MATH-2551 Multivariable Calculus

This is the page for the coordinated course MATH-2551 Multivariable Calculus Studio Sections J01 and J03 at Georgia Tech. Here you can find some resources that may help you review. Feel free to reach out to me with any questions! My email is rhuang346@gatech.edu.

Summarized Notes from Previous Studios

Section Number	Topics	Notes
12.2-12.3	Vector Dot Product Calculus Reviews (u-substitution, extrema, finding bounded area)	w1-1
12.1,12.4	Three-Dimensional Coordinate Systems The Cross Product	w1-2
12.5-12.6	Lines and Planes in Space Cylinders and Quadric Surfaces	w2-2
13.1-13.2	Curves in Space and Their Tangents Integrals of Vector Functions; Projectile Motion	w3-1
13.3-13.4	Arc Length in Space Curvature and Normal Vectors of a Curve	w3-2
12.1-13.4	Notes from studios before Midterm #1 in one file	m1
14.1	Functions of Several Variables	w4-2
14.2-14.3	Limits and Continuity in Higher Dimensions Partial Derivatives	w5-1
14.3-14.4	Partial Derivatives The Chain Rule	w5-2
14.4-14.5	The Chain Rule Directional Derivatives and Gradient Vectors	w6-1
14.6	Tangent Planes, Linearizations, and Differentials	w6-2
14.7	Extreme Values and Saddle Points	w7-1
14.8	Lagrange Multipliers	w7-2
14.1-14.8	Notes from studios between Midterm #1 and Midterm #2 in one file	m2
15.1-15.2	Double and Iterated Integrals over Rectangles Double Integrals over General Regions	w8-2
15.2-15.3	Double Integrals over General Regions Area by Double Integration	w9-1
15.4-15.5	Double Integrals in Polar Form Triple Integrals in Rectangular Coordinates	w9-2
15.5-15.6	Triple Integrals in Rectangular Coordinates Applications of Triple Integral	w10-1
15.7	Triple Integrals in Cylindrical and Spherical Coordinates	w10-2
15.1-15.7	Notes from studios between Midterm #2 and Midterm #3 in one file	m3
16.2	Vector Fields and Line Integrals: Work, Circulation, and Flux	w12-2
16.1-16.2	Line Integrals of Scalar Functions Vector Fields and Line Integrals: Work, Circulation, and Flux	w13-1
16.2-16.3	Vector Fields and Line Integrals: Work, Circulation, and Flux Path Independence, Conservative Fields, and Potential Functions	w13-2
16.3-16.4	Path Independence, Conservative Fields, and Potential Functions Green’s Theorem in the Plane	w14-1
16.4-16.5	Green’s Theorem in the Plane Surfaces and Area	w14-2 Green’s Thm
16.5-16.6	Surfaces and Area Surface Integrals	w15-1Part 1 w15-2Part 2
16.6-16.7	Surface Integrals Stokes’ Theorem	w15-2
12.2-16.7	All notes from studios	all notes

Other Helpful Resources

• Here are some commonly used derivative, integral, and trig formulae: Formulae
• For understanding the shapes of 3D objects, contour maps, level curves, etc.:GeoGebra has a 3D calculator which can give you some visualizations. I recommend you first try to imagine the shape by thinking about the cross sections by yourself and then check your understanding with the calculator for practice.
  • Also, for mac users, mac has a builtin 3D calculator called “Grapher”, and if you choose the “3D Graph” feature, you can make graphs by inputting the equations
    • 
• Calculus playlist by 3Blue1Brown: Essence of Calculus

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