Public learning track
Numerical Methods for Root Finding
12th Grade · Math · Open Global Math
9 lessons
Goal
Locate and approximate roots of algebraic and transcendental equations using sign-change tests, fixed-point iteration, and Newton-Raphson methods while evaluating convergence criteria and failure conditions.
Featured Diagrams
Locating Roots by Sign Change Tests and Continuity
9 lessons
0 of 9 done
- 1Locating Roots by Sign Change Tests and ContinuityUp nextStart
- 2Limitations and Failure Modes of Sign Change MethodsPremiumNot started yet
- 3Rearranging Equations for Fixed-Point Iteration x = g(x)Not started yet
- 4Convergence Criteria for Fixed-Point IterationNot started yet
- 5Staircase and Cobweb Diagrams for IterationNot started yet
- 6Executing Fixed-Point Iterations to Prescribed AccuracyNot started yet
- 7Deriving the Newton-Raphson Formula GeometricallyNot started yet
- 8Applying Newton-Raphson to Polynomial and Transcendental EquationsNot started yet
- 9Failure Cases of the Newton-Raphson MethodNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
9 lessons
Numerical Methods for Root Finding
Locate and approximate roots of algebraic and transcendental equations using sign-change tests, fixed-point iteration, and Newton-Raphson methods while evaluating convergence criteria and failure conditions.
2
5 lessons
Numerical Integration and Approximation Bounds
Approximate definite integrals using the Trapezium Rule, determine upper and lower bounds, analyze error behavior from curve convexity, and solve contextual problems.