Introductory Calculus Sequences
The Mathematics Department offers two versions of secondsemester calculus: MATH 112L and MATH 122L. MATH 112L was designed to follow MATH 111L (or the MATH 105L/106L sequence) as our standard, laboratorybased Calculus II course. A labcalculus version of Calculus II (MATH 122L) is intended for students with AP credit for MATH 21. (Fall 2020  students continuing from 106L or 111L should take 122L, as 112L is not offered.)
Starting Point(See Placement Guidelines for a detailed discussion of where you should start!) 
Your Next Course 
And After That... 
MATH 105L Laboratory Calculus and Functions I 
MATH 106L Laboratory Calculus and Functions II 
MATH 112L (Fall 2020  students should take 122L, as 112L is not offered.) 
MATH 111L Laboratory Calculus I 
MATH 112L Laboratory Calculus II (Offered in spring semester) 
After Introductory Calculus Sequences (see chart below) 
MATH 21 earned through AP 
MATH 122L OR MATH 112L 
After Introductory Calculus Sequences (see chart below) 
MATH 21 & MATH 22 earned through AP 
MATH 122L OR Sophomore Multivariable Calculus Sequence 
NOTE: * In fall semesters, MATH 112L is reserved for continuing students who have taken MATH 106L or MATH 111L. In spring semesters MATH 112L will be the only secondsemester calculus course offered and will be open to any students with AP credit for MATH 21 or Duke credit for MATH 106L or 111L.
After Introductory Calculus


May Be Good Choices for These Majors (*See Major Requirement note below)  
MATH  STAT  COMP SCI 
PHYS  ENGR  CHEM  ECON  
MATH 221 Linear Algebra and Applications  MATH 222 Advanced Multivariable Calculus  X  X  X  X  X  X  X 
MATH 221 Linear Algebra and Applications  MATH 219 Multivariable Calculus  X  X  X  X  X  X  X 
MATH 218^{(*) }Matrices and Vector Spaces  MATH 222 Advanced Multivariable Calculus  X  X  X  X  X  X  X 
MATH 218^{(*) }Matrices and Vector Spaces  MATH 219 Multivariable Calculus  X  X  X  X  X  X  X 
MATH 212^{(**)} Multivariable Calculus  MATH 221 Linear Algebra and Applications  X  X  X  X  X  X  
MATH 212^{(**)} Multivariable Calculus 
MATH 218^{(*) }Matrices and Vector Spaces 
X  X  X  X  X  X  
MATH 202^{(***)} Multivariable Calculus for Economics  MATH 218^{(*) }Matrices and Vector Spaces  X  
MATH 230 Probability 
MATH 218^{(*) }Matrices and Vector Spaces 
X  X  X  X  
MATH 212^{(**)} Multivariable Calculus  MATH 230 Probability  X  X  X  X  X  
MATH 218^{(*) }Matrices and Vector Spaces  MATH 238 Fundamentals of Data Analysis and Decision Science  X  X  X 
Overview Courses Without Prerequisities

NOTE: Major Requirements: These indications are just a guide; the precise requirements for these majors are in the Bulletin. Students who hope to skip any math course should be sure to consider carefully the math requirements of their likely majors, minors, and certificate plans. Those math requirements are overseen and enforced by those departments – not the Department of Mathematics. Enrollment in and successful completion of a higher level course CANNOT be assumed to satisfy a requirement of a lower level course, and very often it will not. You must get written permission from the Director of Undergraduate Studies of the appropriate department before you skip any such required course.
^{(*) }  Math majors can take MATH 218, but should first read the additional related requirements on the list of requirements for the math major.
^{(**)}  MATH 212 however should satisfy requirements very similarly to MATH 219 and MATH 222. Students are advised though to take MATH 212 only if they do not need linear algebra, or if it is necessary due to a scheduling problem. Enrollment in MATH 212 requires credit for second semester calculus (Math 22, 112L, 122L, or 122) on your Duke transcript.
^{(***)}  MATH 202 is intended only for economics majors, and does not satisfy the multivariable requirement for majors in math, physics, engineering, or other majors. Enrollment in MATH 202 requires credit for second semester calculus (Math 22, 112L, 122L, or 122) on your Duke transcript.