# Home

#### 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, 2015.

Week 1:   8/22-8/26

 Mon Topic 1-1 Notes   Slides Introduction to vectors:   Cartesian co-ordinates and vectors in component form. The position vector.    (sec 12.1, 12.2) Wed Topic 1-2 Notes   Slides Working with vectors:   Magnitude. Vector addition and scalar multiplication. Unit vectors. $\boldsymbol{\hat{\imath}}$, $\boldsymbol{\hat{\jmath}}$, $\boldsymbol{\hat{k}}$ basis vectors.    (sec 12.2) Fri Topic 1-3 Notes   Slides Introduction to the dot and cross products:   Definitions and computation.    (sec 12.3, 12.4)

Week 2:   8/29-9/2

 Mon Topic 1-4 Notes   Worksheet   (Key) Group Work:   Geometric properties of the dot and cross products:   angles, area, and orthogonality.    (sec 12.3, 12.4) Wed Topic 1-5 Notes   Slides Applications of the dot product:   Projections and work.    (sec 12.3) Fri Topic 1-6 Notes   Worksheet   (Key) Group Work:   Applications of vectors and vector operations: lines & planes.    (sec 12.5)

Week 3:   9/5-9/9

 Mon No Class (Labor Day) Wed Topic 2-1 Notes   Slides Introduction to vector functions & curves:   The position vector and vector-valued functions. Curves in the plane and in 3-space.    (sec 13.1) Fri Topic 2-1,2-2 Worksheet  (Key) Group Work:   Vector functions and motion on curves: position, velocity, speed, and acceleration.    (sec 12.5)

Week 4:   9/12-9/16

 Mon Topic 2-2 Notes   Slides Derivatives of vector functions:   The tangent vector $\boldsymbol{{r}\,’}(t)$. Application of vector derivatives:   velocity, speed, and acceleration.    (sec 13.2, 13.4) Wed Exam 1: Take-Home Guidelines Hand out take-home section of Exam 1.   (Due in class on Friday.) During class, in our regular classroom. You must come to class to pick up the exam. Fri Exam 1: In-Class Exam Information Take in-class part of Exam 1   ::   Turn in take-home part. During class, in our regular classroom.

Week 5:   9/19-9/23

 Mon Topic 3-1 Notes   Slides Introduction to functions of more than one variable:   Domain and range. Graphs, traces, level curves, and contour maps.    (sec 14.1) Links to online graphing and level curve apps and download sites can be found on the Resources page. Wed Topic 3-2 Notes   Worksheet Group Work:   Partial derivatives.    (sec 14.3) Fri Topic 3-3 Notes   Slides Tangent planes, differentiability, and linear approximations.    (sec 14.4)

Week 6:   9/26-9/30

 Mon Topic 3-4 Notes   Slides Linear approximations and the function differential $df$.   (Group work?)    (sec 14.4) Wed Topic 3-5 Notes Worksheet   (Key) Group Work:   Directional derivatives and the gradient vector field.    (sec 14.5) Fri Topic 3-5, cont Slides Summary: Directional derivatives and the properties of the gradient.    (sec 14.5)

Week 7:   10/3-10/7

 Mon Topic 3-6 Notes   Slides Chain rules for multivariate functions.    (sec 14.5, 14.6) Wed Topic 3-7 Notes   Worksheet Application of partial derivatives/gradient:   Finding maxima and minima of functions of two variables. Critical points, local maxima, and local minima of bivariate functions. The second derivative test. (Group work.)    (sec 14.7) Fri Topic 3-8 Notes   Slides Application of partial derivatives/gradient:   Method of Lagrange Multipliers. Finding the critical points of a multivariate function subject to a constraint.    (sec 14.8)

Week 8:   10/10-10/14

 Mon TBA (Probably either more Lagrange multipliers, or a comparison of applications involving partial derivatives, chain rule, linearization, and differential.) (Group work?) Wed Exam 2: Take-Home Guidelines Hand out take-home section of Exam 2.   (Due in class on Friday.) During class, in our regular classroom. You must come to class to pick up the exam. Fri Exam 2: In-Class Exam Information Take in-class part of Exam 2   ::   Turn in take-home part. During class, in our regular classroom.

