Michigan MATH 116: Calculus II
MATH 116 covers integration techniques, applications of integrals, sequences and series, and Taylor series, the second course in Michigan's standardized calculus sequence. It feeds directly into engineering and physics requirements and uses the same uniform team-exam format as MATH 115.
Fennie is independent and not affiliated with University of Michigan. This is an unofficial study guide.
What makes it hard
116 has a reputation as the harder half of the sequence. Series convergence is abstract and unforgiving, and the uniform exams continue Michigan's style of conceptual, multi-part word problems. A lot of students who cruised through 115 hit a wall when sequences and series arrive in the back half.
What you'll cover
- • Techniques of integration
- • Improper integrals
- • Applications: volume, work, and probability
- • Sequences and series
- • Taylor polynomials and Taylor series
The MATH 116 study guide
How to study for Michigan MATH 116, step by step.
- 1
Get integration techniques reflexive early
The front half of MATH 116 is learnable through volume: do integration problems daily until technique selection is automatic. You'll need that bandwidth free when series arrives.
- 2
Start series practice the day the unit opens
Sequences and series are where 116 grades are won or lost, and the abstraction takes weeks to settle. Classify a handful of series every day rather than saving the unit for exam week.
- 3
Build a convergence-test decision process
Write out an ordered checklist for choosing convergence tests and run it on dozens of examples until selection is fast and automatic. It's the single highest-value skill on the final.
- 4
Drill old uniform exams under evening-exam conditions
The team-written uniform exams are consistent year to year in style. Work past exams timed, and practice the multi-part conceptual word problems Michigan favors.
Today
Today's MATH 116 plan
What a Fennie Daily Plan looks like for MATH 116. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is MATH 116 harder than MATH 115?
Most Michigan students say yes. Integration techniques are manageable, but sequences and series are more abstract than anything in 115, and the uniform exams stay conceptual. The back half of the course is where grades are won or lost.
How do I study for MATH 116 exams?
Work old uniform exams under timed conditions. The question style is consistent year to year. For series, build a decision process for choosing convergence tests and practice it until it's automatic; that's the single highest-value skill on the final.
What comes after MATH 116 at Michigan?
Most STEM tracks continue to MATH 215 (Multivariable Calculus), and engineering students also take MATH 216 (Differential Equations). A solid grasp of series and integration from 116 makes both noticeably easier.
More Michigan courses
MATH 115: Calculus I
MATH 115 is Michigan's first-semester calculus course, covering limits, derivatives, and an introduction to integration, required across engineering, science, and economics tracks. It's taught in small sections but standardized across the department, with uniform team-written exams for everyone.
MATH 214: Applied Linear Algebra
MATH 214 is the applications-focused linear algebra course, covering systems of equations, matrix algebra, eigenvalues, orthogonality, and applications like least squares and dynamical systems. It's the standard linear algebra route for engineering students who don't need the proof-based MATH 217.
MATH 215: Multivariable and Vector Calculus
MATH 215 covers calculus in three dimensions: partial derivatives, multiple integrals, and vector calculus through Green's, Stokes', and the Divergence theorems. It follows MATH 116 in the standard sequence and is required across engineering and physical science programs, with a computer lab component using MATLAB.
MATH 217: Linear Algebra
MATH 217 is Michigan's proof-based linear algebra course: the same core material as MATH 214 plus rigorous proofs, abstract vector spaces, and linear transformations treated properly. It's required for the math major and is the standard transition course into theoretical upper-level mathematics.