# About Calculus

Students pursuing or likely to pursue majors in Mathematics, Chemistry, Geophysics, Geology-Geophysics, or Physics, or following the B.S. program in Computer Science, should take one of the Calculus courses required by their major in the first Fall semester. You will choose from the following:

- MT102 Calculus I - Math & Science Major
- MT105 Calculus II-AP - Math & Science Major
- MT202 Multivariable Calculus

These Calculus courses are also open to, and recommended for, students in other majors who are mathematically inclined and highly motivated.

#### Not Had (Much) Calculus Yet?

If you've taken no more than one semester of Calculus in high school, your choice is simple: take MT102 Calculus I (Math & Science Majors). In the Spring semester, you'll take its direct continuation MT103 Calculus II (Math & Science Majors), and then complete the basic Calculus with MT202 Multivariable Calculus in your third semester.

Even if you've taken no Calculus or PreCalculus, MT102 Calculus I (Math & Science Majors) is still the correct choice for a first-semester Calculus course.

#### Had (a lot of) Calculus Already?

Which of the MT102, MT105, or MT202 courses is the most appropriate for you is determined by these major factors:

- the type of high school Calculus curriculum you studied ("AB," "BC," or "Other");
- the results you achieved in these courses;
- the results you achieved on the AP exam, if you took one;
- your attitude towards mathematics;
- your motivation to pursue a demanding program; and
- your desire to advance more quickly through the requirements of your major.

Our general recommendations on which course you should choose as a first Calculus course can be found in the following table. In all cases where we suggest choosing one of two possible courses, you should almost always take the higher-numbered course if you have a positive attitude towards mathematics and are motivated to pursue a demanding program.

Calculus Curriculum You Studied/AP Test You Took | ||||

BC | AB | Other | ||

The Result You Achieved | AP Score of 5 | MT202 | MT105 | --- |

AP Score of 4 | MT105 or MT202 | MT102 or MT105 | --- | |

A year of high school Calculus with mostly grades of A | MT105 | MT102 or MT105 | MT102 | |

A year of high school Calculus with mostly grades of B | MT102 | MT102 | MT102 |

**Note**

- MT105 Calculus II-AP (Math & Science Majors) assumes that you've studied the transcendental functions (exponential and logarithm). If you studied Calculus but did not learn the Calculus of these functions, then you should take MT102.
- MT105 Calculus II-AP (Math & Science Majors) is a Fall-only course. Its nearest Spring equivalent is MT103 Calculus II (Math & Science Majors), which is the direct continuation of MT102 Calculus I (Math & Science Majors). If you feel you are not strong with integration, but that you know differentiation very well, the best option may be to not take math in the Fall, and then take MT103 in the Spring.
*Secondary Education students in LSOE having an A&S major that requires Calculus for Math and Science Majors (MT102 or MT105)*must ask registration staff to enroll them "by hand" in MT102 (when you register for courses on the second day of Orientation). This is a known problem with the system -- your registration can only be made by registration staff or the Mathematics Undergraduate Vice Chair.*CSOM and CSON students*may register for MT102 only after obtaining permission from the Mathematics Undergraduate Vice Chair.

Students pursuing majors in the Social Sciences, Biology, Geology (excluding Geology-Geophysics), Environmental Sciences, or following the Pre-medical or Pre-dental or Pre-veterinary Programs, and all students in the Carroll School of Management, will usually take their first Mathematics course at Boston College from among the following:

**Not Had (Much) Calculus Yet?**

If you've taken no more than one semester of Calculus in high school, your choice is simple: take MT100 Calculus I. In the Spring semester, if you wish to (or are required to) continue, you'll then take MT101 Calculus II.

Even if you've taken no Calculus or PreCalculus, MT100 Calculus I is still the correct choice for a first-semester Calculus course. The first three weeks of the course are essentially a self-contained (albeit brief) course in PreCalculus.

**Had (A Lot of) Calculus Already?**

Which of the MT100 or MT101 (or even MT202 Multivariable Calculus) courses is most appropriate for you is determined by these major factors:

- the type of high school Calculus curriculum you studied ("AB," "BC," or "Other");
- the results you achieved in these courses;
- the results you achieved on the AP exam, if you took one;
- your attitude towards mathematics;
- your motivation to pursue a demanding program; and
- your desire to advance more quickly through the requirements of your major.

Our general recommendations on which course you should choose as a first Calculus course can be found in the following table. In all cases where we suggest choosing one of two possible courses, you should almost always take the higher-numbered course if you have a positive attitude towards mathematics and are motivated to pursue a demanding program.

