numpy

Connect joint velocities to end-effector velocity through the Jacobian matrix. Learn how to build J, spot singularities where det J = 0, invert J with the pseudoinverse for velocity control, and measure manipulability — with NumPy code for the 2-link arm.

Translate a list of joint angles into an end-effector pose. Learn the four Denavit-Hartenberg parameters, build per-link transforms, multiply them into T_0^n, and implement FK for a 2-link planar arm in NumPy.

Master how roboticists describe rigid-body pose. Build rotation matrices from scratch, pack them into 4x4 homogeneous transforms, and compose multiple frames with NumPy to track every link in a robot arm.

Build intuition for how artificial neurons stack into layers, why nonlinear activations are non-negotiable, and how the chain rule turns a forward pass into exact gradients — illustrated with a tiny numpy forward+backward walk-through.