Elgin Johnston (firstname.lastname@example.org)
MATH 265. Calculus III.
(4-0) Cr. 4. F.S.SS. Prereq: Minimum of C- in MATH 166 or MATH 166H
Analytic geometry and vectors, differential calculus of functions of several variables, multiple integrals, vector calculus.
Thomas' Calculus, Early Transcendentals, Twelfth Edition.
Chapter and Section references are to Thomas' Calculus, Early Transcendentals, 12th ed.
Times are suggested based on a 15-week
semester of 59 class meetings, allowing 8 days for review and
|Chapter & Sections Topics
| Chapter 12 - Vectors and the Geometry of Space
|Chapter 13 - Vector-Valued Functions and Motion in Space
|Chapter 14 - Partial Derivatives
|Chapter 15 - Multiple Integrals
|Chapter 16 - Integration in Vector Fields
Geometry in Space, Vectors
- Use the parallelogram law to add geometric vectors.
Resolve geometric vectors into components parallel to
- Perform the operations of vector addition and scalar multiplication,
and interpret them geometrically.
- Use the dot product to calculate magnitude of a vector, angle
and projection of one vector on another.
- Find and use direction angles and direction cosines of a vector.
- Use parametric equations for plane curves and space curves.
- Use and convert between parametric and symmetric equations for a
- Find a tangent line at a point on a parametric curve; compute the
length of a parametric curve.
- Compute velocity, unit tangent and acceleration vectors along a
resolve acceleration into tangential and normal components and
- Use and interpret geometrically the standard equation for a plane.
- Use the cross product; interpret the cross product geometrically and
as area of a parallelogram;
interpret the vector triple product as volume of a parallelepiped.
- Recognize cylinders and quadric surfaces from their Cartesian
- Use cylindrical and spherical coordinates, and convert among these
two and rectangular coordinates.
Derivatives for Functions of Two or More Variables
- Represent a function of two variables as the graph of a surface;
sketch level curves.
- Calculate partial derivatives and the gradient.
- Use the gradient to find tangent planes, directional derivatives and
Interpret the gradient geometrically.
- Use the Chain Rule.
- Find and classify critical points of functions of two variables, using the second
- Use Lagrange's method to maximize or minimize a function subject to
- Find maximum and minimum values for a function defined on a closed,
bounded, planar set.
- State the definition of the integral of a function over a rectangle.
- Use iterated integrals to evaluate integrals over planar regions, and
to calculate volume.
- Build on elementary integration techniques to evaluate multiple
- Set up and evaluate double integrals in polar coordinates.
- Set up and evaluate integrals to compute surface area.
- Set up and evaluate triple integrals in Cartesian coordinates.
- Use double and triple integrals to compute moments, center of mass,
and moments of inertia.
- Use cylindrical and spherical coordinates; change coordinates from
rectangular to cylindrical or spherical or the reverse.
- Set up and evaluate triple integrals in cylindrical and spherical
- Change the order of variables in multiple integrals.
- Carry out change of variables in multiple integrals.
- Calculate the curl and divergence of a vector field.
- Set up and evaluate line integrals of scalar functions or vector
fields along curves.
- Recognize conservative vector fields, and apply the fundamental
theorem for line integrals of conservative vector fields.
- State and apply Green's Theorem.
- Set up and evaluate surface integrals; compute surface area and
the flux of a vector field through a surface.
- Set up and evaluate integrals over parametric surfaces.
- State and apply the Divergence Theorem.
- State and apply Stokes' Theorem.
There are no common Midterm Exams
Final Fall 2014
Final Spring 2015
Final Fall 2015
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