This is a schedule for a ~15 week course covering
vectors in two- and three-dimensional space,
multivariable functions and their extrema,
double and triple integrals of multivariable functions,
parametrically-defined curves and surfaces,
line and surface integrals in vector fields,
and Green’s and Stokes’ and Ostrogradsky’s theorems.
Within each section are links to notes,
video lectures, technology guides and demos,
practice exercises, problems, and past midterm exams.
Chapters enumerated with § refer to
Calculus 9E by Stewart .
Topics marked like
are extracurricular and won’t appear on exams.
Week One · January 25
Monday – Three-Dimensional Space
Tues/Wednesday – Syllabus Synopsis + Lines, Planes, and Surfaces
Thursday – Syllabus Review + Early-Term Survey
Week Two · February 1
Monday – Vectors in Three-Dimensional Space
Tuesday – The Dot Product and Projections
Wednesday – The Cross Product and Areas
Thursday – Distances Between Points, Lines, and Planes
Week Three · February 8
Mon/Tuesday –
Wednes/Thursday – First Midterm Exam
Past Midterm Exams
Note that prior to this semester,
the first and second midterms were combined.
Week Four · February 15
Monday – Parametrically-Defined Curves and Surfaces
Tuesday – Calculus with Vector-Valued Functions
Wednesday – The Frenet-Serret Frame
Thursday – Curvature and Torsion
Week Five · February 22
Mon/Tuesday –
§13.4 Motion in Space: Velocity and Acceleration
Wednes/Thursday – Second Midterm Exam
Past Midterm Exams
Note that prior to this semester,
the first and second midterms were combined.
Week Six · March 1
Monday – Multivariable Functions and their Graphs
Tuesday – Limits & Continuity
Wednesday – Partial Derivatives
Thursday – Tangent Planes & Taylor Approximations
Week Seven · March 8
Monday – The Chain Rule & Implicit Differentiation
Tuesday – The Gradient Vector & Directional Derivatives
Wednesday – Local and Global Extrema
Thursday – Optimization with Lagrange Multipliers
Week Eight · March 15
Mon/Tuesday –
Wednes/Thursday – Third Midterm Exam
Past Midterm Exams
Week Nine · March 22
Week Ten · March 29
Monday – Introduction to Double and Triple Integrals
Tuesday – Double Integrals in Rectangular Coordinates
Wednesday – Double Integrals in Polar Coordinates
Thursday – Moments of Mass
Week Eleven · April 5
Monday – Triple Integrals in Rectangular Coordinates
Tuesday – Triple Integrals in Cylindrical Coordinates
Wednesday – Triple Integrals in Spherical Coordinates
Thursday – Change of Coordinates and the Jacobian
Week Twelve · April 12
Monday – Moments in General
§15.4 Applications of Double Integrals
§15.6 Triple Integrals
Tuesday –
Wednes/Thursday – Fourth Midterm Exam
Past Midterm Exams
Week Thirteen · April 19
Monday – Vector Fields
Tuesday – Line Integrals in Scalar Fields
Wednesday – Line Integrals in Vector Fields
Thursday – Surface Integrals in Vector Fields
Week Fourteen · April 26
Monday – Surface (Flux) Integrals
Tuesday – Green’s Theorem
Wednesday – Divergence & Curl
Thursday – Stokes’s Theorem & the Divergence Theorem
Week Fifteen · May 3
Monday –
Tuesday –
Wednes/Thursday – Fifth Midterm Exam
Past Midterm Exams
Week Sixteen · May 10
Final Exam