MATH 320 covers both some linear algebra and some differential equation theory. As such, students who complete this course can consider themselves as also having some of the content of MATH 319 (Techniques in Ordinary Differential Equations). The difference between this course and taking both MATH 319 and 340 is that one will be able to see how theory and applications unite in a meaningful way. This course also lends itself to the MATH 321-322 applied analysis sequence.
Students who have completed MATH 320 will need to complete one of MATH 421; the applied analysis sequence MATH 321-322; or MATH 467 before moving on to 500-level courses that require introductory proofs coursework.
In a regular fall or spring semester, MATH 320 is often taught with both general sections and an Accelerated Honors (!) section. There are some differences between the two:
General MATH 320
Differential equations and linear algebra are crucial for the analysis and control of many dynamical systems such as electrical networks, mechanical structures, chemical and biological networks. Those applications lead to often very large systems of coupled differential equations. The study of the equilibria, stability and control of such systems requires the concepts and tools of differential equations and linear algebra. MATH 320 is a first course in the study of differential equations and linear algebra.
MATH 320 Honors
Accelerated Honors at UW-Madison are Honors courses open to anyone and not restricted to students in the L&S Honors program. MATH 320 Honors is recommended for students in all applied areas including all areas of engineering, as well as the physical, chemical, and biological sciences. Differential equations and linear algebra are crucial to the study of dynamical systems such as electrical networks, mechanical structures, and chemical reaction networks. MATH 320 Honors has recently used Gilbert Strang’s Differential Equations and Linear Algebra textbook. MATH 320 Honors covers some material that is important for engineering and data science applications but may not be covered in the general (non-Honors) MATH 320 lectures such as, for example, the Dirac delta function and impulse response, the PLU and CR matrix decompositions, together with an introduction to the use of modern computational tools such as MATLAB (or Python).
In summary, MATH 320…
- Is useful for students interested in classical applications of mathematics (e.g., physics, engineering, continuous modeling, etc.);
- Covers material in MATH 319 and therefore credit for only one of MATH 319 or 320 can be applied to the math major or certificate;
- Is not by itself sufficient for taking advanced math courses;
- Is a good introduction to how theory and applications support each other;
- Is offered with an Accelerated Honors (!) version in some semesters. This version is suggested for potential math majors and those in the AMEP program.
Suggested further courses are…
- The applied analysis sequence MATH 321-322, which covers more mathematics useful for traditional applications;
- MATH 415, which includes both continuous and discrete models of changing systems;
- MATH 421 for an introduction to more formal mathematical arguments.