Final Exam Information
- Wednesday 16 December, 12-2pm in our regular classroom.
- Info/Review
- Equation Sheet
- Common parameterizations of important surfaces.
Announcements
Syllabus
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: 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 |
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, 12-2pm — Info/Review