# Choosing Your First Math Class

## The Math Requirement in Engineering

The core mathematics courses for Engineering students are:

- MATH 1910: Calculus for Engineers
- MATH 1920: Multivariable Calculus for Engineers
- MATH 2930: Differential Equations or MATH 2940: Linear Algebra
- 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: Thursday, August 17th**

**Time: 10:00am-12:00pm**

**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 use 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 Cornell, 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 prior to the start of fall course pre-enrollment in July. 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. More information about what qualifies for transfer credit will be sent to you prior to July.

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.

Math 1910: Calculus for Engineers | Math 1920: Multivariable Calculus For Engineers | Math 2930: Differential Equations for Engineers | Math 2940: Linear Algebra for Engineers |
---|---|---|---|

Prerequisite: Assumes student has successfully completed at least one course in differential and integral calculus. | Prerequisite: Math 1910 | Prerequisite: Math 1910 and Math 1920 | Prerequisite: 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 |