Definitions
The power the differential is raised to.
The dependent variable and its derivatives are all not non-linear. \[\begin{aligned} \underbrace{\frac{d^2 y}{d t}} &\quad \underbrace{\cos(x) \frac{dy}{dx}} &\quad \underbrace{\frac{dy}{dt} \frac{d^3 y}{dt^3}} &\quad \underbrace{y’ = e^y} &\quad \underbrace{y \frac{dy}{dx}} \\ \text{linear} &\quad \text{linear} &\quad \text{non-linear} &\quad \text{non-linear} &\quad \text{non-linear} \end{aligned}\]
Independent variable does not appear in the equation.
Independent variable does appear in the equation.
Topics Surfaces Partial Derivatives & Gradients Multiple Integrals (Double, Triple) Vector Fields & Divergence/Curl Surface Integrals & Line Integrals Integral Theorems in Vector Calculus Important Theorems Gradient & Directional Derivatives Lagrange Multipliers (Optimization with Constraints) Divergence Theorem (Gauss’s Theorem) Green’s Theorem (2D Circulation & Flux) Stokes’ Theorem (Generalization of Green’s Theorem)
Topics Limits & Continuity Derivatives & Differentiation Rules Mean Value Theorems Integrals (Definite & Indefinite) Fundamental Theorem of Calculus Sequences & Series (Convergence, Divergence)
Important Theorems Intermediate Value Theorem Extreme Value Theorem Rolle’s Theorem Mean Value Theorem Taylor’s Theorem Fundamental Theorem of Calculus
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