Mathematically: Linear Mathematics -

Problems that are linear

a) Find all solutions in vector form to

4x + 5y + 6z = 0

x + 2y + 3z = 0

7x + 8y + 9z = 0

b) Find the general solution to

d²y + w² y = 0

dt²

c) Mix This Color from red, green and blue

( ans: This Color = 3 red + 1 green + 2 blue )

d) Find the major and minor axes and the eccentricity of the

ellipse satisfying

6x² + 4xy + 3y² = 196

Additionally:

Classification of problems: linear, non-linear, homogeneous, nonhomogeneous

Classification of solutions: vector, scalar, homogeneous, particular, general

Functions that are linear

e) f(x,y,z) = (7x – 2y + z, -2x + 6y – 8z, 3z – 4y)

f) derivatives ; df/dx

g) antiderivatives / integrals

h) Fourier Transform

F(f) =

i) Laplace Transform

L(f) =

Structures that are linear

vector spaces

vectors

basis of a vector space

Applications:to better understand the concepts and tools of one’s major

§ vibrations and resonance in Mechanical Engineering

§ structures and projects in Civil Engineering

§ signal analysis in Electrical and Computer Engineering

§ music and voice analysis

§ population dynamics and sound in Bio

§ standing waves in physics

§ programming of algorithms in Computer Science