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Engineering Math
COE/Math 4 semester proposal home page
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This page contains links and comparisons to Engineering Math programs at Utah State University (USU), the University of Washington (UWash), University of California at Berkeley (UCB), Stanford University, and UCLA. It is possible to compare their content, texts, credit hours, and sequencing with the current Utah proposal.
USU
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catalog of course descriptions
- course syllabi
- Comparison: The Utah State Math 1210-1220 sequence covers through vectors and parametric curves. Their Math 2210 covers the differential, integral, and vector calculus for functions with multivariable domains. The Utah Math Department will phase in the same topic coverage for 1210-1220-2210 starting in Fall 2012. In terms of the current Utah text, Calculus with Differential Equations, 9th edition by Varberg, Purcell, Rigdon, this will mean covering through Chapter 11 by the end of Math 1220, rather than just through Chapter 10.
Utah State uses Calculus: Concepts and Contexts 4th Edition, by Stewart for Math 1210-1220-2210, which is the same text we will use for 1310-1320 and the multivariable integral and vector calculus in S4a. USU 1210 ends with Chapter 5, whereas we plan for 1310 to also cover 6.1-6.4, some applications of integration. USU 1220 ends with Chapter 10, vectors and parametric curves, whereas we plan for 1320 to also include Chapter 11, differential calculus for scalar functions with multivarible domain. We expect this accelerated pacing is possible because 1310-1320 will be the equivalent of four 50-minute lectures plus one 50-minute section meeting per week, whereas USU has one less weekly contact hour. Pacing and topics can be adjusted downwards during the pilot year, if our plans turn out to have been too ambitious. USU Math 2250 parallels current Utah Math 2250, with the same text and topics. Our S3 should remain close enough to USU 2250 so as to articulate for transfer students. There is no analog to S4b=3150 at USU.
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catalog of course descriptions
- Math Department undergraduate page
- Comparison: Stanford operates on quarters. Engineers are encouraged to learn single variable calculus in the 5CH (3 lectures and two sections per week) two quarter sequence 41- 42, using the USU and proposed Utah text Calculus: Concepts and Contexts 4th Edition, by Stewart.
Engineering students have the option of a 6CH version, 41A-42A, in which the two weekly section meetings are 2 hours long (instead of 1) and emphasize collaborative learning, and which also have a weekly 1 hour problem session. This program appears to be especially designed for at-risk students, and is part of a teaching collaboration between the Stanford Engineering College and Mathematics Department. Math 41-42 pacing is similar to that proposed for 1310-1320, ending its second quarter where the current Utah 1210-1220 ends and not including the vector-curve and multivariable domain differential calculus proposed for the year-long sequence 1310-1320.
The last three quarters of engineering math at Stanford do not follow the Utah order. The topic content is less broad but deeper. The 5CH (3 lecture 2 section) sequence 51- 52- 53 covers linear algebra and multivariable calculus (including the remaining 1320 topics); integral and vector calculus (S4a); and differential equations with linear algebra (S3), respectively. The 6CH 51A-52A-53A is also available.
The 5 quarter 5CH Stanford sequence 41-42-51-52-53 does not include any of the proposed Utah partial differential equations unit S4b=3150. Rather, there is an upper division sequence of two 3CH classes on partial differential equations, 131- 132, of which 131 largely intersects Utah S4b=3150, but at a somewhat higher and in-depth level. In this sequence numerical methods are discusssed in the second quarter. The textbook is Partial Differential Equations: An Introduction, 2nd Edition by Strauss.
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catalog of course descriptions
- course syllabi
- Comparison: UCB engineering students take a 4-semester 4CH (3 lecture, 1 two-hour section) sequence 1A- 1B- 53- 54. The first two semesters are single-variable calculus, and the third semester is multivariable (and vector) calculus. All three semesters use Stewart's Calculus: Early Transcendentals, 7th Edition. The fourth semester is linear algebra and differential equations, using a custom text made by combining Chapters 1-7 of Linear Algebra and its Applications 4th Edition by Lay and chapters 4,6, 9, 10 of Fundamentals of Differential Equations 6th Edition by Nagle, Saff, Snider.
Berkeley covers a substantial 5- week unit on first order and second order differential equations in Math 1B, and uses the saved time in its fourth semester Math 54, where only the second half of the semester is about differential and partial differential equations. Thus the 2-year topic order is not the same as Utah's, but the ultimate content and pacing is substantially the same. Small differences are that the year 2 content at UCB emphasizes more linear algebra that is taught independently of differential equations theory (7.5 weeks at UCB vs. 4 weeks in current S3=2250), and less partial differential equations (2 weeks at UCB vs. 7.5 weeks in S4b=3150).
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catalog of course descriptions
- course syllabi
- Comparison: The University of Washington engineering sequence tracks very closely with Utah's proposal, with slight variations: Washington operates on quarters. Its first year is at a 5CH rate (3 lectures and 2 sections per week), and its second year is at a 3CH rate. There is an additional 3CH course for multivariable integral and vector Calculus.
The first year sequence 124, 125, 126 covers single and multivariable Calculus through multiple integration. The multiple-variable integration chapter (which is the only material not planned for 1310-1320) is repeated in the subsequent 3CH course on vector Calculus 324, which has topics and timing almost idential to Utah's proposed S4a The text for all these courses is Stewart's Calculus: Early Transcendentals, 7th Edition.
The second year sequence 307, 308, 309 covers differential equations, linear algebra, and systems of DE's plus PDE boundary value problems, respectively. The topics and order track pretty closely with our current plans for S3 and S4b=3150. Compared to the current Utah proposal, there is somewhat more emphasis on linear algebra topics, and no treatment of numerical methods for partial differential equations. The texts for the second year are Elementary Differential Equations and Boundary Value Problems, 9th Edition by Boyce and DiPrima and Introduction to Linear Algebra, 5th Edition by Johnson, Riess and Arnold.