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Class Meetings:

Sec 002: MWF 10:30–11:45am, Riverfront Hall (RFH) Room 105.
Sec 003: MWF 12:00–1:15pm, Multipurpose Classroom Building (MPCB) Room 203


Syllabus


Getting Started: Clickers, Textbook, WebAssign


Exam Dates & Information


Course Notes


Workbook

Worksheets and other in-class activities. Updated throughout the semester. Keys to worksheets are posted in the daily schedule below.



Daily Schedule

Updated as necessary throughout the semester. Section numbers refer to the textbook Calculus: Early Transcendentals, James Stewart; Brooks/Cole, 8th edition, 2016.

Week 1 (8/26, 8/28/ 8/30)    Introduction to Vectors & Vector Operations
M    Topic 1.1: Vectors & 3-Space, Introduction (sec 12.1, 12.2)
Cartesian co-ordinates and vectors in component form. The position vector \(\boldsymbol{r}\).
WORKSHEET KEY
Slides
W Topic 1.2: Working with Vectors (sec 12.2)
Magnitude of vectors. Vector addition and scalar multiplication. Unit vectors. \(\boldsymbol{\hat{\imath}}\), \(\boldsymbol{\hat{\jmath}}\), \(\boldsymbol{\hat{k}}\) basis vectors.
WORKSHEET KEY
Slides
F Topic 1.3: Dot and Cross Products, Introduction (sec 12.3, 12.4)
Definitions and computation.
WORKSHEET KEY
Slides
Week 2 (9/2, 9/4, 9/6)    Dot and Cross Products: Geometry & Applications
M (Labor Day)No Class
W Topic 1.4: Geometry & Applications of the Dot Product (sec 12.3)
The dot product, angles and orthogonality. Applications of the dot product: projections and work.
WORKSHEET KEY
Slides
F Topic 1.5: Geometry & Applications of the Cross Product (sec 12.4)
The cross product, area, and normal vectors.
WORKSHEET KEY
Slides
Week 3 (9/9, 9/11, 9/13)    Vector Equations of Lines & Planes // Introduction to Vector Functions & Their Derivatives
M Topic 1.6: Equations of Lines & Planes (sec 12.5)
Applications of vectors and vector operations: equations of lines and planes.
WORKSHEET KEY
Slides
W Topic 1.7: Vector Functions & Curves, Introduction (sec 13.1)
The position vector and vector-valued functions. Curves in the plane and in 3-space.
Common Parameterizations for Some Important Curves
WORKSHEET KEY
Slides
F Topic 1.8: Derivatives of Vector Functions – Computation & Geometry (sec 13.2, 13.3)
The tangent vector \(\boldsymbol{r}'(t)\), the unit tangent vector \(\boldsymbol{\hat{T}}\), and the vector line element \(d\boldsymbol{r}\).
WORKSHEET KEY
Slides
Week 4 (9/16, 9/18, 9/20)    Applications of Vector Derivatives // Introduction to Multivariate Functions
M Topic 1.9: Applications of Vector Derivatives: Velocity, Speed, and Acceleration (sec 13.3, 13.4)
Velocity, speed, and acceleration.
WORKSHEET KEY
Slides
W Topic 2.1: Multivariate Functions, Introduction (sec 14.1)
Domain and range. Graphs, traces, level curves, and contour maps.
Links to online and downloadable graphing apps.
WORKSHEET KEY
Slides
F No Class
Office hours will be held as usual, 1:30–2:30pm.
Week 5 (9/23, 9/25, 9/27)    Partial Derivatives // Differentiability // the Differential \(df\)
M Topic 2.2: Partial Derivatives. (sec 14.3)
Derivatives of functions of two or more variables.
WORKSHEET KEY
Slides
W Topic 2.3: Differentiability & Tangent Planes (sec 14.4)
Higher-dimensional analogues of tangent lines.
Slides / Class Notes
F Topic 2.4: Applications of Differentiability: the Differential \(df\) (sec 14.4)
Differentials of functions.
WORKSHEET KEY
Slides
Week 6 (9/30, 10/2, 10/4)    Exam 1
