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Syllabus


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Exam Dates & Information


Course Notes

Links to the class notes also appear in the schedule. If you use Firefox, the links will take you directly to the relevant section for the day; otherwise, use the table of contents to navigate to the relevant section.



Schedule

This schedule will be updated as necessary throughout the semester. Section numbers refer to the text Calculus: Early Transcendentals, James Stewart; Brooks/Cole, 8th edition, 2016.

Week 1 (8/21–8/25)    Introduction to Vectors
M    No Class: Eclipse Day
W Topic 1.1: Vectors & 3-Space, Introduction (sec 12.1, 12.2)
Cartesian co-ordinates and vectors in component form. The position vector \(\boldsymbol{r}\).
Activity / Key
Slides / Class Notes
F 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.
Activity / Key
Slides
Week 2 (8/28–9/1)    Dot and Cross Products
M Topic 1.3: Dot and Cross Products, Introduction (sec 12.3, 12.4)
Definitions and computation.
Activity / Key
Slides
W Topic 1.4: Geometry of the Dot and Cross Products (sec 12.3, 12.4)
The relationships of the dot and cross products to angles, area, and orthogonality.
Activity / Key
Slides
F Topic 1.5: Projections & Work (sec 12.3)
Applications of the dot product: projections and work.
Draft Activity/Class Notes
Slides
Week 3 (9/4–9/8)    Lines & Planes; Introduction to Vector Functions
M No Class: Labor Day
W Topic 1.6: Lines & Planes (sec 12.5)
Applications of vectors and vector operations: equations of lines and planes.
Activity / Key
Slides
F 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
Activity / Key
Slides
Week 4 (9/11–9/15)    Derivatives of Vector Functions
M 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 and scalar line elements \(d\boldsymbol{r}\) and \(ds\).
Activity / Key
Slides / Class Notes
W Topic 1.9: Applications of Vector Derivatives: Motion on Curves (sec 13.3, 13.4)
Velocity, speed, and acceleration; length of curves & the arc length function.
Activity / Key
Slides
F [Topic 1.10: Applications of Vector Derivatives: Line Elements \(d\boldsymbol{r}\) and \(ds\), and Arc Length][1.10N] (sec 13.3)
Bridge Book: More details on the vector line element \(d\boldsymbol{r}\) and its magnitude \(ds\).
Slides: Topic 1 Review
Class Notes
Week 5 (9/18–9/22)    Multivariate Functions & Partial Derivatives
M 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.
Activity / Key
Slides
W Topic 2.1: Multivariate Functions, Introduction (continued) (sec 14.1)
Domain and range. Graphs, traces, level curves, and contour maps.
Links to online and downloadable graphing apps.
Activity / Key
Slides
F Topic 2.2: Partial Derivatives. (sec 14.3)
Derivatives of functions of two or more variables.
Activity / Key
Slides
Week 6 (9/25–9/29)    TBA & Exam 1
M Topic 2.3: Differentiability & Tangent Planes (sec 14.4)
Higher-dimensional analogues of tangent lines.
Class Notes
Slides
W Exam 1: Take-Home (Due at the beginning of class on Friday)
You must come to class to pick up the take-home exam.
Exam Information
F Exam 1: In-Class
During class, in our regular classroom.
Exam Information
Week 7 (10/2–10/6)    Differentials; Directional Derivatives; the Gradient; Chain Rules
M Topic 2.4: Applications of Differentiability: the Differential \(df\) (sec 14.4)
Differentials of functions.
Activity / Key
Slides
W Topic 2.5: Directional Derivatives & the Gradient (sec 14.6)
More derivatives of functions of two or more variables. The gradient of a function \(\boldsymbol{\nabla}f\).
Activity / Key
Slides
F Topic 2.6: Chain Rules (sec 14.5, 14.6)
Chain rules for multivariate functions.
Class Notes
Slides
Week 8 (10/9–10/13)    Optimization; Introduction to Double Integrals
M 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.
Activity / Key
Slides
W 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.
Class Notes
Slides
F Topic 3.1: Double Integrals, Introduction (sec 15.1, 15.2)
Double integrals in Cartesian cooridinates, and the area element \(dA\).
Activity / Key
Slides
Week 9 (10/16–10/20)    Double Integrals; Polar Coordinates; Introduction to Triple Integrals
M Topic 3.1: Double Integrals, Continued (sec 15.2, 15.4)
Integration over general regions, and applications of the double integral (area, volume, mass).
Class Notes
Slides
W Topic 3.2: Double Integrals in Polar Coordinates (sec 10.3, 15.3)
The area element \(dA\) in polar coordinates. Finding limits of integration.
Activity / Key
Slides
F 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.
Activity / Key
Slides
Week 10 (10/23–10/27)    Triple Integrals in Cylindrical & Spherical Coordinates
M Topic 3.4: Triple Integrals in Cylindrical Coordinates (sec 15.7)
Cylindrical coordinates. The volume element \(dV\) in cylindrical coordinates. Finding limits of integration.
Activity / Key
Slides
W Topic 3.5: Triple Integrals in Spherical Coordinates (sec 15.8)
Spherical coordinates. The volume element \(dV\) in spherical coordinates. Finding limits of integration.
Activity / Key
Slides
F Homework Day
In-class work on assignments #22 & #23 (triple integrals in cylindrical and spherical coordinates).
Class Notes
Week 11 (10/30–11/3)    TBA & Exam 2
M Exam Review Triple Integral Practice
W Exam 2: Take-Home (Due at the beginning of class on Friday)
You must come to class to pick up the take-home exam.
Exam Information
F Exam 2: In-Class
During class, in our regular classroom.
Exam Information
Week 12 (11/6–11/10)    Line Integrals
M Topic 4.1: Line Elements & Scalar Line Integrals (sec 13.3, 16.2)
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
Mini-Activity / Key + Example
Slides
W Topic 4.2: Vector Fields, Introduction (sec 16.1)
Vector fields and the geometry of vector line integrals.
Activity / Key
Slides
F 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
Class Notes
Slides
Week 13 (11/13–11/17)    Integral Theorems: FTLI & Green’s; Introduction to Surfaces
M Topic 4.4: Conservative Vector Fields (sec 16.3)
Conservative vector fields and the Fundamental Theorem of Line Integrals.
Activity / Key
Slides
W Topic 4.5: Green’s Theorem (sec 16.4)
An integral theorem equating line integrals in the plane to double integrals.
Class Notes
Slides
F 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.
Activity / Key
Slides
11/20–11/24: Fall Break – No Class
Week 14 (11/27–12/1)    Surface Integrals; Divergence Theorem
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
W Topic 4.8: Vector Surface Integrals (sec 16.7)
Integrating a vector field over a surface. (Also called a flux integral.)
F Topic 4.9: The Divergence Theorem (sec 16.9)
The Divergence Theorem is an integral theorem equating surface integrals to triple integrals.
Week 15 (12/4–12/8)    Stokes’ Theorem; Catch-up/Review
M 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.)
W Open/TBA
F Open/TBA
Finals Week: 12/11–12/15
M sec 001: Mon 12/11 10am–12pm in our usual classroom.
W sec 002: Wed 12/13 10am–12pm in our usual classroom.
Exam Information