Final Exam Information
When/Where: Wednesday 4 May, 10:00am–12:00pm, in our usual classroom (ILC 118).
Notes allowed during the exam:
 Equation Sheet. The equation sheet will be projected during the exam. You may also bring your own copy.
 common parameterizations of important surfaces. You will need to bring your own copy.
 One side of an 8.5″x11″ sheet of paper for handwritten notes. (Recommendation: write your notes on the back of the equation sheet!).
Review problems: I am trying something a little different this semester. There are two types of reviews posted on WebAssign:
 “Graphs/Diagrams” — This review focuses on using graphs/diagrams to answer questions.
 “Randomized #n” — These generate sets of 11 problems from the material we’ve covered so far. There are five of these currently posted. You can use them as practice problems. You can also use them for practice with categorizing/identifying problem types (based on types of integrals, integration theorems, etc).
These reviews are for practice only: they are not worth credit.
Scores on WebAssign will be recorded as of the time of the final exam. If you are using an extension to finish the last three assignments, make sure you are finished by the time of the final.
Additional office hours:
 Fri 4/29 12:151:15pm
 Tues 5/3 1:303:30 pm
Announcements
Syllabus
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, Rogawski; W.H.Freeman, 2^{nd} edition, 2012.
Week 1: 1/111/15
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. Ways of representing vectors. (sec 12.1, 12.2) 
Fri  Topic 13 Notes Worksheet 
Group Work: Vector equations of lines. (sec 12.2) 
Week 2: 1/181/22
Mon  No Class (MLK day)  
Wed  Topic 14 Notes Slides 
Introduction to the dot and cross products: Definitions and computation. (sec 12.3, 12.4) 
Fri  Topic 15 Notes Worksheet 
Group Work: Geometric properties of the dot and cross products: angles, area, and orthogonality. (sec 12.3, 12.4) 
Week 3: 1/251/29
Mon  Topic 16 Notes Slides 
Applications of the dot product: Projections and orthogonal decompositions. (sec 12.3) 
Wed  Topic 17 Notes Worksheet 
Group Work: Equations of planes in 3space. (sec 12.5) 
Fri  Topic 21 Notes Slides 
Introduction to curves: The position vector and vectorvalued functions. Curves in the plane and in 3space. (sec 13.1) 
Week 4: 2/12/5
Mon  Topic 22 Notes Slides 
Derivatives of vectorvalued functions: The tangent vector $\vec{r}\,'(t)$. Application of vector derivatives: velocity, speed, and acceleration. (sec 13.2, 13.5) 
Wed  Catchup/Review Exam 1 Information :: Exam 1 Equation Sheet :: Link to Exam 1 Fall 2015 

Fri  key Stats  Exam 1 
Week 5: 2/82/12
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: 2/152/19
Mon  No Class (Presidents’ day)  
Wed  Topic 34 Notes Slides 
Linear approximations and the function differential $df$. (Group work?) (sec 14.4) 
Fri  Topic 35 Notes Worksheet 
Group Work: Directional derivatives and the gradient vector field. (sec 14.5) 
Week 7: 2/222/26
Mon  Topic 35, cont Slides 
Summary: Directional derivatives and the properties of the gradient. (sec 14.5) 
Wed  Topic 36 Notes Slides 
Chain rules for multivariate functions. (sec 14.5, 14.6) 
Fri  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) 
Week 8: 2/293/4
Mon  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) 
Wed  Catchup/Review Exam 2 Information :: Exam 2 Equation Sheet :: Link to Exam 2 Fall 2015 

Fri  Key Stats  Exam 2 
Week 9: 3/73/11
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 and volume). (sec 15.2, 15.5) 
Fri  Topic 42 Notes Slides 
Double integrals and area element $dA$ in polar coordinates. (sec 11.3, 15.4) 
Week 10: 3/143/18
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 15.3) 
Wed  Topic 44 Notes Slides 
Triple integrals in cylindrical coordinates: Cylindrical coordinates, the volume element $dV$ in cylindrical coordinates, finding limits of integration. (sec 12.7, 15.4) 
Fri  Topic 45 Notes Slides 
Triple integrals in spherical coordinates: Spherical coordinates, the volume element $dV$ in spherical coordinates, finding limits of integration. (sec 12.7, 15.4) 
3/213/25: Spring Break – no class
Week 11: 3/284/1
Mon  Triple Integral Practice  Group Work: Triple integrals in Cartesian, cylindrical, and spherical coordinates. Triple integrals in spherical coordinates, cont. 
Wed  Triple Integral Practice, cont Worksheet 
Group Work: Triple integrals in Cartesian, cylindrical, and spherical coordinates.
TakeHome Exam (Exam 3) handed out at the end of class. 
Fri  Topic 51 Notes Slides 
Line elements and scalar line integrals: The scalar line element $ds$ and the vector line elements $d\vec{s}$. Scalar line integrals. (sec 13.3, 16.2, and The Vector Differential in the Bridge Book)
Exam 3 (takehome exam) due at the beginning of class. 
Week 12: 4/44/8
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: 4/114/15
Mon  Topic 55 Notes Slides 
Green’s theorem. (sec 17.1) 
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 $d\vec{S}$. (sec 16.5) Common parameterizations of 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 16.4) Warmup: Computing surface elements on a cone. 
Week 14: 4/184/22
Mon  Topic 58 Notes Slides 
Vector surface integrals (“flux integrals”): Integrating vector fields over a surface. (sec 16.5) 
Wed  Topic 59 Notes Slides 
Divergence and the Divergence Theorem. (sec 17.3) 
Fri  Divergence Theorem, continued. (sec 17.3) 
Week 15: 4/254/29
Mon  Topic 510 Notes Slides 
Curl and Stokes’ Theorem. (sec 17.2) 
Wed  Stokes Theorem, continued. Comparison of line and surface integrals. Comparison of integral theorems (FTCVF, Green’s, Stokes’, Divergence) (Group work?)  
Fri  Review 
Exam 4/Final Exam — Wednesday 4 May, 10:00am–12:00pm, in our usual classroom. — Info/Review