Multivariable Calculus
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Tentative Course Schedule
1
Vectors & Matrices
1.1
Basics
Rules to manipulate vectors
Properties of vector operations
1.2
Products
1.2.1
Dot product
Properties of dot product
Projection
1.2.2
3D special: Cross product
1.2.3
Distance from a point
1.3
Matrices
1.3.1
Operations on matrices
1.3.2
Linear transformation
2
Some basic equations in
\(\mathbb{R}^3\)
2.1
Equations for lines
2.2
Equations for planes
2.3
Cylinders
2.4
Quadric surfaces
3
Functions in higher dimensions
3.1
Functions of several variables
3.2
Vector functions
3.2.1
Limit, continuity and differentiation
3.2.2
Integrals
3.2.3
Space curve in
\(\mathbb{R}^3\)
and motion in space
3.3
Activity: on osculating circle and curvature
4
Partial derivatives
4.1
Limits and continuity
4.2
Partial derivatives
4.3
Differentiability
4.4
Chain rule
4.5
Directional derivative
4.6
Tangent planes
5
Optimization
5.1
First and second derivative tests
5.1.1
Algorithm to find absolute maxima and minima on closed bounded regions
5.2
Constrained optimization
6
Multiple integrals
6.1
Basic definition
6.1.1
Some properties of integrals
6.2
Iterated integrals
6.3
Change of coordinates
6.3.1
Applications of change of coordinates
7
Vector Calculus
7.1
Vector fields
7.2
Line integrals
7.2.1
Independence of path
7.3
Green’s Theorem
7.4
Curl and Divergence
7.5
Surface integrals
7.5.1
Parametric surfaces
7.5.2
Surface integral
7.5.3
Orientation of the surface
7.5.4
Surface integral of vector fields
7.6
Stokes’ and Divergence Theorem
MATH 104: Multivariable Calculus (brief notes)
MATH 104: Multivariable Calculus (brief notes)
Truong-Son Van
Spring 2024