# Home

### Final Exam Information

#### Schedule

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:   8/24-8/28

 Mon Topic 1-1 Notes   Slides Introduction to vectors:   Cartesian co-ordinates and vectors in component form.    (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:   8/31-9/4

 Mon Topic 1-4 Notes   Slides Introduction to the dot and cross products:   Definitions and computation.    (sec 12.3, 12.4) Wed Topic 1-5 Notes   Worksheet Group Work:   Geometric properties of the dot and cross products: angles, area, and orthogonality.    (sec 12.3, 12.4) Fri Topic 1-6 Notes   Slides Applications of the dot product:   Projections and orthogonal decompositions.    (sec 12.3)

Week 3:   9/7-9/11

 Mon No Class 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:   Vector-valued functions and the position vector. Parametrizing commonly occurring curves in the plane and in 3-space.    (sec 13.1)

Week 4:   9/14-9/18

 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 Fri Exam Information   Equation Sheet Key   Stats Exam 1

Week 5:   9/21-9/25

 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 and differentiability.    (sec 14.4)

Week 6:   9/28-10/2

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

Week 7:   10/5-10/9

 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) Going over homework problems, and the geometry of the second derivative test.

Week 8:   10/12-10/16

 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 Fri Exam Information   Equation Sheet Key   Stats Exam 2

Week 9:   10/19-10/23

 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 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:   10/26-10/30

 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)

Week 11:   11/2-11/6

 Mon Triple Integral Practice Worksheet Group Work:   Triple integrals in Cartesian, cylindrical, and spherical coordinates. Wed Catch-up/Review Fri Exam Information   Equation Sheet Key   Stats Exam 3

Week 12:   11/9-11/13

 Mon 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) Wed Topic 5-2 Notes   Worksheet Group work: Introduction to vector fields.    (sec 16.1) Fri Topic 5-3 Notes   Slides Vector line integrals.   (sec 16.2)

Week 13:   11/16-11/20

 Mon Topic 5-4 Worksheet Group Work:   Conservative vs. non-conservative vector fields.    (sec 16.3) Wed Topic 5-5 Notes   Slides Green’s theorem.    (sec 17.1) Fri 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.

11/23-11/27:   Fall Break   –   no class

Week 14:   11/30-12/4

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

Week 15:   12/7-12/11

 Mon Topic 5-10 Notes   Slides Divergence and the Divergence Theorem, continued.    (sec 17.3) Wed Topic 5-9 Notes   Slides Curl and Stokes’ Theorem.    (sec 17.2) Fri Review

Exam 4/Final Exam — Wednesday 16 December, 12-2pmInfo/Review