TA's should emphasize this fact.

Description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. (F,SP)

Textbooks: Lay, Linear Algebra and It's Applications, 3rd edition, UC Berkeley paperback edition.

Nagle, Saff and Snider, Fundamentals of Differential Equations and Boundary Value Problems, UC Berkeley paperback edition.

Lay, Ch. 1: Linear Equations	4 hours
(Sections 1.1-1.5, 1.7-1.9)
Lay, Ch. 2: Matrix Algebra	4 hours
(Sections 2.1-2.3, 2.8-2.9)
Lay, Ch. 3: Determinants	2 hours
(Sections 3.1-3.3)
Lay, Ch. 4: Vector Spaces	6 hours
(Sections 4.1-4.7)
(Spend more than 1 hour on Section 4.7)
Lay, Ch. 5: Eigenvalues and Eigenvectors	4 hours
(Sections 5.1-5.4)
Lay, Ch. 6: Orthogonality	5 hours
(Sections 6.1-6.5, 6.7)
Lay, Ch. 7: Symmetric Matrices	1 hour
(Sections 7.1)
Total No. of Hours on Linear Algebra	26 hours
NS&S, Ch. 4: Second Order Linear ODE	3 hours
(Sections 4.2-4.5)
Note: Sections 4.3 and 4.4 review Math 1B.
NS&S, Ch. 6: Higher Order Linear ODE	2 hours
(Sections 6.1-6.2)
NS&S, Ch. 9: Systems of Linear ODE	3 hours
(Sections 9.1, 9.4, 9.5, 9.6)
NS&S, Ch. 10: Fourier Series, PDE	7 hours
(Sections 10.1-10.6)
Total No. of Hours on ODE, Fourier Analysis	15 hours
Total	41 hours
Midterms	2 hours
Holidays & Reviews	2 hours
	45 hours