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multivariable calculus

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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
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Model Perspective
Jul 26, 2022 · Fundamentals

Understanding Continuity in Multivariable Functions: Key Definitions and Theorems

This article introduces the definition of continuity for multivariable functions, distinguishes between continuous points and discontinuities, presents fundamental theorems such as boundedness, extreme value, intermediate value, and uniform continuity on closed domains, and works through illustrative examples.

continuitymathematical analysismultivariable calculus
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Understanding Continuity in Multivariable Functions: Key Definitions and Theorems