Syllabus
Exam Dates & Information
Getting Started: Clickers, Textbook, and WebAssign
Schedule
This schedule will be updated as necessary throughout the semester. Section numbers refer to the text Calculus: Early Transcendentals, James Stewart; Brooks/Cole, 8^{th} edition, 2015.
Week 1: 8/228/26
Mon  Topic 11 Notes Slides 
Introduction to vectors: Cartesian coordinates and vectors in component form. The position vector. (sec 12.1, 12.2) 
Wed  Topic 12 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 13 Notes Slides 
Introduction to the dot and cross products: Definitions and computation. (sec 12.3, 12.4) 
Week 2: 8/299/2
Mon  Topic 14 Notes Worksheet (Key) 
Group Work: Geometric properties of the dot and cross products: angles, area, and orthogonality. (sec 12.3, 12.4) 
Wed  Topic 15 Notes Slides 
Applications of the dot product: Projections and work. (sec 12.3) 
Fri  Topic 16 Notes Worksheet (Key) 
Group Work: Applications of vectors and vector operations: lines & planes. (sec 12.5) 
Week 3: 9/59/9
Mon  No Class (Labor Day)  
Wed  Topic 21 Notes Slides 
Introduction to vector functions & curves: The position vector and vectorvalued functions. Curves in the plane and in 3space. (sec 13.1) 
Fri  Topic 21,22 Worksheet (Key) 
Group Work: Vector functions and motion on curves: position, velocity, speed, and acceleration. (sec 12.5) 
Week 4: 9/129/16
Mon  Topic 22 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: TakeHome Guidelines 
Hand out takehome 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: InClass Exam Information 
Take inclass part of Exam 1 :: Turn in takehome part. During class, in our regular classroom. 
Week 5: 9/199/23
Mon  Topic 31 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 32 Notes Worksheet 
Group Work: Partial derivatives. (sec 14.3) 
Fri  Topic 33 Notes Slides 
Tangent planes, differentiability, and linear approximations. (sec 14.4) 
Week 6: 9/269/30
Mon  Topic 34 Notes Slides 
Linear approximations and the function differential $df$. (Group work?) (sec 14.4) 
Wed  Topic 35 Notes Worksheet (Key) 
Group Work: Directional derivatives and the gradient vector field. (sec 14.5) 
Fri  Topic 35, cont Slides 
Summary: Directional derivatives and the properties of the gradient. (sec 14.5) 
Week 7: 10/310/7
Mon  Topic 36 Notes Slides 
Chain rules for multivariate functions. (sec 14.5, 14.6) 
Wed  Topic 37 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 38 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: 10/1010/14
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: TakeHome Guidelines 
Hand out takehome 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: InClass Exam Information 
Take inclass part of Exam 2 :: Turn in takehome part. During class, in our regular classroom. 
Week 9: 10/1710/21
Mon  Topic 41 Notes Worksheet 
Group Work: Double integrals in Cartesian coordinates and the area element $dA$. (sec 15.1, 15.2) 
Wed  Topic 41, 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 42 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: 10/2410/28
Mon  Topic 43 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 44 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 45 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: 10/3111/4
Mon  Triple integrals in spherical coordinates. 

Wed  Exam 3: TakeHome 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 takehome only. There is no inclass part. 
Fri  Topic 51 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 takehome exam at the beginning of class. 
Week 12: 11/711/11
Mon  Topic 52 Notes Worksheet 
Group work: Introduction to vector fields. (sec 16.1) 
Wed  Topic 53 Notes Slides 
Vector line integrals. (sec 16.2) 
Fri  Topic 54 Notes Worksheet 
Group Work: Conservative vs. nonconservative vector fields. (sec 16.3) 
Week 13: 11/1411/18
Mon  Topic 55 Notes Slides 
Green’s theorem. (sec 16.4) 
Wed  Topic 56 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 57 Notes Slides 
Scalar surface integrals: Integrating scalar functions over a surface. Applications of scalar surface integrals: surface area and mass. (sec 16.7) Warmup: Computing surface elements on a cone. 
11/2111/25: Fall Break – no class
Week 14: 11/2812/2
Mon  Topic 58 Notes Slides 
Vector surface integrals (“flux integrals”): Integrating vector fields over a surface. (sec 16.7) 
Wed  Topic 59 Notes Slides 
Divergence and the Divergence Theorem. (sec 16.5, 16.9) 
Fri  Topic 510 Notes Slides 
Curl and Stokes’ Theorem. (sec 16.8) 
Week 15: 12/512/9
Mon  Divergence Theorem and Stokes’ Theorem, continued (Group work?)  
Wed  Topic 511 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, 10am12pm, in our usual classroom. — Exam Information