College of the Holy Cross, Spring 2021

Syllabus for Math 241 (Multivariable Calculus)

Professor Hwang, (rhymes with song)

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Do not make travel plans that conflict with the midterm tests or your final exam. If an emergency prevents you from taking the final exam at the allotted time, speak to your Class Dean immediately to arrange for an incomplete grade, and to me to schedule a make-up exam.

The schedule below is subject to minor changes. Any substantial corrections will be announced by email and/or in class.

Day Date Section Topics
M Feb 1  
W Feb 3 Section 1.1 Vectors
R Feb 4 Section 1.2 Lines and Parametric Equations
F Feb 5 Section 1.3 The Dot Product, Orthogonal Projection
M Feb 8 Section 1.4 The Cross Product
W Feb 10 Section 1.6 Vectors
R Feb 11 Section 1.6 Matrices
F Feb 12 Section 1.6 Geometry of Matrix Multiplication
M Feb 15 Section 1.7 Polar and Cylindrical Coordinates
W Feb 17 Section 1.7 Spherical Coordinates
R Feb 18   Review
F Feb 19   Midterm 1
M Feb 22 Section 2.1 Graphs and Level Sets
W Feb 24 Section 2.2 Functions and Limits
R Feb 25 Section 2.2 Continuity
F Feb 26 Section 2.3 Partial Derivatives
M Mar 1 Section 2.3 The Derivative
W Mar 3 Section 2.3 The Derivative
R Mar 4 Section 2.4 Higher-order Partials
F Mar 5 Section 2.5 The Chain Rule
M Mar 8 Section 2.5 The Chain Rule
W Mar 10 Section 2.6 Directional Derivatives
R Mar 11   Review
F Mar 12   Midterm 2
M Mar 15 Section 3.1--3.2 Curves and Arclength
W Mar 17 Section 3.3 Vector Fields and Flows
R Mar 18 Section 3.3 Vector Fields and Flows
F Mar 19 Section 3.4 Grad, Curl, and Div
M Mar 22 Section 4.1 Quadratic Approximation
W Mar 24 Section 4.2 Optimization
R Mar 25 Section 4.2 Optimization
F Mar 26 Section 4.2 The Second Derivative Test
M Mar 29 Section 4.3 Lagrange Multipliers
W Mar 31 Section 4.3 Lagrange Multipliers
R Apr 1   Easter
F Apr 2   Easter
M Apr 5   Easter
W Apr 7 Section 4.4 Statistics, the Geometry of Data
R Apr 8   Review
F Apr 9   Midterm 3
M Apr 12 Section 5.2 Double Integrals
W Apr 14 Section 5.2 Integrating over General Regions
R Apr 15 Section 5.3 Changing the Order of Integration
F Apr 16 Section 5.4 Triple Integrals
M Apr 19 Section 5.5 Polar and Spherical Integration
W Apr 21 Section 5.6 Applications to Physics
R Apr 22 Section 6.1 Scalar Line Integrals
F Apr 23 Section 6.1 Vector Line Integrals
M Apr 26 Section 6.2 Green's Theorem
W Apr 28   Academic Conference
R Apr 29 Section 6.3 Conservative Fields
F Apr 30   Midterm 4
M May 3 Section 7.1 Parametrized Surfaces
W May 5 Section 7.1 Surface Area
R May 6 Section 7.2 Scalar Surface Integrals
F May 7 Section 7.4 Differential Forms and Green's Theorem