#### 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 ClassOffice 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 IntegralsUsing “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 CurvesGuide 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 DivergenceThe “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 | ||||