English series
AI
English editions of Guozhen AI articles. The text is localized for global readers while the original diagrams, screenshots, and code examples remain aligned with the Chinese source.
Use this series as the technical reading layer, then continue into AI software buyer guides, tool comparisons, benchmarks, API platform decisions, coding agents, and LLM security research.
From Series Reading to Tool Decisions
Turn this AI series into practical software, model, API, and security choices.
English Series FAQ
Use this series as evidence before choosing AI tools.
How should I use the AI English series?
Use the series as the learning layer for concepts, screenshots, prompts, and implementation details, then continue into buyer guides, tool comparisons, benchmarks, API decisions, and security checks.
Is the AI series enough to choose an AI tool?
No. The series gives context and practical examples, but production choices still need pricing review, privacy checks, integration testing, benchmark evidence, and fallback planning.
What should I read after this 21-lesson series?
Open AI Software Buyer Guides, AI Tools Workbench, Best AI Coding Agents, AI Model Benchmarks, OpenAI vs Anthropic API, or LLM Security Tools depending on your next decision.
Why keep the original diagrams and screenshots?
The visuals preserve source evidence from the Chinese articles, so global readers can inspect interfaces, outputs, and workflows instead of relying only on a translated summary.
A minimal example: model input is time t and current state y
Differential equations are well suited for modeling systems whose states evolve continuously over time. In AI, they help us understand time series data, control prob...
Read lessonSolving Common Differential Equations: A Brief Introduction
Differential equations are first classified, then solved. When an analytical solution exists, we express it as an explicit function; when no closed form solution is...
Read lessonDecay constant
Differential equations describe laws of change themselves—not just a single number, but rather the function(s) that satisfy a given relationship governing how quanti...
Read lessonCompute partial derivatives
Multivariable calculus enables us to model situations where multiple inputs jointly influence an output. Both loss surfaces and gradient descent in machine learning...
Read lessonDefine the integrand
Multiple integrals extend summation from one dimension to two or higher dimensions. The key is not to compute first—but to clearly sketch the region of integration.
Read lessonDefine symbolic variables
A partial derivative measures how the output changes with respect to one input variable while holding all other variables constant. Collectively, all first order par...
Read lesson15. Computing and Applying Basic Definite Integrals
The key to applying definite integrals lies in modeling. First, clarify what is being accumulated—area, distance, probability, or total cost—then write the correspon...
Read lessonDefine the function
A definite integral yields signed area . If the graph lies below the x axis, the result is negative; to compute actual (geometric) area , we often need to split the...
Read lesson13. Definite Integrals: Definition and Properties
A definite integral can be understood as the limit of the sum of areas of many small rectangles. Its properties help you split, combine, and simplify integrals over...
Read lessonCalculus for AI Beginners: Basic Integration Rules and Substitution Method
Substitution is essentially the reverse application of the chain rule. The key is complete substitution—not only replacing the function, but also properly transformi...
Read lessonHow to Compute Indefinite Integrals: Core Formulas, Antiderivatives, and Common Examples
The result of an indefinite integral must be differentiable back to the original function. The constant $C$ at the end must never be omitted—because any two antideri...
Read lesson10. Fundamentals of Integration: Core Concepts
Integration can be understood as accumulation . Without limits, we seek an antiderivative; with upper and lower limits, we compute the cumulative effect over a given...
Read lessonDefine symbolic variable
A tangent line approximates a curve locally by a straight line; the rate of change tells you how sensitive the output is to small changes in the input near a given p...
Read lesson8. Derivative Rules and Derivatives of Basic Functions
Differentiation rules allow us to break down complex functions into manageable parts. The most error prone case is the composite function—both the outer and inner la...
Read lessonDefine the function
A derivative is the instantaneous rate of change obtained by compressing a change down to an infinitesimally small scale. Geometrically, it corresponds to the slope...
Read lessonContinuity and Differentiability of Functions
Continuity means the graph has no breaks; differentiability means the function has a well defined, stable tangent line locally. Differentiability is a stronger condi...
Read lessonCalculus for AI Beginners, Part 5: Definition and Properties of Limits
Limits describe trends as inputs approach a point , not just the function’s value at that point. Understanding limits is foundational for grasping continuity and der...
Read lessonDefine the function
A function is a rule that maps inputs to outputs. All subsequent concepts—derivatives, integrals, and model predictions—rest fundamentally on this input output relat...
Read lessonCalculus Overview: Course Structure and Learning Objectives
This content is best approached problem first: first understand how functions change , then learn how to compute rates of change , followed by how to accumulate tota...
Read lessonGenerate sample data
The most frequent use of calculus in AI is optimization . A model first computes its loss, then uses gradients to determine how and in which direction to adjust its...
Read lessonCalculus Fundamentals: Definition and Why It Matters for AI
At its core, calculus is not about complicated notation—it’s about describing continuous change . Derivatives capture instantaneous change , while integrals capture...
Read lesson