Public learning track
Numerical Calculus and Iterative Methods
11th Grade · Math · Open Global Math
7 lessons
Goal
Locate roots via sign change, solve equations using fixed-point iteration and Newton-Raphson, and approximate integrals with the trapezium rule.
Featured Diagrams
Locating Roots Using the Intermediate Value Property
7 lessons
0 of 7 done
- 1Locating Roots Using the Intermediate Value PropertyUp nextStart
- 2Rearranging Equations for Fixed-Point Iteration: x = g(x)PremiumNot started yet
- 3Analyzing Convergence with Staircase and Cobweb DiagramsNot started yet
- 4The Newton-Raphson Method for Finding RootsNot started yet
- 5Failure Modes and Limitations of the Newton-Raphson MethodNot started yet
- 6Numerical Integration Using the Trapezium RuleNot started yet
- 7Over- and Under-Estimation and Error Analysis in the Trapezium RuleNot started yet
Standards Covered
- OGM.12.CAL.7Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Locate roots using sign-change intervals and analyze failure conditions; solve equations iteratively using fixed-point iteration x_(n+1) = g(x_n) (with cobweb/staircase diagrams) and the Newton-Raphson method; perform numerical integration via the trapezium rule.
- OGM.12.CAL.1Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Understand the derivative f'(x) as the limit of the difference quotient and as the gradient of the tangent; differentiate x^n, sin(x), cos(x) from first principles; compute second derivatives to determine convexity, concavity, and points of inflection.
Curriculum Framework
11th Grade · Math · Open Global Math
1
7 lessons
First Principles and Foundations of Derivatives
Derive the derivative definition from difference quotients, prove standard derivatives from first principles, and analyze second derivatives and curvature.
2
11 lessons
Advanced Differentiation Rules and Transcendental Functions
Differentiate exponential, logarithmic, and trigonometric functions using chain, product, and quotient rules.
3
7 lessons
Implicit and Parametric Differentiation and Rates of Change
Differentiate implicit equations and parametric curves, and solve connected rates of change modeling problems.
4
8 lessons
Applications of Derivatives: Tangents, Extrema, and Curve Sketching
Construct tangent and normal lines, classify local and global extrema, and sketch complex transcendental curves.
5
8 lessons
Definite Integrals, Riemann Sums, and the Fundamental Theorem of Calculus
Interpret definite integrals as limits of Riemann sums, apply the Fundamental Theorem of Calculus, and calculate areas under and between curves.
6
9 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Evaluate non-standard integrals using algebraic substitution, integration by parts, and partial fraction decompositions.
7
6 lessons
First-Order Differential Equations and Modeling
Formulate, solve, and interpret separable first-order differential equations in physical, biological, and kinematic contexts.
8
7 lessons
Numerical Calculus and Iterative Methods
Locate roots via sign change, solve equations using fixed-point iteration and Newton-Raphson, and approximate integrals with the trapezium rule.