MATH 2551 - Multivariable Calculus

MATH 2551 is a 4 credit core math class in multivariable calculus.

Topic List

1. 3D Coordinates and Vectors
   1. 3D Coordinates
   2. Vectors
   3. The Dot Product
   4. The Cross Product
   5. Lines and Planes
   6. Cylinders and Quadric Surfaces
2. Vector Functions
   1. Domain, Limits, and Continuity
   2. Derivatives
   3. Integrals and Projectile Motion
   4. Arc Length
   5. Curvature and Normal Vectors
   6. Tangential and Normal Components of Acceleration
   7. Velocity and Acceleration in Polar Coordinates
3. Multivariable Functions and Partial Derivatives
   1. Multivariable Functions
   2. Limits and Continuity
   3. Partial Derivatives
   4. Chain Rule
   5. Directional Derivatives and Gradient
   6. Tangent Planes and Differentials
   7. Extreme Values
   8. Lagrange Multipliers
   9. Taylor Polynomials
   10. Partial Derivatives with Constrained Variables
4. Double and Triple Integrals
   1. Double Integrals
   2. Double Integrals in Polar Coordinates
   3. Triple Integrals
   4. Applications
   5. Triple Integrals in Cylindrical and Spherical Coordinates
   6. Integral by Substitution
5. Vector Fields and Integration*
   1. Line Integrals of Scalar Fields*
   2. Line Integrals of Vector Fields*
   3. Conservative Vector Fields and Potential Functions*
   4. Green's Theorem*
   5. Parametric Surfaces*
   6. Surface Integrals*
   7. Stokes' Theorem and Divergence Theorem*

• 3D Coordinates and Vectors
  • 3D Coordinates
  • Vectors
  • The Dot Product
  • The Cross Product
  • Lines and Planes
  • Cylinders and Quadric Surfaces

• Vector Functions
  • Domain, Limits, and Continuity
  • Derivatives
  • Integrals and Projectile Motion
  • Arc Length
  • Curvature and Normal Vectors
  • Tangential and Normal Components of Acceleration
  • Velocity and Acceleration in Polar Coordinates

• Multivariable Functions and Partial Derivatives
  • Multivariable Functions
  • Limits and Continuity
  • Partial Derivatives
  • Chain Rule
  • Directional Derivatives and Gradient
  • Tangent Planes and Differentials
  • Extreme Values
  • Lagrange Multipliers
  • Taylor Polynomials
  • Partial Derivatives with Constrained Variables

• Double and Triple Integrals
  • Double Integrals
  • Double Integrals in Polar Coordinates
  • Triple Integrals
  • Applications
  • Triple Integrals in Cylindrical and Spherical Coordinates
  • Integral by Substitution

• Vector Fields and Integration*
  • Line Integrals of Scalar Fields*
  • Line Integrals of Vector Fields*
  • Conservative Vector Fields and Potential Functions*
  • Green's Theorem*
  • Parametric Surfaces*
  • Surface Integrals*
  • Stokes' Theorem and Divergence Theorem*

* Topic not covered in MATH 2550

Workload

Content in MATH 2551 is typically assessed through homework, quizzes, and exams. Homework tends to very time-consuming and focuses heavily on computation. Quizzes and exams also focus more on computation but do contain a couple theoretical questions, often presented in a true/false format. Exam problems are usually shorter than homework problems due to time constraints.

Prerequisite Knowledge

Single Variable Calculus

Single variable calculus, covered in MATH 1551, 1552, and AP Calculus, is an important prerequisite for MATH 2551. Multivariable calculus applies single variable calculus concepts such as limits, derivatives, and integrals to functions with more than one input and/or output. Multivariable calculus should not be seen as the next course in a linear sequence of calculus courses; rather, it should be seen as an outward expansion of all single variable calculus topics. For example, while no new integration techniques are introduced in multivariable calculus, with the exception of the Jacobian, the concept of integration is extended in multivariable calculus by applying it to 2D and 3D regions in new coordinate systems.

Linear Algebra

Although linear algebra, covered in MATH 1553, 1554, and 1564, is listed as a prerequisite for MATH 2551, topics that require prior knowledge of linear algebra are rarely seen in MATH 2551. For example, while multiple topics in MATH 2551 use vectors extensively, vectors are reviewed at the beginning of the course, making prior knowledge of vectors unrequired. However, linear algebra does provide a more theoretical background for concepts such as the dot product and matrix determinant, which may be helpful for MATH 2551.

Equivalent Courses

• MATH 2550 is the introduction equivalent, which does not cover the final unit of MATH 2551, Vector Fields and Integration.
• MATH 2561 is the honors equivalent, which includes additional topics and goes into more depth in general

Future Outlook

MATH 2551 is generally taken sometime between late freshmen year and early sophomore year due to it having a couple prerequisites. Furthermore, MATH 2551 itself is an important requirement and prerequisite for all engineering majors, with the exception of computer engineering, which requires MATH 2550 instead.

Multivariable calculus concepts, such as vector functions and Green's Theorem, are also used in PHYS 2212.

Registration

MATH 2551 is a linked course with a studio.

Resources

No resources are currently listed for MATH 2551.