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📘 Multivariate Calculus

From functions of one variable to many: partial derivatives, multi-variable optimization, the method of least squares, Lagrange multipliers, and double integrals — the foundation of statistics and ML.

Topics

📋 Introduction (Pretest)

Diagnostic: see what you remember and what needs work.

Coming when we start

🌐 Functions of Several Variables

From $f(x)$ to $f(x, y, z)$ — what changes and what doesn't.

Coming when we start

∂ Partial Derivatives

Differentiate with respect to one variable, holding the others fixed.

Coming when we start

🔝 Maxima and Minima of Functions of Several Variables

Find critical points in multiple dimensions.

Coming when we start

🎯 Applications of Min/Max Problems

Multi-variable optimization in real problems.

Coming when we start

📉 The Method of Least Squares

The foundation of regression — minimize squared residuals.

Coming when we start

λ Lagrange Multipliers

Optimize subject to a constraint.

Coming when we start

∬ Double Integrals

Integrate over a 2D region — volume under a surface.

Coming when we start

📦 Volumes

3D volumes via double integrals and other methods.

Coming when we start

✅ Conclusion (Posttest)

End-of-module assessment.

Coming when we start

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