calculus | BestHub

Model Perspective

Jun 12, 2025 · Fundamentals

Why Did Newton Call Calculus ‘God’s Language’? The Story Behind the Equation

From a wartime interview where Feynman urged a novelist to learn calculus as the language of God, through Newton's plague‑ridden youth and his hidden use of infinitesimals, to the Leibniz‑Newton controversy and modern applications, this article traces how calculus became the indispensable tool of science and engineering.

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0 likes · 22 min read

Why Did Newton Call Calculus ‘God’s Language’? The Story Behind the Equation

Model Perspective

Dec 19, 2024 · Fundamentals

How Calculus Powers Optimal Investment Strategies

This article explains how calculus and mathematical modeling can maximize investment returns, balance risk and reward, and optimize portfolio allocation, using derivative analysis, utility functions, Lagrange multipliers, and integration for long‑term planning, illustrating the scientific power behind financial decision‑making.

Investmentcalculusmathematical modeling

0 likes · 5 min read

How Calculus Powers Optimal Investment Strategies

Model Perspective

Aug 28, 2024 · Fundamentals

Why Calculus Matters: From Static Geometry to Dynamic Change

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.

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0 likes · 8 min read

Why Calculus Matters: From Static Geometry to Dynamic Change

Model Perspective

Dec 28, 2023 · Fundamentals

How Modern Mathematics Solves Zeno’s Classic Paradoxes

This article explains Zeno’s four classic paradoxes—Achilles and the Tortoise, the Dichotomy, the Arrow, and the Stadium—and shows how modern mathematics, especially infinite series and calculus, resolves each paradox, illustrating the bridge between ancient philosophy and contemporary mathematical thought.

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How Modern Mathematics Solves Zeno’s Classic Paradoxes

Model Perspective

Oct 3, 2023 · Fundamentals

Infinite Series Explained: Concepts, Convergence Tests, Real-World Uses

This article introduces infinite series, outlines common types such as arithmetic, geometric, harmonic, p‑series, Taylor, and Fourier series, explains key convergence tests, and demonstrates practical applications in physics, engineering, economics, and mathematical modeling.

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0 likes · 8 min read

Infinite Series Explained: Concepts, Convergence Tests, Real-World Uses

Model Perspective

Sep 2, 2023 · Fundamentals

How Calculus Evolved: From Ancient Approximations to Modern Mathematics

Calculus, the study of change and limits, has evolved over millennia—from ancient Greek approximations by Archimedes, through medieval contributions in the Islamic world, to the independent breakthroughs of Newton and Leibniz in the 17th century, and later formalizations by Cauchy and others that shaped modern science.

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0 likes · 6 min read

How Calculus Evolved: From Ancient Approximations to Modern Mathematics

Model Perspective

Feb 23, 2023 · Fundamentals

Why Derivatives Matter: From Motion to Modern Science

Derivatives, the core concept of calculus, originated from Newton’s instantaneous speed, Leibniz’s tangent, and Fermat’s extremum problems, and are defined as the limit of a function’s change ratio, linking continuity, geometry, and physics, while finding extensive applications across science, economics, and biology.

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0 likes · 10 min read

Why Derivatives Matter: From Motion to Modern Science

Model Perspective

Feb 22, 2023 · Fundamentals

Why Is the Natural Logarithm Base Called ‘e’? History and Proof Explained

This article explores the origin and meaning of the natural logarithm base e, covering its mathematical definition as a limit, historical naming by Euler and Leibniz, why it simplifies logarithmic derivatives, and a proof of its existence using the monotone bounded theorem.

calculuscompound intereste constant

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Why Is the Natural Logarithm Base Called ‘e’? History and Proof Explained

Model Perspective

Nov 10, 2022 · Fundamentals

Why the Gradient Points to the Steepest Ascent: Understanding Directional Derivatives

This article explains that the gradient of a multivariable function is a vector indicating the direction of greatest increase, shows how directional derivatives are computed, and demonstrates that the maximum rate of change occurs when moving along the gradient direction.

calculusdirectional derivativegradient

0 likes · 2 min read

Why the Gradient Points to the Steepest Ascent: Understanding Directional Derivatives

Model Perspective

Nov 10, 2022 · Fundamentals

How Integrals Capture the Area Under a Curve: From Riemann Sums to Limits

This article explains the definition of integrals by illustrating how the area under a curve can be approximated with increasingly fine rectangles, leading to the limit that forms the integral, and connects this geometric intuition to the formal calculus theorem.