Week 9:   10/17-10/21

 Mon Topic 4-1 Notes   Worksheet Group Work:   Double integrals in Cartesian coordinates and the area element $dA$.    (sec 15.1, 15.2) Wed Topic 4-1, cont Slides Double integrals in Cartesian coordinates, continued: integration over general regions, and applications of the double integral (area, volume, mass).    (sec 15.2, 15.4) Fri Topic 4-2 Notes   Slides Double integrals in polar coordinates. The area element $dA$ in polar coordinates. Finding limits of integration.    (sec 10.3, 15.3)

Week 10:   10/24-10/28

 Mon Topic 4-3 Notes   Worksheet Group Work:   Triple integrals in Cartesian coordinates. The volume element $dV$. Finding limits of integration. Applications of triple integrals: volume and mass.    (sec 15.6) Wed Topic 4-4 Notes   Slides Triple integrals in cylindrical coordinates: Cylindrical coordinates. The volume element $dV$ in cylindrical coordinates. Finding limits of integration.    (sec 15.7) Fri Topic 4-5 Notes   Slides Triple integrals in spherical coordinates:   Spherical coordinates. The volume element $dV$ in spherical coordinates. Finding limits of integration.    (sec 15.8)

Week 11:   10/31-11/4

 Mon Triple Integral Practice Worksheet Group Work:   Triple integrals in Cartesian, cylindrical, and spherical coordinates.     (sec 15.6-15.8) Triple integrals in spherical coordinates. Wed Exam 3: Take-Home Guidelines Hand out Exam 3.   (Due at the beginning of class on Friday.) During class, in our regular classroom. You must come to class to pick up the exam. Note: Exam 3 is take-home only. There is no in-class part. Fri Topic 5-1 Notes   Slides Line elements and scalar line integrals:   The scalar line element $ds$ and the vector line elements $d\boldsymbol{r}$. Scalar line integrals. (sec 13.3, 16.2, and The Vector Differential in the Bridge Book) Common Parametrizations for Some Important Curves Exam 3: Turn in take-home exam at the beginning of class.

Week 12:   11/7-11/11

 Mon Topic 5-2 Notes   Worksheet Group work: Introduction to vector fields.    (sec 16.1) Wed Topic 5-3 Notes   Slides Vector line integrals.   (sec 16.2) Fri Topic 5-4 Notes   Worksheet Group Work:   Conservative vs. non-conservative vector fields.    (sec 16.3)

Week 13:   11/14-11/18

 Mon Topic 5-5 Notes   Slides Green’s theorem.    (sec 16.4) Wed Topic 5-6 Notes   Slides Surfaces and surface elements:   Commonly encountered surfaces and their parameterizations, the scalar surface element $dS$, and the vector surface element $d\boldsymbol{S}$.    (sec 16.6) Common Parametrizations for Some Important Surfaces Fri Topic 5-7 Notes   Slides Scalar surface integrals:   Integrating scalar functions over a surface. Applications of scalar surface integrals: surface area and mass.    (sec 16.7) Warm-up: Computing surface elements on a cone.

11/21-11/25:   Fall Break   –   no class

Week 14:   11/28-12/2

 Mon Topic 5-8 Notes   Slides Vector surface integrals (“flux integrals”):   Integrating vector fields over a surface.    (sec 16.7) Wed Topic 5-9 Notes   Slides Divergence and the Divergence Theorem.    (sec 16.5, 16.9) Fri Topic 5-10 Notes   Slides Curl and Stokes’ Theorem.    (sec 16.8)

Week 15:   12/5-12/9

 Mon Divergence Theorem and Stokes’ Theorem, continued (Group work?) Wed Topic 5-11 Notes   Slides Summary:     Comparison of line and surface integrals. Comparison of integral theorems (FTCVF, Green’s, Stokes’, Divergence) (Group work?) Fri Review

Exam 4/Final Exam — Wednesday 12/14, 10am-12pm, in our usual classroom.Exam Information