MTH1125 Calculus for Engineers III

Course Description

Student Population: First year engineering and computer science students (some architecture, math and science majors)

Note: There are several versions of this course:

• MTH1142 is for mathematics and science majors and is effectively interchangeable with MTH1125
• MTH1725 and MTH1742 are the honors versions of 1125 and 1142.

Note: Students who have taken MTH1120/1121 will join those who have taken 1123/1124 at this time.

Goals: The first goal of this course is to introduce students to differential equations: their application and their solution. This is done visually through the use of slope field diagrams and solution curves, and numerically through the use of Euler's method and its refinements. Students will be expected to use calculators and computer software, especially spreadsheets, to compute and visualize solutions. Separation of varibles will be used to find explicit algebraic solutions as well. Each student will be expected to work on a modeling project which will apply differential equations to some problem of individual interest.

The second goal of the course is to acquaint students with series approximations to functions. They will see how these can be used to calculate ``standard functions'' as well as solutions to differential equations. Students will also learn elementary error estimates for series approximations. If time permits, topics from Fourier analysis will be introduced.

Topics:

• Differential equations and slope (flow) fields
• Solutions: Euler's method and separation of variables.
• Applications: growth-decay, logistic growth
• Systems and 2nd order equations: spread of disease, predator-prey, oscillatory motion
• Taylor polynomials and power series
• Geometric series and operations on series (algebraic manipulation, differentiation, integration)
• Error estimates, convergence issues
• Fourier series
• Calculator/computer problems using slope fields; Computer labs on solving differential equations (including systems) using spreadsheets; labs on Taylor and Fourier series using a computer algebra system such as Maple.

URL:   http://www.math.neu.edu/undergrad/course_descr/MTH1125CD.html