MTH 1125 - Calculus 3

This course has two main goals: to have students understand the concepts of differential equations and infinite series, and to enable students to display that understanding through a variety of applications. Specific, measurable, manifestations of your understanding that will be tested during the quarter include your ability to:

• Solve separable differential equations and initial value problems, including those involving position, velocity, and acceleration
• Identify autonomous differential equations and analyze them graphically
• Calculate equilibrium solutions for autonomous differential equations and determine which are stable
• Model and solve population problems
• Approximate solutions to differential equations via Euler's method
• Determine whether given sequences converge or diverge
• Use summation notation to write series, and identify terms in a series from the summation notation
• Calculate specific partial sums of series
• Determine whether given series of numbers converge or diverge by using the monotonic sequence theorem, the n-th term test for divergence, the integral test, the p-series test, the direct comparison test, the limit comparison test, the ratio test, and the root test
• Determine whether a given series of numbers converges absolutely or conditionally
• Determine if an alternating series of numbers converges by using the alternating series test
• Bound the error in approximating the sum of a convergent alternating series by its partial sums
• Identify the harmonic series and the alternating harmonic series, and discuss their importance as examples
• Produce closed formulas for the n-th partial sum of a geometric series, and take the limit to sum the series
• Model physical problems using geometric series
• Manipulate series of numbers algebraically
• Write the general form of a power series and identify the center of a power series
• Determine the radius and interval of convergence of a given power series
• Differentiate, integrate, and algebraically manipulate power series
• Calculate the Taylor or Maclaurin polynomials and series of a given function via the definition
• Calculate the Taylor or Maclaurin polynomials and series of a given function by manipulating known series
• Estimate the error in approximating a given function by Taylor or Maclaurin polynomials
• Use the binomial series to find approximations of functions

There are many resources for improving your algebra and Calculus skills. The best one is to go over any problems with your instructor. Other resources: walk-in tutoring in Cahners Hall and from Engineering tutors in 222 Snell Engineering, tutoring by appointment (sign up in the Media Center in the library), and study aids in the library (Schaum's Outlines are great). Most students find infinite series to be the single hardest topic in first- and second-year Calculus.

It is essential that you keep up with the material, and -- if you are confused -- immediately go over the material with your instructor or a tutor.

It is essential that you attend class regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day. Students are responsible for finding out what material has been covered or what announcements have been made on days that they miss class.

In order to turn in assignments late or to take make-up quizzes/tests, students must bring written proof of some emergency situation; notes from doctors or nurses, documents verifying court appearances, receipts from having a car towed are all examples of valid documentation. Notes from family members are not acceptable. If a situation is of a personal nature, discuss the matter with your academic advisor; an e-mail message from your advisor saying that they believe that you should be allowed to make-up work is acceptable.

Cheating is an insult to honest students -- it will not be tolerated. The University's cheating policy and related disciplinary actions are detailed in the Student Handbook; the Handbook also includes a description of what is considered cheating by the University. Cheating in this class includes (but is not limited to): looking at the papers of others during a quiz or test, talking to other students during a quiz/test, looking at notes during a quiz/test (unless it is specifically announced that you may), copying other students' work outside of class, and obtaining help from others on take-home tests. In this class, working together on homework assignments is NOT considered cheating; however, you MUST write up your homework individually. Please be aware that this policy on working together outside of class varies greatly from one course to the next; the policy on what is allowed, that has been described in this paragraph, may well be considered cheating in your other classes. The use of advanced calculators is NOT considered cheating in this course. Be aware, however, that other courses may well have a policy barring such calculators. Also, your instructor reserves the right to decide on-the-spot between what constitutes a "calculator" and what constitutes a full-fledged "computer". All incidents of cheating will be reported to the Office of Judicial Affairs. If you have any questions as to what constitutes cheating, please ask your instructor.

• Course Coordinator: Prof. David Massey, dmassey@neu.edu, 529 NI, 373-5527
• Vice-chairman of Math. Dept.: Prof. Donald King, donking@neu.edu, 447 LA, 373-5679