Mon Apr 19 09:52:33 2010
Approvals Received: 



Approvals Pending:  College/Dean > Catalog > PeopleSoft Manual Entry  
Effective Status:  Active  
Effective Term:  1113  Spring 2011  
Course:  MATH 4604  
Institution: Campus: 
UMNTC  Twin Cities UMNTC  Twin Cities 

Career:  UGRD  
College:  TIOT  Institute of Technology  
Department:  11133  Mathematics, Sch of  
General  
Course Title Short:  Advanced Calculus II  
Course Title Long:  Advanced Calculus II  
MaxMin Credits for Course: 
4.0 to 4.0 credit(s)  
Catalog Description: 
Sequel to Math 4603. Topology of ndimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem.  
Print in Catalog?:  Yes  
CCE Catalog Description: 
<no text provided>  
Grading Basis:  Stdnt Opt  
Topics Course:  No  
Honors Course:  No  
Delivery Mode(s):  Classroom  
Instructor Contact Hours: 
3.0 hours per week  
Years most frequently offered: 
Every academic year  
Term(s) most frequently offered: 
Spring  
Component 1: 
LEC (with final exam) 

AutoEnroll Course: 
No  
Graded Component: 
LEC  
Academic Progress Units: 
Not allowed to bypass limits. 4.0 credit(s) 

Financial Aid Progress Units: 
Not allowed to bypass limits. 4.0 credit(s) 

Repetition of Course: 
Repetition not allowed.  
Course Prerequisites for Catalog: 
4603 or 5615 or #  
Course Equivalency: 
Math 5616  
Consent Requirement: 
No required consent  
Enforced Prerequisites: (coursebased or noncoursebased) 
No prerequisites  
Editor Comments:  <no text provided>  
Proposal Changes:  New course. The intention is to replace Math 4606 by Math 4603/4604. Some students will only take Math 4603, others will take both 4603 and 4604, and still others will skip 4603 and enter 4604 after taking Math 5615. It is also possible for students who have taken Math 4606 to take Math 4604 (but not Math 4603).  
History Information:  <no text provided>  
Faculty Sponsor Name: 
Lawrence Gray (Director of Undergrad Studies)  
Faculty Sponsor Email Address: 
gray@math.umn.edu  
Student Learning Outcomes  
Student Learning Outcomes: 
* Student in the course:
 Can identify, define, and solve problems
Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome. This course is the second semester of an introduction to the foundations of calculus and techniques of rigorous proof. When a student is asked to prove something, he/she must identify exactly what part of the statement needs proof, what part consists of assumptions, and what is the background knowledge that can be used to create the proof. The student must learn and understanding precise mathematical definitions, and also make new definitions. Students are repeatedly asked to find proofs of mathematical facts. Creating and communicating such proofs is a very rich form of problemsolving. How will you assess the students' learning related to this outcome? Give brief examples of how class work related to the outcome will be evaluated. Students will be asked to write and/or analyze proofs in homework assignments and for exams. They may also be asked to present and/or explain proofs at the blackboard and in class discussion. 

Liberal Education  
Requirement this course fulfills: 
None  
Other requirement this course fulfills: 
None  
Criteria for Core Courses: 
Describe how the course meets the specific bullet points for the proposed core
requirement. Give concrete and detailed examples for the course syllabus, detailed
outline, laboratory material, student projects, or other instructional materials or method.
Core courses must meet the following requirements:
<no text provided> 

Criteria for Theme Courses: 
Describe how the course meets the specific bullet points for the proposed theme
requirement. Give concrete and detailed examples for the course syllabus, detailed outline,
laboratory material, student projects, or other instructional materials or methods. Theme courses have the common goal of cultivating in students a number of habits of mind:
<no text provided> 

Writing Intensive  
Propose this course as Writing Intensive curriculum: 
No  
Question 1: 
What
types of writing (e.g., reading essay, formal lab reports, journaling)
are likely to be assigned? Include the page total for each writing
assignment. Indicate which assignment(s) students will be required to
revise and resubmit after feedback by the instructor or the graduate TA. <no text provided> 

Question 2: 
How does assigning a significant amount of writing serve the purpose
of this course? <no text provided> 

Question 3: 
What types of instruction will students receive on the writing aspect
of the assignments? <no text provided> 

Question 4: 
How will the students' grades depend on their writing performance?
What percentage of the overall grade will be dependent on the quality and level of the students'
writing compared with the course content? <no text provided> 

Question 5: 
If graduate students or peer tutors will be assisting in this course,
what role will they play in regard to teaching writing? <no text provided> 

Question 6: 
How will the assistants be trained and
supervised? <no text provided> 

Question 7: 
Write up a sample assignment handout here for a paper
that students will revise and resubmit after receiving feedback on the initial
draft. <no text provided> 

Readme link.
Course Syllabus requirement section begins below


Course Syllabus  
Course Syllabus: 
For new courses and courses in which changes in content and/or description and/or credits
are proposed, please provide a syllabus that includes the following information: course goals
and description; format;structure of the course (proposed number of instructor contact
hours per week, student workload effort per week, etc.); topics to be covered; scope and
nature of assigned readings (text, authors, frequency, amount per week); required course
assignments; nature of any student projects; and how students will be
evaluated. The University "Syllabi Policy" can be
found here
The University policy on credits is found under Section 4A of "Standards for Semester Conversion" found here. Course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification. This course syllabus information may not correspond to the course as offered in a particular semester. (Please limit text to about 12 pages. Text copied and pasted from other sources will not retain formatting and special characters might not copy properly.) Syllabus for Mathematics 4604, Advanced Calculus II This is the second semester of a rigorous treatment of mathematical analysis, building on the first semester, Math 4603. It is expected that students in Math 4604 will have already completed Math 4603 or Math 5615 or a similar course. In Math 4604, differentiation and integration theorems for functions of several variables will be the central topic. As time permits, additional topics may include convergence properties for sequences and series of functions of several variables. This is is a 4.0 credit course, involving at least three hours of regular class lectures per week, as well as office hours with the lecturer. Students should normally expect to spend at least 12 hours per week on this course, including time in class. Student grades will be determined by examinations (two midterm exams and a final examination), as well as regular homework assignments. Textbook: Advanced Calculus of Several Variables, by C.H. Edwards, Jr., Dover Publications, New York, 1994. Summary outline of the topics by week: Week 1: Review of ndimensional vectors. Vector algebra, inner products, linearity. Week 2: Basic topics in matrices and determinants. Week 3: Topology and convergence in nspace. Week 4: Curves, velocities and potentials. General derivatives of functions on nspace. Week 5: The chain rule and its consequences. Optimization and Lagrange multipliers. Week 6: Taylor's Formula, Newton's Method. Week 7: The Implicit Mapping Theorem. Week 8: Area and Integration. Fubini's Theorem. Week 9: Fubini's Theorem, Change of Variable. Week 10: Arclength, line integrals, notion of a linear differential form. Week 11: Multilinear Functions. Surface area. Week 12: The classical versions of the Divergence Theorem and the Theorem of Stokes. Week 13: Multilinear differential forms. Week 14: The General Theorem of Stokes. [Note: Standard components of a syllabus, such as statements about the university definitions of grades, scholastic dishonesty, etc., have been omitted from this sample, even though they will be part of any actual syllabus used for the course.] 
