Mon May 23 10:24:04 2011
Effective Term: |
New:
1119 - Fall 2011 Old: 1113 - Spring 2011 |
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Consent Requirement: |
New:
No required consent Old: College |
Proposal Changes: |
New:
Being submitted for certification for the Lib Ed Mathematical Thinking Core. Change enforced requirement: to no consent to allow registration without permission numbers. Old: Removed "prereq IT Honors office approval" as permission for entry is now UHP rather than ITH; changed "meets Honors req of Honors" to "meets HonorsUHP req of UHP". |
Faculty Sponsor Name: |
New:
Bryan Mosher Old: David Frank |
Faculty Sponsor E-mail Address: |
New:
mosher@math.umn.edu Old: frank@umn.edu |
Student Learning Outcomes: |
* Student in the course:
- Can identify, define, and solve problems
New:
Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome. Problem solving is at the heart of any mathematics course. In this course some problems would involve purely mathematical issues, like finding the derivative of a polynomial or determining the features of the graph of a rational function. Other problems involve taking a real world situation like predicting the trajectory of a projectile or analyzing population growth and decline, requiring students to first identify the mathematically relevant aspects, then define appropriate mathematical variables and relations, and finally solve the resulting mathematics problem. 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. Practically every homework assignment, quiz, and exam requires students to solve problems. Students receive ample feedback about this learning outcome during the semester. Old: Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome. To be completed later 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. To be completed later |
Requirement this course fulfills: |
New:
MATH
- MATH Mathematical Thinking
Old: |
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:
New: Calculus I (Math 1571H) is the first semester in a multi-semester calculus sequence, primarily for honor students in engineering, science, and economics. This course requires students to have a real understanding of the symbolic language of mathematics, giving them ample opportunity to see how mathematics is done by mathematicians and to engage in that same work by solving problems for themselves. In this way, they see how abstract mathematical concepts can find applications in the real world. An important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia, both for aesthetic reasons and to solve concrete problems. Calculus is one of the pillars of modern mathematics, and it has important applications in science and everyday life. Calculus was first developed by Newton and Leibniz in the 17th century to solve many types of problems. For example, using calculus, Newton was able to derive the equations of planetary motion from basic physical laws. Since that time, calculus has touched virtually every part of modern life, through its use in areas like engineering, the stock market, agriculture, psychology, and all the physical and biological sciences. While it is beyond the scope of a 1-semester course to cover even a small fraction of all these applications, students will be exposed to a variety of simplified versions of them, preparing them for later advanced study in their fields of interest. In this way, students experience both the fundamental nature of the questions and the usefulness of abstract reasoning in finding elegant and efficient solutions. Students meet twice a week in TA recitation sections, where they can ask questions, work problems together, and discussion important points in the material. The prerequisite for this course is being an honors student and permission of University Honors Program. Math 1571H is offered Fall semester. The course is taught primarily by regular faculty. Old: <no text provided> |
Provisional Syllabus: |
Please provide a provisional syllabus for new courses
and courses in which changes in content and/or description and/or credits are proposed that include 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 (texts, authors, frequency, amount
per week); required course assignments; nature of any student projects; and how students will be evaluated.
The University policy on credits is found under Section 4A of "Standards for Semester Conversion" at http://www.fpd.finop.umn.edu/groups/senate/documents/policy/semestercon.html . Provisional course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification, This provisional course syllabus information may not correspond to the course as offered in a particular semester. New: Math 1571H -- Fall 2010 Syllabus Instructor: Karel Prikry Office: 214 Vincent Hall, Office Hours MW 2:30 to 4:00 pm Phone: 612-625-4514 email: prikry@math.umn.edu We will cover differential calculus as well as the main techniques of integral calculus and applications. Prerequisites in college algebra, trigonometry, and precalculus will be assumed although I will restate important facts, as practicable, when I have to use such. The Textbook is Calculus with Analytic Geometry, 2nd edition, by George F. Simmons. There will be three