Spring 2022: Math 2153 (Calculus III)

Below are the handouts (with solutions) that I used while teaching Math 2153 recitations at the Ohio State University in the Spring of 2022. Students from future sections of this class may use these as a list of practice problems with solutions to study with. TAs for future sections of this class may decide to present these problems in their recitation sections, possibly even presenting their own solutions, then making these typed solutions available to their students for review later on. For the documents that are typed, I have also separately included the source files in case any other instructor wants to use a modified version of them in their own courses.


Dot Products and Projections

Recitation Handout for 1/13/2022 Blank Template

Recitation Handout for 1/13/2022 Typed Solutions

Recitation Handout for 1/13/2022 Notability Solutions

Source Files

Recitation Handout for 1/13/2022 Blank Template Tex File

Recitation Handout for 1/13/2022 Typed Solutions Tex File
proc-l.cls
WorkFormula.png
BoxOnRamp.png
BoxOnRampBruteForce.png
BoxOnRampLabeled.png

ProblemAboutPool.png
ProblemAboutPoolParta.png
ProblemAboutPoolPartb.png
ProblemAboutPoolPartc.png


Cross Products, Vector-valued Functions, and Paramterization of Curves

Recitation Handout for 1/20/2022 Blank Template

Recitation Handout for 1/20/2022 Typed Solutions

Lecturer’s Notes (today’s recitation was used as an additional lecture)

Notability Recitation Notes for 1/20/2022

Source Files

Recitation Handout for 1/20/2022 Blank Template Tex File

Recitation Handout for 1/20/2022 Typed Solutions Tex File
Matching.png
IntersectionCurve.png


Quadric Surfaces, Vector Calculus, and Motion in Space

Today after administering Quiz 1 we lectured about some quadric surfaces and how certain elliptic paraboloids are used in satellite design. The recitation handout was left as a list of optional practice problems.

Recitation Handout for 1/27/2022 Blank Template

Recitation Handout for 1/27/2022 Typed Solutions

Notability Recitation Notes for 1/27/2022

Source Files

Recitation Handout for 1/27/2022 Blank Template Tex File

Recitation Handout for 1/27/2022 Typed Solutions Tex File
GolfShot.png


Unit Normal Vectors, Unit Binormal Vectors, Torsion, and Level Sets

Class was cancelled today due to the weather so I just held office hours instead and left the handout problems as optional practice.

Recitation Handout for 2/03/2022 Blank Template

Recitation Handout for 2/03/2022 Typed Solutions

Source Files

Recitation Handout for 2/03/2022 Blank Template Tex File

Recitation Handout for 2/03/2022 Typed Solutions Tex File
RotationPreservesCurvature.png
MatchingGraphsAndLevelCurves.png
MatchingFunctionsAndGraphs.png
Clothoid.png


Limits, Continuity, Differentiability, and Partial Derivatives

Recitation Handout for 2/10/2022 Blank Template

Recitation Handout for 2/10/2022 Typed Solutions

Notability Recitation Notes for 2/10/2022

Source Files

Recitation Handout for 2/10/2022 Blank Template Tex File

Recitation Handout for 2/10/2022 Typed Solutions Tex File
NonDifferentiableGraph.png
WaveSnapshots.png


Directional Derivatives, Gradient Vectors, and the Multivariable Chain Rule

Recitation Handout for 2/17/2022 Blank Template

Recitation Handout for 2/17/2022 Typed Solutions

Notability Recitation Notes for 2/17/2022

Source Files

Recitation Handout for 2/17/2022 Blank Template Tex File

Recitation Handout for 2/17/2022 Typed Solutions Tex File
ContourPlot.png
SomeLevelCurvesAndGradientVectors.png
SubtletiesOfTheChainRuleDiagram.png


Optimization Problems

Recitation Handout for 2/24/2022 Blank Template

Recitation Handout for 2/24/2022 Typed Solutions

Notability Recitation Notes for 2/24/2022

Source Files

Recitation Handout for 2/24/2022 Blank Template Tex File

Recitation Handout for 2/24/2022 Typed Solutions Tex File
Argument.png
DomainForProblem16.png
LineSegmentForProblem54.png
PictureOfEllipticRegion.png
SquareInDomain.png
LidlessBox.png
Cylinder.png
Distance.png


