This article provides a comprehensive, easy‑to‑understand overview of futures contract concepts, trading systems, clearing and settlement processes, margin rules, participant roles, accounting treatment, and data considerations across China’s six major futures exchanges, illustrated with clear diagrams and examples.
Calculus, the dynamic mathematics of infinitesimals, emerged to solve problems like instantaneous velocity, tangent slopes, and areas under curves, transforming static algebra and geometry into tools for analyzing continuous change, as illustrated by examples of expanding squares, sphere volumes, and tidal movements.
This article compiles a comprehensive list of previously published WeChat posts from the “Model Perspective” series covering core calculus topics such as single‑variable functions, derivatives, integrals, and multivariable calculus, providing readers with quick access to each detailed tutorial.
This article explains the chain rule for vector‑to‑vector derivatives, scalar‑to‑multiple‑vector and scalar‑to‑matrix cases, illustrates how to handle dimensional compatibility, provides concrete examples such as least‑squares optimization, and summarizes four key matrix‑vector derivative conclusions for efficient machine‑learning calculations.
This article introduces matrix differential calculus, explains its relationship to scalar and vector differentials, outlines key properties such as addition, multiplication, transpose, trace and determinant rules, and demonstrates how to compute matrix‑vector derivatives using trace tricks.
This article compiles a series of WeChat posts covering calculus fundamentals—including limits, derivatives, integration techniques, gradient descent, and multivariable concepts—providing direct links to each detailed tutorial for learners to explore.
This article explains how the Fundamental Theorem of Calculus bridges derivatives and integrals, provides a straightforward method for evaluating integrals via antiderivatives, illustrates the concept with telescopic sums, and walks through several concrete examples to demonstrate its practical use.
This article explains how to differentiate sums, differences, and products of functions, introduces function composition, and derives the chain rule, providing proofs and clear examples to help readers master fundamental calculus differentiation techniques.
This article explains how derivatives can be used to locate global and local minima or maxima, defines critical points—including saddle points—and demonstrates the process with quadratic and cubic function examples, illustrating each concept with clear diagrams.
This article explains how to use derivatives to locate a function’s global and local minimum or maximum points, defines critical points, distinguishes between global and local extrema, and demonstrates the process with quadratic and cubic examples illustrated by diagrams.
Explore the core differentiation rules—including the sum, difference, and product rules—followed by functional composition and the chain rule, with clear derivations and proofs that build on basic calculus concepts to help you differentiate complex functions confidently.
This article explains the chain rule for composite functions, covering both single‑variable and multi‑variable scenarios, illustrating how derivatives of nested functions are computed and how the rule applies to common machine‑learning expressions such as the sigmoid of a linear combination.
This article introduces the mathematical foundations of derivatives and partial derivatives, explains their role in optimizing neural network parameters, covers basic derivative formulas, linear properties, sigmoid derivative, minimum conditions, and constrained optimization using Lagrange multipliers, providing a comprehensive guide for machine‑learning practitioners.
Despite the hype that deep learning demands heavy calculus and linear algebra, this article shows beginners how basic concepts like derivatives and partial derivatives can be grasped with simple analogies, explains activation functions, learning rates, and the role of training and testing data in neural networks.
