Differential Equations

Applying Calculus to Natural Sciences

Physics has given me a thorough understanding of both the material found in calculus classes as well as how to apply it to physical and scientific problems. Calculus is another language of math to learn and Differential Equations are used throughout all of physics (the Schrödinger equation in quantum mechanics, the Euler equations, Einstein’s Equation for general relativity, etc.) I have taught multiple students throughout their entire classes and can help you prepare for exams and understand the concepts of this class with extra help on applications and meanings behind these trickier principles.

~ Solving basic differential equations

~ Initial value problems

~ Separation of variables

~ Uniqueness theorem

~ Exponential growth and decay

~ Integration factors

~ Slope fields

~ Solving constant-coefficient equations

~ Indicial/characteristic equation solutions

~ Harmonic solutions

~ Phase diagrams and equilibrium analysis

~ Euler’s method

~ Method of undetermined coefficients

~ Linear independence and the Wronskian matrix

~ Laplace transforms to solve differential equations

~ The Dirac delta and Heaviside step functions

~ Power series solutions and the Frobenius method

~ Taylor series and convergence

~ Physical systems (mass-spring, air resistance and drag, etc.)

~ Population models