Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 320: Linear Algebra and Differential Equations

Students in the physical sciences, engineering, Applied Math, Engr and Physics (AMEP)
 
Background and Goals: 

Differential equations arise in many areas of science and engineering to model continuous change, in particular to model time evolution of a system.  Linear algebra is the study of linear systems of equations, linear functions, matrices and vector spaces. In math 320, we shall study these subjects together for three reasons: (1) The viewpoint of linear algebra is immensely helpful in uncovering the order underlying the topic of differential equations; it helps us understand the ``why'' and not just the ``how'' of our calculations, (2) Linear algebra is essential to the theory of differential equations, and (3) linear algebra is crucial to the computer approximations which are often the only way to solve the most challenging ordinary and partial differential equations.

Alternatives: Math 319 focuses on differential equations and avoids using linear algebra concepts.  Math 340 is a standard first course in linear algebra. Combining both topics in a single course, as in Math 320, is intellectually sensible but demanding since both differential equations and linear algebra are covered in a single course. Math 320 focuses on linear systems of differential equations such as those arising from modeling of electrical networks and coupled mass-spring systems.
 
Subsequent Courses: Math 320, 321, 322 are a core mathematics sequence for the physical sciences. Math 513 (numerical linear algebra) and 514 (numerical analysis) investigate the numerical methods and algorithms needed to construct approximations to calculus, differential equations and linear algebra problems. 
 
Course Content: 
  • First-Order ODEs
  • Mathematical Modeling and Numerical Methods
  • Linear Systems and Matrices
  • Vector Spaces
  • Higher-Order Linear ODEs
  • Eigenvalues and Eigenvectors
  • Linear Systems of ODEs
  • Matrix Exponential Methods (to solve non-homogeneous systems)
  • Nonlinear Systems
credits: 
3. (N-A)
semester: 
FallSpring
prereqs: 
MATH 222 or 276 or graduate or professional standing

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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