one-hour exams: Thursday, September 30, Monday, October 25, and Thursday, November 18. The one-hour exams will be worth 20% of your grade, Final Exam will be worth 30%, and quizzes and home works will be worth 10%. Final Exam will be given Thursday, December 16, 1:30 pm to 4:30 pm. All exams will be about 50% multiple choice (no partial credit) and 50% hand graded (for partial credit). Only scientific calculators without graphing/symbolic manipulation capability will be allowed on the exams. Approximate Schedule: September 8-24: Chapter 2 [The Derivative of a Function] and Chapter 3 [The Computation of Derivatives] September 27-October 8: Chapter 4 [Applications of Derivatives] October 11-22: Chapter 5 [Indefinite Integrals and Differential Equations] October 25-November 1: Chapter 6 [Definite Integrals] November 3-10: Chapter 8 [Exponential and Logarithm Functions] November 12-22: Chapter 7 [Applications of Integration] November 22-December 3: Chapter 9, sections 1-4: [Trigonometric Functions] December 6-December 10: Chapter 10, sections 2,7,8 [Methods of Integration] December 13,15: Review Exercises: Those students who wish to review some of the prerequisites should work the following exercises from Chapter 1 [Numbers, Functions and Graphs], section 1.3 (equations of lines) #7a,b,d,g; section 1.4: (equations of circles) # 3 a,c, 6a,c; section 1.5 (working with functions--domain, graphing, algebra) # 5,6,7,8 13d; section 1.6 (more graphing) #1a,b, 2d, 3c; section 1.7: (trig functions) 5a,9. Chapter 2 [The Derivative of a Function] Exercises: section 2.2 (calculate slope of the tangent): 1a,b, 5,6,7; section 2.3 (definition of derivative): 29, 30, 37; section 2.4 (velocity and rates of change): 8, 10, 15; section 2.5 (concept of limit): 4,5,6,9, 15, 18c,d,e, 20; section 2.6 (mean value theorem and other theorems: 2,5,7,12,20,30,31. Chapter 3 [The Computation of Derivatives] Exercises: section 3.1 (derivatives and polynomials): 1i,j, 2h,i.4,6,18; section 3.2 (product and quotient rules): 6,8,10,14,17, 38; section 3.3 (composite functions and the chain rule) : 8,9, 14,24,26,33,36,37,44,45,46; section 3.4 (trigonometric derivatives): 2,3,5,6,7,9,12,21,33, 23, 24,30,34; section 3.5 (implicit functions and fractional exponents): 2,3,5,9,10,24,25,29b,36,37,39,42,46; section 3.6 (Derivatives of higher order): 2a-d, 4b,d,6,9.13. Chapter 4 [Applications of Derivatives] Exercises: 4.1 (increasing and decreasing functions. Maxima and Minima): 5,6,7,8,12,23,25,26b, 30a; section 4.2 (concavity and points of inflection): 3,4,5,11,12; section 4.3 (applied maximum and minimum problems): 8,10,11,18 21; section 4.4 (maximum-minimum problems. reflection and refraction): 1,2,5,6,8; section 4.5 (related rates); 2,4,5,9,10,13,; 4.7(marginal analysis) 1,6,12,18,21 Chapter 5 [Indefinite Integrals and Differential Equations] Exercises: section 5.2 (differentials and tangent line approximations): 1,3,4,6,9,11,13,14,15,20,21,23; section 5.3 (indefinite integrals. integration by substitution): 3,8,9,13,14,32,33,40,41,42,45-51,54,56,63c,d,66,67; section 5.4 (differential equations. separation of variables): 2,6-10,12,14,15 Chapter 6 [Definite Integrals] Exercises: 6.3 (sigma notation and certain special sums); 2c,f, 5a,b; 6.5 (computation of areas of limits): variations on 2 and 3; section 6.6 (fundamental theorem of calculus): 3,4,8,10,15,16,23,27,38,39,41,42; section 6.7 (properties of definite integrals): 1,3, 16 a-d. Chapter 7 [Applications of Integration] Exercises: section 7.2 (area between two curves): 4,6,10,14,15,18; section 7.3 (volumes: the disk method): 1b,c,d, 2,5,6,13,14; section 7.4 (volumes: method of cylindrical shells): 1-6,8,10,16,17,; section 7.5 (arc length): 1,2,4,5,8; section 7.6 (area of surface of revolution):1-6. Chapter 8 [Exponential and Logarithm Functions] Exercises: section 8.3 (number e and function y = e^x): 4,6,10,12,14,16,25,27,29; section 8.4 (natural logarithm function y =ln x. Euler): 4a,c,d,k, 5a,b,d,g,h,k,l; section 8.5 (applications. population growth and radioactive decay): 1,5,6,7,11,13; section 8.6 (applications. inhibited population growth, etc): 5, 8.9 Chapter 9 [Trigonmetric Functions] Exercises: section 9.2 (derivatives of sine and cosine): 10,11,15-18,33-38; section 9.3 (integrals of the sine and cosine): 6-10; section 9.4 (derivatives of the other four functions): 1,3,4,8,10,11,14-18 Chapter 10 [Methods of Integration] Exercises: section 10.2 (method of substitution): 1-4,8,9,12,13,20,23,37,39,40; section 10.7 (integration of parts): 1,5,11,14,16,17,18: section 10.8 (strategy for dealing with integrals of miscellaneous types): 1,2,6,8,11,13,16,18.19 Liberal Education: This course fulfills the Mathematical Thinking component of the Liberal Education requirements at the University of Minnesota. An important part of any liberal education is learning to use abstract thinking and symbolic language to solve practical problems. Calculus is one of the pillars of modern mathematical thought, and has diverse applications essential to our complex world. In this course, students will be exposed to theoretical concepts at the heart of calculus and to numerous examples of real-world applications. Old: <no text provided> |