Difference between revisions of "Math 410: Intro to Numerical Methods"
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=== Offered === | === Offered === | ||
− | F | + | F (even years) |
=== Prerequisite === | === Prerequisite === | ||
− | [[Math 314]]. | + | [[Math 314]]. CS 111 |
=== Description === | === Description === | ||
− | Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods. | + | Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods. [This official course description appears to differ with current standard practice, in that iterative solvers of linear systems are taught in this course, while "Fourier and other orthogonal methods" are postponed until [[Math 411]].] |
== Desired Learning Outcomes == | == Desired Learning Outcomes == | ||
Line 24: | Line 24: | ||
=== Minimal learning outcomes === | === Minimal learning outcomes === | ||
− | + | Students should be able to describe, derive, and implement the numerical methods listed below. They should be able to explain the advantages and disadvantages of each method. They should understand error analysis and be able to make practical decisions based on the outcomes of that analysis. | |
+ | <div style="-moz-column-count:2; column-count:2;"> | ||
# Numerical solution of equations of one variable | # Numerical solution of equations of one variable | ||
#* Bisection method | #* Bisection method | ||
+ | #* Secant method | ||
#* Fixed-point iteration | #* Fixed-point iteration | ||
#** Newton's method | #** Newton's method | ||
Line 38: | Line 40: | ||
#* Cubic spline interpolation | #* Cubic spline interpolation | ||
# Numerical differentiation | # Numerical differentiation | ||
+ | #* Derivation of formulas | ||
+ | #** Backward-difference | ||
+ | #** Forward-difference | ||
+ | #** Centered-difference | ||
+ | #** Error analysis | ||
#* Richardson's extrapolation | #* Richardson's extrapolation | ||
# Numerical integration | # Numerical integration | ||
Line 45: | Line 52: | ||
#* Gaussian quadrature | #* Gaussian quadrature | ||
#* Multiple integrals | #* Multiple integrals | ||
+ | #* Error analysis | ||
# Numerical solution of linear systems | # Numerical solution of linear systems | ||
#* Direct methods | #* Direct methods | ||
Line 54: | Line 62: | ||
#** Gauss-Seidel iteration | #** Gauss-Seidel iteration | ||
#** Relaxation methods | #** Relaxation methods | ||
+ | |||
+ | |||
+ | |||
+ | |||
</div> | </div> | ||
+ | |||
+ | === Textbooks === | ||
+ | Possible textbooks for this course include (but are not limited to): | ||
+ | |||
+ | * Richard L. Burde and J. Douglas Faires, ''Numerical Analysis (9th Edition)'', Brooks Cole, 2010. | ||
=== Additional topics === | === Additional topics === |
Latest revision as of 11:36, 14 March 2024
Contents
Catalog Information
Title
Introduction to Numerical Methods.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F (even years)
Prerequisite
Math 314. CS 111
Description
Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods. [This official course description appears to differ with current standard practice, in that iterative solvers of linear systems are taught in this course, while "Fourier and other orthogonal methods" are postponed until Math 411.]
Desired Learning Outcomes
Prerequisites
Students are required to have had multivariable calculus.
Minimal learning outcomes
Students should be able to describe, derive, and implement the numerical methods listed below. They should be able to explain the advantages and disadvantages of each method. They should understand error analysis and be able to make practical decisions based on the outcomes of that analysis.
- Numerical solution of equations of one variable
- Bisection method
- Secant method
- Fixed-point iteration
- Newton's method
- Error analysis
- Polynomial equations
- Interpolation
- Lagrange interpolation
- Divided-difference methods
- Hermite interpolation
- Cubic spline interpolation
- Numerical differentiation
- Derivation of formulas
- Backward-difference
- Forward-difference
- Centered-difference
- Error analysis
- Richardson's extrapolation
- Derivation of formulas
- Numerical integration
- Newton-Cotes formulas
- Composite integration
- Adaptive quadrature
- Gaussian quadrature
- Multiple integrals
- Error analysis
- Numerical solution of linear systems
- Direct methods
- Gaussian elimination
- Pivoting strategies
- Factorization methods
- Gaussian elimination
- Iterative methods
- Jacobi iteration
- Gauss-Seidel iteration
- Relaxation methods
- Direct methods
Textbooks
Possible textbooks for this course include (but are not limited to):
- Richard L. Burde and J. Douglas Faires, Numerical Analysis (9th Edition), Brooks Cole, 2010.
Additional topics
Courses for which this course is prerequisite
Math 410 is the introductory numerical analysis course and is a prerequisite for the other 3 numerical analysis courses: Math 411, 510, and 511. It is also a prerequisite for Math 480.