# Home

#### 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

#### 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 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 CurvesGuide to Setting Up Scalar Line Integrals from a Parameterization WORKSHEET KEYSlides / 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