Double Integration

Recitation Handout for 3/03/2022 Blank Template

Recitation Handout for 3/03/2022 Typed Solutions

Notability Recitation Notes for 3/03/2022

Source Files

Recitation Handout for 3/03/2022 Blank Template Tex File

Recitation Handout for 3/03/2022 Typed Solutions Tex File
Limacon.png
DomainForProblem16.png
LineSegmentForProblem54.png
FirstProblem.png
SecondProblem.png
Symmetry1.png
Symmetry2.png
TopViewFor14-3-22.png
ViewOfSolidFor14-3-22.png
Cardiods.png
2DimensionalFTCAnalog.png
ThirdProblem1.png
ThirdProblem2.png
ThirdProblem3.png
ThirdProblem4.png


Triple Integration

Recitation Handout for 3/10/2022 Blank Template

Recitation Handout for 3/10/2022 Typed Solutions

Notability Recitation Notes for 3/10/2022

Source Files

Recitation Handout for 3/10/2022 Blank Template Tex File

Recitation Handout for 3/10/2022 Typed Solutions Tex File
Problem49Solid.png
Problem45.png
Graph.png
CrossSectionForProblem45.png
CrossSection.png
Problem49XZSphericalCrosssection.png
Problem49XZCylindricalCrosssection.png
Problem50XZSphericalCrosssection.png
Problem50XZCylindricalCrosssection.png
Problem78CylindricalCrosssection.png
Problem78SphericalCrosssection.png
Problem78Solid.png


Change of Variables in Double and Triple Integrals

Recitation Handout for 3/24/2022 Blank Template

Recitation Handout for 3/24/2022 Typed Solutions

Notability Recitation Notes for 3/24/2022

Source Files

Recitation Handout for 3/24/2022 Blank Template Tex File

Recitation Handout for 3/24/2022 Typed Solutions Tex File
ImageOfu=a.png
ImageOfv=b.png
AnotherImageOfu=a.png
AnotherImageOfvb.png
ParabolicCoordinates.png
ParabolicRectangle.png
ParabolicRegion.png
ParabolicRegionTesselation.png
PartitionOfRegion.png
PerpendicularParabolas.png
PerpendicularParabolasZoomIn.png
Problem14-7-32uvplane.png
Problem14-7-32xyplane.png
Problem14-7-42p1.png
Problem14-7-42P2.png
Problem14-7-42P3.png
Problem14-7-42r.png
Problem14-7-57-NewRegionPe.png
Problem14-r-77-uvplane.png
Problem14-r-77-xyplane.png
ulines.png
vlines.png


Line Integrals

Recitation Handout for 3/31/2022 Blank Template

Recitation Handout for 3/31/2022 Typed Solutions

Notability Recitation Notes for 3/31/2022

Source Files

Recitation Handout for 3/31/2022 Blank Template Tex File

Recitation Handout for 3/31/2022 Typed Solutions Tex File
RotationFields.png


Conservative Vector Fields, Flux, and Circulation

Recitation Handout for 4/07/2022 Blank Template

Recitation Handout for 4/07/2022 Typed Solutions

Notability Recitation Notes for 4/07/2022

Source Files

Recitation Handout for 4/07/2022 Blank Template Tex File

Recitation Handout for 4/07/2022 Typed Solutions Tex File
Problem15-2-66.png
Vector-Field.png
Conservative.png
Square.png


Green’s Theorem

Recitation Handout for 4/14/2022 Blank Template

Recitation Handout for 4/14/2022 Typed Solutions

Notability Recitation Notes for 4/14/2022

Source Files

Recitation Handout for 4/14/2022 Blank Template Tex File

Recitation Handout for 4/14/2022 Typed Solutions Tex File
Problem15-2-66.png


Surface Integrals, the Divergence Theorem, and Stoke’s Theorem

Recitation Handout for 4/21/2022 Blank Template

Recitation Handout for 4/21/2022 Typed Solutions

Notability Recitation Notes for 4/21/2022

Source Files

Recitation Handout for 4/21/2022 Blank Template Tex File

Recitation Handout for 4/21/2022 Typed Solutions Tex File
CircleCirculationWithStokes.png
EllipseCirculationWithStokes.png
GeneralTorus.png
GeneralTorusProofOfParametrization.png
ParametrizingSurfacesOfRevolution.png
SphericalStripsOfConstantWidth.png