Final Exam Information

When/Where: Wednesday 4 May, 10:00am–12:00pm, in our usual classroom (ILC 118).

General exam information.

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 12:15-1:15pm
  • Tues 5/3 1:30-3:30 pm



Getting Started: Clickers, Textbook, and WebAssign


This schedule will be updated as necessary throughout the semester. Section numbers refer to the text Calculus: Early Transcendentals, Rogawski; W.H.Freeman, 2nd edition, 2012.

Week 1:   1/11-1/15

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. Ways of representing vectors.    (sec 12.1, 12.2)
Fri Topic 1-3
Notes   Worksheet
Group Work:   Vector equations of lines.    (sec 12.2)

Week 2:   1/18-1/22

Mon No Class (MLK day)
Wed Topic 1-4
Notes   Slides
Introduction to the dot and cross products:   Definitions and computation.    (sec 12.3, 12.4)
Fri Topic 1-5
Notes   Worksheet
Group Work:   Geometric properties of the dot and cross products: angles, area, and orthogonality.    (sec 12.3, 12.4)

Week 3:   1/25-1/29

Mon Topic 1-6
Notes   Slides
Applications of the dot product:   Projections and orthogonal decompositions.    (sec 12.3)
Wed Topic 1-7
Notes   Worksheet
Group Work:   Equations of planes in 3-space.    (sec 12.5)
Fri Topic 2-1
Notes   Slides
Introduction to curves:   The position vector and vector-valued functions. Curves in the plane and in 3-space.    (sec 13.1)

Week 4:   2/1-2/5

Mon Topic 2-2
Notes   Slides
Derivatives of vector-valued functions:   The tangent vector $\vec{r}\,'(t)$. Application of vector derivatives:   velocity, speed, and acceleration.    (sec 13.2, 13.5)
Wed Catch-up/Review
Exam 1 Information   ::   Exam 1 Equation Sheet   ::   Link to Exam 1 Fall 2015
Fri key   Stats Exam 1

Week 5:   2/8-2/12

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:   2/15-2/19

Mon No Class (Presidents’ day)
Wed Topic 3-4
Notes   Slides
Linear approximations and the function differential $df$. (Group work?)    (sec 14.4)
Fri Topic 3-5
Notes   Worksheet
Group Work:   Directional derivatives and the gradient vector field.    (sec 14.5)

Week 7:   2/22-2/26

Mon Topic 3-5, cont
Summary: Directional derivatives and the properties of the gradient.    (sec 14.5)
Wed Topic 3-6
Notes   Slides
Chain rules for multivariate functions.    (sec 14.5, 14.6)
Fri 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)

Week 8:   2/29-3/4

Mon 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)
Wed Catch-up/Review
Exam 2 Information   ::   Exam 2 Equation Sheet   ::   Link to Exam 2 Fall 2015
Fri Key   Stats Exam 2

Week 9:   3/7-3/11

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
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 4-2
Notes   Slides
Double integrals and area element $dA$ in polar coordinates.    (sec 11.3, 15.4)

Week 10:   3/14-3/18

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 15.3)
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 12.7, 15.4)
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 12.7, 15.4)

3/21-3/25:   Spring Break   –   no class

Week 11:   3/28-4/1

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
Group Work:   Triple integrals in Cartesian, cylindrical, and spherical coordinates.

Take-Home Exam (Exam 3) handed out at the end of class.
Exam 3 Guidelines

Fri Topic 5-1
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 (take-home exam) due at the beginning of class.
Key   Stats

Week 12:   4/4-4/8

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:   4/11-4/15

Mon Topic 5-5
Notes   Slides
Green’s theorem.    (sec 17.1)
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 $d\vec{S}$.    (sec 16.5)
Common parameterizations of 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 16.4)
Warm-up: Computing surface elements on a cone.

Week 14:   4/18-4/22

Mon Topic 5-8
Notes   Slides
Vector surface integrals (“flux integrals”):   Integrating vector fields over a surface.    (sec 16.5)
Wed Topic 5-9
Notes   Slides
Divergence and the Divergence Theorem.    (sec 17.3)
Fri Divergence Theorem, continued.    (sec 17.3)

Week 15:   4/25-4/29

Mon Topic 5-10
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