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How Integrals Capture the Area Under a Curve: From Riemann Sums to Limits

Model Perspective

Nov 10, 2022 · Fundamentals

Deriving Scalars with Respect to Vectors Using the Definition Method

This article explains how to compute the derivative of a scalar-valued function with respect to a vector by applying the definition method, illustrating the process with simple and more complex examples, outlining basic differentiation rules, and discussing the limitations of the definition approach for vector‑matrix derivatives.

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Deriving Scalars with Respect to Vectors Using the Definition Method

Model Perspective

Aug 13, 2022 · Fundamentals

Essential Linear Algebra Resources: A Curated Guide to Vectors, Matrices, and Python NumPy

This article aggregates the "Model Perspective" public account's past posts on linear algebra and upcoming calculus summaries, links to comprehensive model‑related articles, and provides a collection of Python NumPy tutorials for applying linear‑algebra concepts in programming.

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Essential Linear Algebra Resources: A Curated Guide to Vectors, Matrices, and Python NumPy

Model Perspective

Aug 12, 2022 · Fundamentals

Comprehensive Calculus Resource Guide: From Limits to Multivariable Integration

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.

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0 likes · 2 min read

Comprehensive Calculus Resource Guide: From Limits to Multivariable Integration

Model Perspective

Aug 11, 2022 · Fundamentals

Understanding Gradients: How Directional Derivatives Reveal Maximum Change

The article explains that the gradient of a function is a vector pointing in the direction of greatest increase, representing the maximal directional derivative, and illustrates this concept for single‑variable and two‑variable functions with diagrams, showing how unit vectors determine rates of change along any direction.

calculusdirectional derivativegradient

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Understanding Gradients: How Directional Derivatives Reveal Maximum Change

Model Perspective

Jul 14, 2022 · Fundamentals

Master Integration by Parts: Step‑by‑Step Examples and Tricks

This article explains the integration by parts technique, derived from the product rule, and walks through five detailed examples that show how to rewrite integrals as products of functions, apply the formula, and solve the resulting equations.

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0 likes · 2 min read

Master Integration by Parts: Step‑by‑Step Examples and Tricks

Model Perspective

Jul 13, 2022 · Fundamentals

Key Properties of Integrals and Differentials Explained

This article outlines the fundamental properties of integrals—including the sum rule, constant factor rule, interval splitting, and limit‑based computation—and introduces differentials, their basic properties, and how they relate to integral calculus.

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Key Properties of Integrals and Differentials Explained

Model Perspective

Jul 10, 2022 · Fundamentals

Definite Integrals Demystified: Tables, Properties, and an Oil Consumption Case

This article presents a concise reference of basic integral tables, explains key properties of definite integrals such as additivity and scalar multiplication, and demonstrates their practical use through a detailed case calculating total oil consumption between 1970 and 1990 via differential methods.

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Definite Integrals Demystified: Tables, Properties, and an Oil Consumption Case

Model Perspective

Jul 9, 2022 · Fundamentals

Unlocking the Power of the Fundamental Theorem of Calculus

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.

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0 likes · 2 min read

Unlocking the Power of the Fundamental Theorem of Calculus

Model Perspective

Jul 7, 2022 · Fundamentals

Understanding Definite Integrals: From Geometry to the Fundamental Theorem

This article explains the concept of definite integrals by illustrating how the area under a curve can be approximated with rectangles, leading to the formal definition of integration as the limit of these sums, and connects it to the Fundamental Theorem of Calculus.

Integrationarea under curvecalculus

0 likes · 3 min read

Understanding Definite Integrals: From Geometry to the Fundamental Theorem