M Exam 1: Group Project/Take-Home – Day 1 (Due at the beginning of class on Friday)
You must come to class to pick up the take-home exam. Problems(s) will be handed out. Begin working on them with your group.
Exam Information
W Exam 1: Group Project/Take-Home – Day 2 (Due at the beginning of class on Friday)
You must come to class to pick up the take-home exam. Write-up sheets will be handed out. Discuss and write-up the problems.
Exam Information
F Exam 1: In-Class
During class, in our regular classroom.
Exam Information
Week 7 (10/7, 10/9, 10/11)    Chain Rules // Local Extrema & the Second Derivative Test // the Gradient \(\nabla f\) & Directional Derivatives
M Topic 2.5: Directional Derivatives & the Gradient (sec 14.6)
More derivatives of functions of two or more variables. The gradient of a function \(\boldsymbol{\nabla}f\).
WORKSHEET KEY
Slides
W Topic 2.6: Chain Rules (sec 14.5, 14.6)
Chain rules for multivariate functions.
Slides / Class Notes
F Topic 2.7: Local Extrema & the Second Derivative Test (sec 14.7)
Application of partial derivatives and the gradient: Finding maxima and minima of functions of two variables. Critical points, local maxima and minima, and the second derivative test.
WORKSHEET KEY
Slides
Week 8 (10/14, 10/16, 10/18)    Optimization (Method of Lagrange Multipliers) // Introduction to Double Integrals
M (Indigenous Peoples Day)Topic 2.8: Method of Lagrange Multipliers (sec 14.8)
Application of partial derivatives and the gradient: Finding the critical points of a multivariate function subject to a constraint using the method of Lagrange multipliers.
Slides / Class Notes
W Topic 3.1: Double Integrals, Introduction (sec 15.1, 15.2)
Double integrals in Cartesian cooridinates, and the area element \(dA\).
WORKSHEET KEY
Slides
F Topic 3.1: Double Integrals, Continued (sec 15.2, 15.4)
Integration over general regions, and applications of the double integral (area, volume, mass).
Slides / Class Notes
Week 9 (10/21, 10/23, 10/25)    Double Integrals in Polar Coordinates // Introduction to Triple Integrals // Triple Integrals in Cylindrical Coordinates
M Topic 3.2: Double Integrals in Polar Coordinates (sec 10.3, 15.3)
The area element \(dA\) in polar coordinates. Finding limits of integration.
WORKSHEET KEY
Slides
W Topic 3.3: Triple Integrals in Cartesian Coordinates (sec 15.6)
The volume element \(dV\). Finding limits of integration. Applications of triple integrals: volume and mass.
WORKSHEET KEY
Slides
F Topic 3.4: Triple Integrals in Cylindrical Coordinates (sec 15.7)
Cylindrical coordinates. The volume element \(dV\) in cylindrical coordinates. Finding limits of integration.
WORKSHEET KEY
Slides
Week 10 (10/28, 10/30, 11/1)    Triple Integrals in Spherical Coordinates // Line Elements & Scalar Line Integrals
M Topic 3.5: Triple Integrals in Spherical Coordinates (sec 15.8)
Spherical coordinates. The volume element \(dV\) in spherical coordinates. Finding limits of integration.
WORKSHEET KEY
Slides
W Workshopping Triple Integrals
Using “slices” to determine limits of integration for 3-d regions with rotational symmetry (cylindrical & spherical coordinates)
Class Notes
F Topic 4.1: Line Elements & Scalar Line Integrals (sec 13.3, 16.2)
Review of the scalar line element \(ds\) and the vector line element \(d\boldsymbol{r}\). Scalar line integrals.
Bridge Book: More details on the vector line element \(d\boldsymbol{r}\).
Common Parameterizations for Some Important Curves
