# Home

#### Syllabus

(Edited 1/8 to clarify course exam grading scheme.)

#### 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 (1/8–1/12)    Introduction to Vectors M Topic 1.1: Vectors & 3-Space, Introduction (sec 12.1, 12.2) Cartesian co-ordinates and vectors in component form. The position vector $\boldsymbol{r}$. Activity / Key Slides / Class Notes 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. Activity / Key Slides F Topic 1.3: Dot and Cross Products, Introduction (sec 12.3, 12.4) Definitions and computation. Activity / Key Slides Week 2 (1/15–1/19)    Dot and Cross Products M No Class (Dr. Martin Luther King Day/Idaho Human Rights Day) 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. Slides / Class Notes Week 3 (1/22–1/26)    Lines & Planes; Introduction to Vector Functions M Topic 1.5: Projections & Work (sec 12.3) Applications of the dot product: projections and work. Slides / Class Notes 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 (1/29–2/2)    Derivatives of Vector Functions; Introduction to Multivariate 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 (sec 13.3) Bridge Book: More details on the vector line element $d\boldsymbol{r}$ and its magnitude $ds$. Class Notes Week 5 (2/5–2/9)    Partial Derivatives: Geometry, Computation & Applications 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 2.2: Partial Derivatives. (sec 14.3) Derivatives of functions of two or more variables. Activity / Key Slides F Topic 2.3: Differentiability & Tangent Planes (sec 14.4) Higher-dimensional analogues of tangent lines. Slides / Class Notes Week 6 (2/12–2/16)    Differentials & Exam 1 M Topic 2.4: Applications of Differentiability: the Differential $df$ (sec 14.4) Differentials of functions. Activity / Key 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 (2/19–2/23)    Directional Derivatives; the Gradient; Chain Rules M No Class (Presidents Day) 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. Slides / Class Notes Week 8 (2/26–3/2)    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. 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. F Topic 3.1: Double Integrals, Introduction (sec 15.1, 15.2) Double integrals in Cartesian cooridinates, and the area element $dA$. Week 9 (3/5–3/9))    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). 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. 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. Week 10 (3/12–3/16)    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. 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. F Homework Day In-class work on assignments #22 & #23 (triple integrals in cylindrical and spherical coordinates). Week 11 (3/19–3/23)    Scalar Line Integrals; Introduction to Vector Fields 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 CurvesGuide to Setting Up Scalar Line Integrals from a Parameterization W Topic 4.2: Vector Fields, Introduction (sec 16.1) Vector fields and the geometry of vector line integrals. F Open/TBA 3/26–3/30: Spring Break – No Class Week 12 (4/2–4/6)    Vector Line Integrals & Exam 2 M 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 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 13 (4/9–4/13)    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. W Topic 4.5: Green’s Theorem (sec 16.4) An integral theorem equating line integrals in the plane to double integrals. 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. Week 14 (4/16–4/20)    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 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. Week 15 (4/23–4/27)    Stokes’ Theorem; Catch-up/Review M Topic 4.9: The Divergence Theorem (sec 16.9)The Divergence Theorem is an integral theorem equating surface integrals to triple integrals. 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.) F Work on problems for final. Finals Week: 4/30–5/4 M sec 001: Mon 4/30 10am–12pm in our usual classroom. W sec 002: Wed 5/2 10am–12pm in our usual classroom. Exam Information