NUMERICAL ANALYSIS

Prerequisites & course information

Requisites: ( MATH 320 , 340 , 341 , 345 , or 375 ), ( MATH 322 , 341 , 375 , 421 , or 521 ), and ( COMP SCI 200 , 220 , 300 , or placement into COMP SCI 300 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in numerical analysis (e.g., Lagrange polynomials, Gibbs phenomenon, Runge phenomenon, orthogonal polynomials, recurrence relation, Gaussian quadrature points, splines, etc.). Audience: Both Grad & Undergrad 2. Use different techniques of numerical analysis in their appropriate settings (e.g., polynomial interpolation, least square approximation, discrete Fourier transform, the Golub-Welsch algorithm, fast Fourier transform, trapezoidal rule and Simpson's rule, numerical differentiation, forward and backward Euler's method, etc.). Audience: Both Grad & Undergrad 3. State the main theoretical results related to the error analysis for different methods (e.g., least square error, numerical integration using a Riemann sum, the trapezoidal rule, Simpson's rule and Gaussian quadratures, (semi-)discrete Fourier transform, forward and backward Euler, etc.), and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 5. Identify applications of course content in current areas of research. Audience: Graduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in numerical analysis (e.g., Lagrange polynomials, Gibbs phenomenon, Runge phenomenon, orthogonal polynomials, recurrence relation, Gaussian quadrature points, splines, etc.). Audience: Both Grad & Undergrad 2. Use different techniques of numerical analysis in their appropriate settings (e.g., polynomial interpolation, least square approximation, discrete Fourier transform, the Golub-Welsch algorithm, fast Fourier transform, trapezoidal rule and Simpson's rule, numerical differentiation, forward and backward Euler's method, etc.). Audience: Both Grad & Undergrad 3. State the main theoretical results related to the error analysis for different methods (e.g., least square error, numerical integration using a Riemann sum, the trapezoidal rule, Simpson's rule and Gaussian quadratures, (semi-)discrete Fourier transform, forward and backward Euler, etc.), and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 5. Identify applications of course content in current areas of research. Audience: Graduate