Guide to Setting Up Scalar Line Integrals from a Parameterization
WORKSHEET KEY
Slides / Class Notes
Week 11 (11/4, 11/6, 11/8)    Exam 2
M Exam 2: Group Project/Take-Home – Day 1 (Due at the beginning of class on Friday)
You must come to class to pick up the take-home exam. Problems(s) will be handed out. Begin working on them with your group.
Exam Information
W Exam 2: Group Project/Take-Home – Day 2 (Due at the beginning of class on Friday)
You must come to class to pick up the take-home exam. Write-up sheets will be handed out. Discuss and write-up the problems.
Exam Information
F Exam 2: In-Class
During class, in our regular classroom.
Exam Information
Week 12 (11/11, 11/13, 11/15)    Introduction to Vector Fields & Vector Line Integrals // Green’s Theorem
M (Veterans Day) Topic 4.2: Vector Fields, Introduction (sec 16.1)
Vector fields and the geometry of vector line integrals.
WORKSHEET KEY
Slides
W Topic 4.3: Vector Line Integrals (sec 16.2)
Vector line element \(d\boldsymbol{r}\) and vector line integrals.
Guide to Setting up Vector Line Integrals from a Parameterization
Slides / Class Notes
F Topic 4.5: Green’s Theorem (sec 16.4)
An integral theorem equating line integrals in the plane to double integrals.
Slides / Class Notes
Week 13 (11/18, 11/20, 11/22)    Conservative Vector Fields // Introduction to Surfaces
M Topic 4.4: Conservative Vector Fields (sec 16.3)
Conservative vector fields and the Fundamental Theorem of Line Integrals.
WORKSHEET KEY
Slides
W Topic 4.6: Surfaces & Surface Elements (sec 16.6)
Surfaces, parameterizations, grid curves, and the geometry of the scalar surface element \(dS\) and the vector surface element \(d\boldsymbol{S}\).
Common parameterizations for some important surfaces.
WORKSHEET KEY
Slides / Class Notes
F Open/TBA [Slides][] / [Class Notes][]
11/25–11/29    Fall Break — No Class
Week 14 (12/2, 12/4, 12/6)    Surface Integrals // Curl & Divergence
M Topic 4.7: Scalar Surface Integrals (sec 16.7)
Integrating a scalar function over a surface. Applications of scalar surface integrals: surface area, mass.
Guide to Setting Up Surface Integrals from a Parameterization
Slides / Class Notes
W Topic 4.8: Vector Surface Integrals (sec 16.7)
Integrating a vector field over a surface. (Also called a flux integral.)
Slides / Class Notes
F Interlude: Gradient, Curl, and Divergence
The “nabla” (or “del”) operator \(\boldsymbol{\nabla}\) is a vector made up of partial derivative operators:
   \(\boldsymbol{\nabla} = \frac{\partial}{\partial x}\boldsymbol{\hat{\imath}} + \frac{\partial}{\partial y} \boldsymbol{\hat{\jmath}} + \frac{\partial}{\partial z}\boldsymbol{\hat{k}}\)
\(\boldsymbol{\nabla}\) is used to compute the gradient of a scalar-valued function, and the vector field “derivatives” curl and divergence.
Slides / Class Notes
Week 15 (12/9, 12/11, 12/13)    Divergence Theorem & Stokes’ Theorem
M Topic 4.9: The Divergence Theorem (sec 16.9)
The Divergence Theorem is an integral theorem equating surface integrals to triple integrals.
Slides / Class Notes
W Topic 4.10: Stokes’ Theorem (sec 16.8)
Stokes’ Theorem is an integral theorem equating line integrals and surface integrals. (Green’s Theorem is a special case of Stokes’ Theorem.)
Slides / Class Notes
F Work on problems for final.
Finals Week: 12/16–12/20
M sec 003: 12/16 12–2pm in our usual classroom.
W sec 002: 12/18 12–2pm in our usual classroom.
Exam Information