Differential Equations and Series
PHYS 110 · Module 6
This module previews mathematical tools used to model changing physical systems. Students learn first-order and second-order differential equations, oscillations, Taylor series, approximations, complex numbers, and Euler's formula.
Lessons in this module
First-order ODEs
First-order ordinary differential equations relate a function to its first derivative. This lesson introduces separation of variables and simple growth, decay, and motion models.
Second-order ODEs and oscillations
Second-order differential equations involve second derivatives and naturally describe acceleration. This lesson introduces simple harmonic motion and oscillatory solutions.
Taylor series and approximations
Taylor series approximate functions near a point using polynomials. This lesson explains linearization, small-angle approximations, and why approximation is central in physics.
Complex numbers and Euler's formula
Complex numbers extend the number system and simplify oscillations and waves. This lesson introduces imaginary numbers, complex planes, exponentials, and Euler's formula.
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