Numerical Analysis

Lecture 2-1: The Art of Numerical Analysis

Introduction to numerical approximation, errors, and floating point arithmetic.

Lecture 2-2: Interpolation

Polynomials, Splines, and B-Splines for connecting data points.

Lecture 2-3: Numerical Differentiation & Integration

Numerical derivatives, central difference, and integration rules (Trapezoidal, Simpson's, Gaussian).

Lecture 2-5: Root Finding & Minimization

Bisection, Newton-Raphson, and Genetic Algorithms for optimization.

Lecture 2-6: Solving ODEs

Euler, Runge-Kutta, and Applications (Pendulum, Springs).

Lecture 2-7: Random Numbers

LCG, Distributions, and Monte Carlo Integration.

Lecture 3-1: Machine Learning

Introduction, MNIST, Features, LDA, SVM, and non-linear kernels.

Lecture 3-2: Nonlinear Models & Neural Networks

Nonlinear SVM, Kernel Trick, Backpropagation, and Neural Networks.

Lecture 3-3: Improving Neural Networks

Keras, Overfitting, Optimization & Deep Networks

Lecture 3-4: Deep Structured Learning

CNN, RNN/LSTM, GANs, and AI Music Generation.