Math 54

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

Course Format: Three hours of lecture and three hours of discussion per week.

Prerequisites: 1A-1B, 10A-10B or equivalent. 

Description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations, symmetric matrices. Linear ordinary differential equations (ODE); systems of linear ODE.  Fourier series. (F,SP)

Textbook: Lay-Lay-McDonald, Linear Algebra and its Applications (5th ed) and Nagle-Saff-Snider, Fundamentals of Differential Equations and Boundary Value Problems (6th ed). A specially priced UC Berkeley paperback edition of both books is available.

Part One: (Lay et al)

Chapter 1: Linear Equations in linear algebra
4 hours
Sections 1.1-1.5, 1.7-1.9

Chapter 2: Matrix Algebra
2 hours
Sections 2.1-2.3

Chapter 3: Determinants
3 hours
Sections 3.1-3.3

Chapter 4: Vector Spaces
5 hours
Sections 4.1-4.7

Chapter 5: Eigenvalues and eigenvectors
4 hours
Sections 5.1-5.4

Chapter 6: Orthogonality, least Squares
5 hours
Sections 6.1-6.5, 6.7

Chapter 7: Symmetric matrices, applications
3 hours
Sections 7.1, 7.3-7.5

          Total hours on Linear Algebra
26 hours
Part Two: (Nagle et al)

Chapter 4: Linear Second-Order ODE
4 hours
Sections 4.2-4.6

Chapter 9: Systems of linear ODE
4 hours
Sections 9.1, 9.4-9.7 (Also Section 5.7 in Lay et al)

Chapter 10: Fourier Series, application to PDE
4 hours
Sections 10.3-10.5

          Total hours on Differential Equations
12 hours
Total for Parts One and Two
38 hours
Midterms + holidays 
4 hours

The total number of class hours may vary during the Fall and Spring semesters.

42 hours