Public learning track
First-Order Differential Equations and Modeling
11th Grade · Math · Open Global Math
6 lessons
Goal
Formulate, solve, and interpret separable first-order differential equations in physical, biological, and kinematic contexts.
Featured Diagrams
Solving Separable Differential Equations: General Solutions
6 lessons
0 of 6 done
- 1Solving Separable Differential Equations: General SolutionsUp nextStart
- 2Finding Particular Solutions Using Initial ConditionsPremiumNot started yet
- 3Constructing Differential Equations from Growth and Decay ContextsNot started yet
- 4Modeling with Newton's Law of Cooling and Chemical MixingNot started yet
- 5Modelling with First-Order Differential Equations in KinematicsNot started yet
- 6Logistic Growth and Carrying Capacity Differential EquationsNot started yet
Standards Covered
- OGM.12.CAL.6Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Construct and solve first-order differential equations with separable variables dy/dx = f(x)g(y); determine general and particular solutions with initial conditions; interpret solutions in kinematics, growth/decay, and physical contexts.
- OGM.12.CAL.5Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Integrate functions using integration by substitution, integration by parts, and partial fractions with linear denominators.
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.