UMD MATH141 Calculus II: Syllabus, Topics and Practice

UMD MATH141 (Calculus II) is the second course in the University of Maryland, College Park calculus sequence. It carries 4 credits and needs a C- or better in MATH140. This guide maps every topic in the official description to a lesson you can practice right now.

What UMD MATH141 covers

The UMD Schedule of Classes describes MATH141 as a continuation of MATH140, including techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, and sequences and series. Like MATH140, it notes that graphing calculators, or computers with suitable software, will be needed.

That is a full Calculus 2 course. The official description does not list parametric equations or polar coordinates, so if your section covers them, your instructor's syllabus is the place to check. The description also does not spell out a weekly schedule or textbook.

MATH141 topic map

MATH141 in the UMD sequence

MATH141 is a gateway course: MATH240 (linear algebra), MATH246 (differential equations) and MATH241 all list a C- or better in MATH141 as the prerequisite.

How MATH141 builds on MATH140

MATH141 assumes you can differentiate quickly and evaluate basic definite integrals with the Fundamental Theorem of Calculus. The course then asks harder questions: how to integrate products, powers of trig functions and rational functions, what an integral over an infinite interval means, and when an infinite sum adds up to a finite number. If your MATH140 skills are rusty, spend the first week on the antiderivative practice and u-substitution lessons before new material piles up.

Example problems at the MATH141 level

1. Integration by parts. With u = x and dv = e^x\,dx:

2. An improper integral.

3. A geometric series. With first term 3 and ratio \frac{1}{2}:

How to do well in MATH141

• Practice choosing a method, not just executing it. The choosing a strategy lesson mixes integrals so you have to decide which technique fits.
• Draw every volume problem. Sketch the region and one slice before writing an integral.
• Make a series test flowchart and check it against the convergence tests guide.
• Review exponentials and logs early, since they appear in almost every integration technique.
• Use practice problems on integration by parts and timed practice exams before each test.

Tip: before testing a series for convergence, check the nth term. If the terms do not go to 0, the series diverges and you are done.