Logic, Computational & Advanced Mathematics
Numerical Methods and Optimization
Use numerical algorithms and optimization methods to approximate solutions, assess error, and make defensible model-based decisions.
- Level
- Level 5 — Higher Mathematics
- Learning time
- 20 hours
- Format
- Extended Course
- Modules
- 10
Course structure
A clear outline before lessons begin.
This course is published as a development map. Full lessons, practice, and assessments will be added after content review.
Prerequisites
Complete these courses before beginning when they are available.
Learning outcomes
By the end, learners will be able to…
- Formulate numerical problems with stated assumptions and error tolerance.
- Approximate roots, systems, derivatives, integrals, and differential-equation solutions.
- Compare numerical methods for accuracy, efficiency, and stability.
- Apply unconstrained and constrained optimization concepts to models.
- Interpret iterative results and communicate numerical uncertainty.
- Select a method appropriate to the scale and structure of a problem.
Module outline preview
10 planned modules
Estimated times add up to the course’s planned learning time. Every module is in development.
- 012 hours · In Development
Computation, Error, and Stability
Measure approximation error and recognize numerical limitations.
- 022 hours · In Development
Root-Finding Methods
Approximate equation solutions with bracketing and iterative methods.
- 032 hours · In Development
Numerical Linear Systems
Solve matrix systems computationally and evaluate conditioning.
- 042 hours · In Development
Interpolation and Approximation
Build approximating functions from discrete values.
- 052 hours · In Development
Numerical Differentiation and Integration
Estimate rates and accumulated quantities from sampled data.
- 062 hours · In Development
Numerical Differential Equations
Approximate initial-value solutions with step-based methods.
- 072 hours · In Development
Optimization Models
Express objectives, variables, and constraints mathematically.
- 082 hours · In Development
Unconstrained Optimization
Use derivative and iterative ideas to locate extrema.
- 092 hours · In Development
Constrained and Linear Optimization
Analyze feasible regions and optimize subject to limits.
- 102 hours · In Development
Validation and Optimization Synthesis
Compare methods, test results, and communicate a defensible recommendation.
Course status
Course coming soon
This course is not yet open for enrollment and does not include lessons, practice, assessments, or formal credit. You can review the outline while it is developed.