Unit 1
Vectors & Parameterized Curves
- Vectors in 2D and 3D
- Vector-valued functions
- Velocity and acceleration
- Arc length
- Curvature and motion in space
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College Mathematics
MATH 234 — Calculus: Functions of Several Variables
A multivariable calculus pathway covering functions of several variables, parameterized curves, derivatives, multiple integrals, and vector calculus.
Course overview
A multivariable calculus pathway covering functions of several variables, parameterized curves, derivatives, multiple integrals, and vector calculus.
Math Aficionado uses this structure as a tutoring roadmap: lessons can be paced around the student's current level, school sequence, assignments, and assessment goals rather than forcing every student through the same timetable.
Units & topics
Unit 2
Functions of Several Variables
- Domains and level sets
- Limits and continuity
- Partial derivatives
- Tangent planes
- Differentiability and local approximation
Unit 3
Directional Derivatives & Gradients
- Directional derivatives
- Gradient vectors
- Chain rule in several variables
- Normal vectors
- Optimization interpretation
Unit 4
Multivariable Optimization
- Critical points
- Second-derivative tests
- Constrained optimization
- Lagrange multipliers
- Applications and modeling
Unit 5
Double Integrals
- Iterated integrals
- Regions in the plane
- Changing order of integration
- Area and volume
- Average values
Unit 6
Coordinate Transformations
- Polar coordinates
- Jacobian concept
- Change of variables
- Applications to area and mass
- Geometric interpretation
Unit 7
Triple Integrals
- Three-dimensional regions
- Iterated triple integrals
- Cylindrical coordinates
- Spherical coordinates
- Volume and physical applications
Unit 8
Vector Fields & Line Integrals
- Vector fields
- Line integrals
- Conservative fields
- Potential functions
- Work and circulation
Unit 9
Surface Integrals & Vector Calculus
- Parametric surfaces
- Surface area
- Flux
- Green’s Theorem
- Divergence and Stokes’ Theorems
Curriculum reference: University of Wisconsin–Madison Guide / Department of Mathematics. The page is an independent tutoring roadmap and is not an official course page of the source institution.
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