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

Index C

canonical form

• parabola(1.2.5.23)
• ellipse(1.2.5.36)
• hyperbola(1.2.5.40)

Cartesian coordinates

• 2 dimensional definition, scales
• 3 dimensional right-handed, inversion, rotation, display

Cauchy principal value

centre of mass

centroid definition

chain rule

• differentiation(1.3.1.11)
• function of functions(3.1.2.17)
• change of variables (3.1.4.4)
• Jacobian (3.1.7.16)

change of variables → variable

circle

• presentation(1.2.5.39)
• circumference(2.2.4.8)
• area(3.2.3.26)
• circular disc moment of inertia(3.2.3.27-29)

closed

• interval of a variable
• region of variables

cone

• of revolution volume (exercise 2), equation, level lines (3.1.1.10), spherical coordinates
• general volume(3.2.2.16), centroid(3.2.2.20)
• surface integration(3.2.4.41), area(3.2.4.42), centroid(3.2.4.43-44)

conic sections

• definition(1.2.5.22)
• deduction
• parabola → parabola
• ellipse → ellipse
• hyperbola → hyperbola

constraints definition, examples

continuity of a function

• single variable
• many variables

contradiction - proof by

convergence of

• sequence
• function
• series

convex region

coordinate system

• Cartesian see: Cartesian coordinates
• polar → polar coordinates
• curvilinear 2 dimensions, 3 dimensions
• cylindrical see: cylindrical coordinates
• spherical → spherical coordinates
• transformation of coordinates → Transformation of variables

countability

• definition, rational numbers
• irrational numbers
• sequence

cuboid example(3.2.2.21-22)

curve

• presentation

curvilinear coordinates 2 dimensions, 3 dimensions

cyclic permutation(3.1.1.19)

cycloid

• definition
• area(2.2.1.28)
• length and surface of revolution(exercise 4)
• volume of revolution(exercise 5)

cylindrical coordiantes

• definition(3.1.4.17-19)
• orthogonality, triple integrals
• surface integrals