Math Animated™
Mathematical Introduction for Physics and Engineering
by Samuel Dagan (Copyright © 2007-2020)

Index D

D'Alambert test for convergence(1.3.5.22)

decimal presentation of a number

decreasing function

definite integral

• Riemann's definition (2.2.1.5), sign(2.2.1.7)
• over points of discontinuity(2.2.1.11)

denominator of a ratio

derivative

• definition and notation(1.3.1.1)
• parity
• sign
• order, physical dimensions
• maximum, minimum
• infinity
• partial → partial derivative

Descartes(folium of)

• implicit
• parametric(exercise 4)
• asymptote(1.3.4.23)
• area of loop(2.2.2.7)

determinant definition, characteristics, evaluation

differentiability of function

• with a single vatiable
• with many vatiables

differential

• definition and rules
• total differential, definition and properties

differential equations - introduction

• definition(2.1.4.1), order
• Newton's second law(2.1.4.2) and initial conditions(2.1.4.3)

differential equations - simple cases:

1. derivative as function of the independent variable: $\frac{{\text{d}}^{n}y}{\text{d}{x}^n}=f_n\left(x\right)$
2. separation of variables: $\frac{\text{d}y}{\text{d}x}=f_y\left(y\right)f_x\left(x\right)$
3. missing independent variable: $F_1\left(y,\frac{\text{d}y}{\text{d}x},\mathrm{....},\frac{{\text{d}}^{n}y}{\text{d}{x}^n}\right)=0$
4. missing dependent variable: $F_1\left(x,\frac{\text{d}y}{\text{d}x},\mathrm{....},\frac{{\text{d}}^{n}y}{\text{d}{x}^n}\right)=0$

differentiation

• basic rules
• elementary(functions)
• implicit(functions), by partial derivatives
• parametric(functions)
• function of functions
• under the integral sign

dimensions physical, see physical dimensions

directrix of a parabola

discontinuity of a function

• with a single variable
• with many variables

distance between 2 points(1.2.5.10)

divergence

• of a sequence
• of a series

divergence to $\infty$ of a

• sequence
• function
• derivative
• function, as an asymptote(1.3.4.26)

division of polynomials

domain

• single variable
• many variables