Calculus Curriculum You Studied/AP Test You Took | ||||

BC | AB | Other | ||

The Result You Achieved | AP Score of 5 | MT101 or MT202 | MT101 | --- |

AP Score of 4 | MT101 | MT100 or MT101 | --- | |

A year of high school Calculus with mostly grades of A | MT101 | MT100 or MT101 | MT100 or MT101 | |

A year of high school Calculus with mostly grades of B | MT100 | MT100 | MT100 |

##### Note

- Please remember that these are only general guidelines, and no student will be forced to register for one of the courses that might be suggested by the table above.
- For students who have reservations about their abilities, or who are taking multiple science courses with labs, or who have heavy commitments in other disciplines, a conservative choice would be to "drop back" from a suggested course of MT202 to MT101, or similarly, to "drop back" to MT100 if MT101 is suggested.
- Nevertheless, be careful to not be overly conservative if you choose to "drop back" from our suggestions. Taking a course that mostly repeats your high school Calculus curriculum will not receive your full attention, can lead to poor study habits, and sometimes even results in a poor grade.
- Students looking for a deeper or more challenging mathematical preparation -- e.g., for those thinking about graduate work in Economics -- and students who would consider majoring in Mathematics, Physics, Chemistry, Computer Science/BS, or Geology-Geophysics -- should see our advisement page for Math and Physical Science majors. In particular, there may be better options for students having a strong mathematical background and AP credit.

**Two Curricula for Single Variable Calculus**

Our Calculus offerings very much mirror the familiar "AB" and "BC" Advanced Placement curricula.

- We offer the
*MT100 - MT101*Calculus sequence mostly for majors in the Social Sciences, Biology and Geology majors, students in pre-Medical/pre-Dental/pre-Veterinary programs, and students in the Carroll School of Management. The topics covered in these two courses are almost identical to the*Calculus AB curriculum.* - We offer the
*MT102 - MT103*Calculus sequence for Math and Science majors, as well as for students looking for a more challenging alternative to the MT100-MT101 sequence. The topics covered in these two courses are almost identical to the*Calculus BC curriculum*.

There is a stronger emphasis on technical (algebraic) detail in the MT102-MT103 sequence for Math and Science majors. The MT100-MT101 sequence places less emphasis on algebra and more emphasis on the use of a graphing calculator, the interpretation of numeric data, and overall conceptual language.

#### For Those with AP Credit

Students who have completed a year of an Advanced Placement Calculus curriculum in high school should strongly consider bypassing the first course in either of these curricula.

- For students taking the
*MT100 - MT101*Calculus curriculum, MT101 is often an appropriate choice for your first semester. Please see the page describing this curriculum for more info about whether skipping MT100 and starting with MT101 is the right choice for you. - For students who will take the Math and Science curriculum
*MT102 - MT103*, a special version of MT103 is offered in each Fall semester, labeled*MT105 Calculus II-AP (Math and Science majors)*. This course very nicely bridges your high school Calculus background with the goals of the MT102 - MT103 sequence, allowing you to move more quickly to Multivariable Calculus after only one semester of study. Please see the Math and Physical Science Major Calculus page for more detail on whether MT105 would be the correct starting point for you.

#### Continuing to Multivariable Calculus

Students who complete either the MT102-MT103 (Math and Science Major) sequence or the MT105 Calculus II-AP course, and wish to pursue more mathematics, should continue to MT202 Multivariable Calculus.

Students who complete the MT100-MT101 sequence and wish to pursue more mathematics may continue to MT202 Multivariable Calculus. (Although some topics such as sequences and series may have been omitted in this transition, none is prerequisite to MT202.) However, it may be appropriate for students to first complete either MT103 (in Spring) or MT105 (in Fall) before entering MT202. Please consult your MT101 instructor or the Math Advisor for a personal recommendation on which choice is appropriate for you.

#### More Detail on the Differences

You can compare topic coverages of these courses and sequences in the following table.

First Course Differential Calculus | Second Course Integral Calculus | Third Course Multivariable Calculus | |

The Basic Calculus Sequence | MT100 (4 hours) Some pre-Calculus, derivatives, applications of derivatives, introduction to integration. | MT101 (4 hours) Basic integration notions, basic techniques of integration, applications of integration, and an introduction to differential equations. | MT202 (4 hours) Partial derivatives, gradient, level curves and surfaces, optimization in several variables, multiple integration, alternative coordinate systems for double and triple integration, parametric curves in the plane and in space, line integrals, and Green's Theorem. |

Math & Science Major Sequence | MT102 (Fall: 4 hours)In addition to the topics of MT100, this course includes technical notions of limits and continuity, as well as more depth on applications of derivatives, especially in optimization techniques. | MT103 (Spring: 4 hours)In addition to the topics of MT101, this course includes several more integration methods, and provides an introduction to infinite sequences and series (including Taylor series). | |

MT105 (Fall: 3 hours)This course reviews the major integration methods and their interesting applications, then provides an introduction to infinite sequences and series (including Taylor series). |

##### Note

- Any student who thinks he or she may eventually become a major in Math, Physics, Geophysics, Geology-Geophysics, Computer Science/BS, or Chemistry should take the Science major sequence.
- Any student who would prefer a deeper, more demanding program in Mathematics should also prefer the Science major sequence.