Topical

March 12 2018

Vectors - scalars describe physical quantities by a single number - vectors describe physical quantities with both magnitude and direction - scalar product / dot product is a scalar value - which equals the magnitude of one vector times the magnitude of projection of the other vector - A dot B = |A| |B| cos angle - A dot B = AxBx + AyBy + AzBz - work = force dot displacement - work is the amount of force applied in the direction of movement - work = change in energy - vector product / cross product is a perpendicular vector - direction of this vector is given by the right-hand rule - magnitude of this vector is the area of the parallelogram - A x B = |A| |B| sin angle - Cx = AyBz - AzBy - applications - force through electric and magnetic field = vqE + qv x B - torque = r x force Others - exponential and logarithm functions y = ex - trigonometric functions, harmonics - infinite series - conic sections, polar coordinates, vectors - partial derivatives, multiple integrals, line integrals