Study Guide

Objective

You are able to find limits and extrema of functions and identify continuity. You have the capability to compute derivates for functions and partial derivatives for multivariable functions, and apply differentiation rules. You can compute simple integrals and apply your skills in fields such as area calculation and cumulative distribution functions.

You are able to utilize estimation methods, such as Maximum Likelihood Estimation (MLE), to infer parameters from data. You can implement gradient-based optimization algorithms, such as gradient descent, to efficiently minimize loss functions in machine learning and optimization tasks. You are able to understand the basic concept of a neural network, and identify the importance of activation functions, such as ReLu and Sigmoid, as well as forward propagation and backpropagation algorithms.

By the end of the course, you will have a solid understanding of these foundational concepts and techniques in differential calculus, optimization, and machine learning, empowering you to apply them in various problem-solving scenarios.

Content

Limit of a function, continuity, extrema
Differentiation rules, partial derivate and critical points
Optimization problems
Basics of integration
Estimation methods
Gradient-based optimization
Basic neural network concepts: functions and propagation

Assessment criteria, satisfactory (1)

You can perform simple derivation tasks, examine the continuity of simple functions and find their extrema. You can also compute some partial derivatives for multivariable functions.

Assessment criteria, good (3)

You can perform various derivation tasks and find critical points for functions also with multiple variables. You have the capability to apply partial derivate and chain rule. You are able to compute the training process of a simple neural network, including forward pass and backpropagation.

Assessment criteria, excellent (5)

You can find the limit of a function, perform complex derivation tasks, and apply differentiation rules. You can compute integrals and find the value for definite integrals. You are able to compute the training process of a simple neural network, including forward pass and backpropagation. You are able to alternate the structure of a neural network, including amount of neurons, layers and different activation functions.