This course starts with an introduction to the key concepts and outlines the roadmap to success in the field. You'll begin by understanding the foundational elements of matrix and vector derivatives, exploring topics like linear and quadratic forms, chain rules in matrix form, and the derivative of determinants. Each concept is reinforced with exercises, ranging from quadratic challenges to least squares and Gaussian methods. The course progresses into optimization techniques essential in data science and machine learning. Delve into multi-dimensional second derivative tests, gradient descent in one and multiple dimensions, and Newton's method, including practical exercises in Newton's Method for least squares. An additional focus is set on setting up your environment, where you'll learn to establish an Anaconda environment and install crucial tools like Numpy, Scipy, and TensorFlow. The course also addresses effective learning strategies, answering pivotal questions like the suitability of YouTube for learning calculus and the recommended order for taking courses in this field. As you journey through the course, you'll transition from foundational concepts to advanced applications, equipping yourself with the skills needed to excel in data science and machine learning.