Choosing Your First Math Class

The Math Requirement in Engineering

The core mathematics courses for Engineering students are:

  1. MATH 1910: Calculus for Engineers
  2. MATH 1920: Multivariable Calculus for Engineers
  3. MATH 2930: Differential Equations or MATH 2940: Linear Algebra
  4. A math course chosen by major

Students must enroll in one (and only one) math course for the fall term in order to be in good academic standing in the College of Engineering.  A list of the topics covered in each course is located at the bottom of this webpage.  More information about good academic standing is available in the most recent Engineering Undergraduate Handbook.

Students are encouraged to consider the following when selecting their first math course during course pre-enrollment in July:

  • Satisfactory performance on a standardized advanced placement exam (CEEB or GCE) and coursework completed at another accredited college may be used toward the math requirement if the student wishes to use the credit.  Consult the Engineering Handbook for details concerning how Engineering awards advanced placement and transfer credit.
  • Because your performance in the mathematics curriculum is critical to your academic success in Engineering, we encourage you to realistically assess your abilities and avoid creating a schedule that is overly ambitious or demanding your first semester.
  • You will be able to change your math enrollment during the Add/Drop period in August, after you take any desired CASE exams and meet with your faculty advisor during Orientation.

Cornell Advanced Standing Exam (CASE) for MATH 1910 and 1920

Date:             TBD

Time:             TBD

Location:      TBD

You may wish to take this optional exam if:

  • you are unsure of which math course is the best match for your knowledge or skill level;
  • you have no advanced placement (AP) credit for math, but wish to try to earn credit for MATH 1910 and/or MATH 1920;
  • you are unsure whether to accept your AP or transfer credit, and wish to test your knowledge against what Cornell faculty would expect you to know if you were to complete the class at Cornell.

You will not lose any math credits you already earned via your scores on a standardized exam (AP, GCE, IB) or prior coursework as a result of your performance on this exam.

CASE exams are not offered for MATH 2930 or MATH 2940.

Deciding on a First Math Course

MATH 1910 (Calculus for Engineers)

You should enroll in a lecture and discussion of MATH 1910 if:

(1)  You do not have advanced placement or transfer credit for MATH 1910; or

(2)  You have advanced placement or transfer credit for MATH 1910 but do not wish to use it.

MATH 1920 (Multivariable Calculus for Engineers)

You should enroll in a lecture and discussion of MATH 1920 if:

(1)  You have advanced placement credit — a score of 5 on the College Board (CEEB) AP Calculus BC exam (not the AB exam) or a score of A, B, or C on the General Certificate of Education (GCE) Advanced (A-Level) exam in Math or Pure Math (if taken in Singapore) — and plan to accept this credit in place of MATH 1910; or

(2)  You have earned transfer credit for MATH 1910 from another institution (must be pre-approved); or

(3)  You plan to complete MATH 1910 this summer at Cornell or an equivalent course at another institution (must be pre-approved).

MATH 2930 (Differential Equations for Engineers) or MATH 2940 (Linear Algebra for Engineers)

You should enroll in a lecture and discussion of MATH 2930 or MATH 2940 only if you have already earned credit for both MATH 1910 and MATH 1920, through advanced placement, transfer credit, or a combination of the two (confirmed by the Engineering Advising Office).

Please remember:  Detailed information and step by step instructions for selecting all of your courses, including math, will be available on the Engineering Advising New Students website in early July, prior to the start of fall course pre-enrollment.  Additionally, you will have an opportunity to adjust your fall course enrollment during Add/Drop in late August, after you take any desired CASE exams and meet with your faculty advisor during Orientation.

What if I don’t yet know my AP exam scores and/or I plan to take the CASE?

If you have taken an advanced placement exam (CEEB, GCE A-Level, or IB) but do not know your final results, or you wish to take the CASE exam for math during Orientation, select a class in July based on your expected results or how confident you feel about the topics.

Transferring Credit

Credit will be awarded for a math course taken at another institution only if the course is highly comparable in both content and rigor to MATH 1910, 1920, 2930, or 2940.  The student must provide a syllabus that includes an outline of the topics covered in the course, as well as the final exam or sample exams.  If the course was taken online, the student must also provide proof that the final exam was proctored on the university’s campus by the department running the program rather than by a proctor agreed upon by the student and the program.

Courses equivalent to MATH 1110 (Calculus I) are not evaluated for transfer credit in Engineering.  Differential Equations courses may be transferrable if a substantial part of the course involves partial differential equations.  Credit for MATH 2930 will not be awarded for courses that cover only ordinary differential equations.

Engineering Math Sequence Topics

Math 1910: Calculus for Engineers

Math 1920: Multivariable Calculus For EngineersMath 2930: Differential Equations for EngineersMath 2940: Linear Algebra for Engineers
Prerequisite:  Assumes student has successfully completed at least one course in differential and integral calculus.Prerequisite: Math 1910Prerequisite: Math 1910 and Math 1920Prerequisite: Math 1910 and Math 1920

Fundamental theorem

Substitution in definite integrals

Numerical integration

Areas between curves

Volumes by slicing

Volumes of revolution

Cylindrical shells

Curve length/surface area

Inverse functions and derivatives

Natural logarithms

The exponential/other bases

Growth and Decay

Inverse trig functions

Hyperbolic functions

Basic integration formulae

Integration by parts

Trig substitutions

Improper integrals

Limits of sequences of numbers

Theorems for limits

Infinite series

Integral test

Comparison tests

Ratio tests

Absolute convergence

Power series

Taylor and Maclaurin series

Taylor series convergence

Applications of power series

Probability

Polar coordinates

Conic sections

Vectors in a plane

Cartesian coordinates/vectors in space

Dot products

Cross products

Lines and planes in space

Vector-valued functions

Arc length/unit tangent vector

Functions of several variables

Limits and continuity

Partial derivatives

Differentiability/linearization

The chain rule

Directional derivative

Extreme values/saddle points

Double integrals

Applications: mass/ center of mass/ average value

Integrals in polar coordinates

Triple integrals

Spherical, cylindrical coordinates

Line integral

Vector fields

Flux and circulation

Green’s Theorem

Surface integrals

Stokes’ Theorem

Divergence theorem

Curl/potential functions

Change of variables

Parametrized and implicit surfaces

Tangent plane to a surface

Joint probability distribution

First order differential equations

Initial value problem/existence theorem

Separable equations

Linear equations

Exact equations

Math models

Qualitative methods

Numerical methods

Linear differential operators

Second order differential equations

Constant coefficients/ homogeny

Complex roots

Nonhomogeneous equations

Undetermined coefficients

Direction fields

Boundary value problems and eigenvalue problems

Introduction to PDE

Fourier series

Sine and cosine series

Separation of variables

Heat equation

Wave equation

Laplace’s equation

Partial differential equations

Superposition principle

Forced oscillations

Introduction/linear systems

Row reduction

Vectors, linear combinations

Matrix equations

Solution sets of Ax=b

Linear transformations

Matrix of linear transformation

Matrix operations, inverse

Invertible matrices

Partitioned matrices

Determinants

Vector spaces

Null and column spaces

Linear independence

Dimension

Rank

Applications

Eigenvectors

Diagonalization

Linear transformations

Complex eigenvalues

Apps to differential equations

Orthogonal sets

Inner products

Orthogonal projection

Gram-Schmidt process

Least squares problems

Inner product spaces

Diagonalization of symmetric matrices

Orthogonal matrix

Markov chains

Singular value decomposition