[INSTRUCTORS: We have included a general description here as a place holder. As with all sections, feel free to keep this information, replace it with your local course description, or remove this section entirely.]
This course extends the concepts of limits, derivatives, and integrals to vector-valued functions and functions of more than one variable. The topics covered include three-dimensional analytic geometry and vectors, partial derivatives, multiple integrals, line integrals, surface integrals, and the theorems of Green, Gauss (Divergence), and Stokes. Many applications of calculus are included.
Student Learning Outcomes:
[INSTRUCTORS: We have included general student learning outcomes here as a place holder. As with all sections, feel free to keep this information, replace it with your local Student Learning Outcomes, or remove this section entirely.]
Upon successful completion of the course, students will be able to:
- find the distance between a point and a line, a point and a plane, two parallel planes, or two skew lines; Find the equations of lines and planes.
- calculate the arc length and curvature at any point for a space curve.
- evaluate partial derivatives and directional derivatives. Find the extrema for functions of two variables; find the maximum and minimum values of a function subject to the given constraints.
- evaluate double and triple integrals using rectangular, polar, cylindrical, and spherical coordinate systems as well as change of variables using the Jacobian; apply double and triple integrals to solving geometry and physics problems.
- evaluate line and surface integrals using Green’s Theorem, Stoke’s Theorem, and the Divergence Theorem
[INSTRUCTORS: Insert course content.]
- Vectors in two and three dimensions; perform vector operations including dot product, cross product, triple products and projections; find vector and parametric equations of lines and planes, rectangular equation of a plane, and parametric representations of lines and planes; find parametric representations of surfaces
- Vector-valued functions and space curves; find limits, determine continuity, determine differentiability; find derivatives, integrals, and arc lengths; analyze the path of a particle using vectors to describe position, velocity, acceleration, speed, curvature, and tangential and normal components of acceleration, binormal vectors
- Functions of several variables, graph functions of several variables; find and graph level curves, surfaces and contour diagrams; find the limit of function at a point; determine continuity; find partial derivatives and differentials, including chain rules, higher-order partial derivatives, gradients, and directional derivatives; determine differentiability; find the equations of tangent planes and normal lines at a point; identify and classify local and global extrema and saddle points with and without Lagrange multipliers; solve constraint problems using Lagrange multipliers
- Evaluate double integrals and use them to calculate areas and volumes; construct and evaluate double integrals in polar coordinates; use iterated integrals to calculate surface area, evaluate and utilize triple integrals; calculate first and second moments and center of mass; construct and evaluate triple integrals in cylindrical coordinates and spherical coordinates; use the change of variables formula including calculating Jacobians
- Vector fields; find the gradient vector field and flow of a vector field; evaluate line integrals using parametrizations and the Fundamental Theorem of Line Integrals; apply theorems on independence of path and conservative vector fields; apply Green's Theorem; interpret flux in terms of surface integrals; evaluate surface integrals using parametrizations; find the curl and divergence of a vector field; apply Stokes' Theorem and the Divergence Theorem
Great news: your textbook for this class is available for free online!
Calculus, Volume 3 from OpenStax, ISBN 1-947172-16-6
You have several options to obtain this book:
- View online (Links to an external site.) (Links to an external site.)
- Download a PDF (Links to an external site.) (Links to an external site.)
You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.
- All first week assignments need to be completed and submitted by the due date to avoid possibly being dropped from the class.
- Any student needing accommodations should inform the instructor. Students with disabilities who may need accommodations for this class are encouraged to notify the instructor and contact the Disability Resource Center (DRC) [link to your college's DSPS website] early in the quarter so that reasonable accommodations may be implemented as soon as possible. Students may contact the DRC by visiting the Center (located in room A205) or by phone (541-4660 ext. 249 voice or 542-1870 TTY for deaf students). All information will remain confidential.
- Academic dishonesty and plagiarism will result in a failing grade on the assignment. Using someone else's ideas or phrasing and representing those ideas or phrasing as our own, either on purpose or through carelessness, is a serious offense known as plagiarism. "Ideas or phrasing" includes written or spoken material, from whole papers and paragraphs to sentences, and, indeed, phrases but it also includes statistics, lab results, art work, etc. Please see the YourCollegeName handbook for policies regarding plagiarism, harassment, etc. [link to your college's academic honesty policies]
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