Math 275 (Analytic Goemetry and calculus III)
Office Hours Monday, Tuesday 2:30-4:30 pm;
Thursday 9-10 am; or by appointment email@example.com
time MWF 9:30-10:20 am, NICCOL 06
by Briggs and Cochran, 11th complete edition (You may use “volume 2:
multivariable” instead of the complete edition. The only difference is the
chapter labeling: Chapter 12 in the complete edition corresponds to Chapter 11
in “volume 2: multivariable”, and so forth.)
Homework (30%) Homework assignment is the most important part of this course.
Homework will be assigned during the semester. There are two kinds of assignments.
The first is basic skills. You do these problems on Mymathlab
(you will receive the course ID in email); the second is more advanced problems.
These assignments will be posted on the course webpage. You do these problems on paper,
write the solutions following basic mathematics writing standards (to be introduced),
and hand in for grading. After an assignment has been turned in, the solution to the
problems will be posted on the course webpage. Late homework (after the solution has
been posted) will not be accepted.
The lowest homework assignment score will be dropped when calculating the final course grade.
Midterm Exams (15% X 3) Three midterm examinations are
scheduled on the days specified on the tentative schedule. A make-up examination
is possible only if you get my permission before the examination, or with a
Final Exam (25%) Final examination is scheduled on
Monday, May 6, 10:00 am—12:00 pm.
Grading Course grades are
determined by: A (90.0%-100%); B (80.0%-89.9%); C (70.0%-79.9%); D
(60.0%-69.9%); F (<60.0%).
On-paper Assignment 1
Here is a Sample Solution
||Martin Luther King.
||Feb 11 13.2
||Presidents’ Day. No
Short Summary This course covers multivariable calculus using
a highly geometric approach. We first give a treatment of three-dimensional
geometry; introduce vectors, dot product, cross product, lines, planes, and how
to visualize a surface in three-dimensional space using contour maps and level
curves. Then, we cover vector-valued functions (parametric curves), and their
derivatives, integrals, curve length, curvature. Next, we extend single variable
calculus to multivariable; cover functions of several variables, and their
limits and partial derivatives, gradients, directional derivatives, local and
absolute maximum/minimum, and Lagrange Multipliers. We then cover two- and
three-dimensional integrals in rectangular, polar, cylindrical, and sphere
coordinates, and changing variables. Finally, we cover line integrals in two-
and three-dimensional spaces, and put the capstone of the course: the
Fundamental Theorem of Line Integrals which relates gradients with integrals,
and Green’s Theorem which relates line integrals with double integrals. If time
permits, we also briefly introduce curl and divergence, surface integrals,
Stokes’ Theorem and Gauss’ Theorem.
Course Content Outline
Fundamental notions of higher dimensions (Chapters 12 of the textbook)----
Vector geometry and analytic geometry of R3
• Calculus of vector valued
functions with applications to motion in space
• Functions of several
variables, including graphs and level curves
2. Differential calculus in
higher dimensions (Chapters 13 of the textbook)----
• Differentiation of
functions of several variables, including partial derivatives, the chain rule,
directional derivatives, gradients, and differentials
problems for functions of more than one variable, including critical point
analysis and Lagrange multipliers
3. Integral calculus in higher
dimensions (Chapters 14 of the textbook)----
• Double integrals in both
rectangular and polar coordinates
• Triple integrals in rectangular,
cylindrical, and spherical coordinates
• Change of variable theorem
4. Vector calculus o Vector fields (Chapters 15 of the
• Line integrals
• Conservative vector fields and the
fundamental theorem of line integrals
• Green’s Theorem
• The student will develop the ability
to reason geometrically in dimensions higher than two, including mastery of
basic notions of vector geometry and equations of lines, planes, and spheres.
• The student will develop the ability to think geometrically about the
graphs of functions of two variables, including the significance of partial
derivatives, directional derivatives, and gradients.
• The student will
learn to do the standard differential operations including partial derivatives
and gradients, and how to use them to do simple optimization problems.
student will learn to set up and evaluate integrals in two and three variables,
including working with any of the standard coordinate systems.
• The student
will understand and correctly interpret the basic notions of vector calculus,
including line integrals of vector fields and Green’s