Difference between revisions of "MATH 2551"

From Georgia Tech Student Wiki
m
(Overhauled content section)
Line 1: Line 1:
  +
'''MATH 2551''' is a 4 credit core [[Mathematics|math]] class in multivariable calculus. MATH 2551 covers all topics in [[MATH 2550]] and includes an extra unit on vector fields and integration.
−
==Overview==
  
⚫
[https://math.gatech.edu/courses/math/2551 Course page]
  
   
  +
== Content ==
−
MATH 2551 is a 4 credit MATH core class with a linked studio period. It is an enhanced version of [[MATH 2550]] that adds a couple of extra chapters.
 
   
−
==== Topic List ====
 +
=== Topic List ===
  +
# 3D Coordinates and Vectors
−
All topics exclusive to MATH 2551 are marked with an (*):
  
  +
## 3D Coordinates
−  
−
# Vectors
 +
## Vectors
  +
## The Dot Product
−
# 3D Geometry
  
  +
## The Cross Product
⚫
# Quadric Surfaces
  
  +
## Lines and Planes
⚫
# Polar, Cylindrical, and Spherical Coordinate Systems
  
  ⚫
## Cylinders and Quadric Surfaces
−
# Vector-Valued Functions
 +
# Vector Functions
⚫
# Multivariable Limits and Continuity
  
  +
## Domain, Limits, and Continuity
⚫
# Partial Derivatives, Directional Derivatives, and Gradients
  
  +
## Derivatives
−
# Multivariable Function Analysis and Optimization
  
  +
## 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 and Triple Integrals
−
# Line and Surface Integrals (*)
 +
## Double Integrals
  +
## Double Integrals in Polar Coordinates
−
# Green's, Gauss', and Stokes' Theorems (*)
  
  +
## 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
  +
<nowiki>*</nowiki> Vector Fields and Integration is not covered in [[MATH 2550]]
   
  +
=== Prerequisite Knowledge ===
−
====How it fits in the curriculum====
  
  +
−
MATH 2551 is generally taken in late first-year, early second-year, as it requires and uses both Linear Algebra and Calculus topics. Furthermore, it is an important prerequisite for nearly all engineering majors (except Computer Engineering), as all of these majors have at least 1 class that has MATH 2551 as a prerequisite.
 
  +
==== Single Variable Calculus ====
  +
Single variable calculus, covered in [[MATH 1551]], [[MATH 1552|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 applied to 2D and 3D regions in multiple coordinate systems.
  +
  +
==== Linear Algebra ====
  +
While linear algebra, covered in [[MATH 1553]], [[MATH 1554|1554]], and [[MATH 1564|1564]], is listed as a prerequisite for MATH 2551, topics that require prerequisite knowledge of linear algebra are rarely seen in MATH 2551, with the exception of the matrix determinant. However, linear algebra may provide a theoretical background for concepts such as vectors and determinants.
  +
  +
===Relation to the Overall Curriculum===
  +
MATH 2551 is generally taken sometime between late freshmen year and early sophomore year due to having a couple prerequisites. Furthermore, MATH 2551 itself is an important requirement and prerequisite for all engineering majors, with the exception of [[Computer Engineering|computer engineering]].
   
 
==Current Registration Info==
  
==Current Registration Info==
Line 26: Line 62:
   
 
And while it isn't a prerequisite, you will use some Multivariable Calculus concepts (such as vector valued functions and Green's theorem) in [[PHYS 2212]].
  
And while it isn't a prerequisite, you will use some Multivariable Calculus concepts (such as vector valued functions and Green's theorem) in [[PHYS 2212]].
  +
  ⚫
[https://math.gatech.edu/courses/math/2551 Course page]
   
 
===[https://oscar.gatech.edu/bprod/bwckctlg.p_disp_course_detail?cat_term_in=202108&subj_code_in=MATH&crse_numb_in=2551 Prerequisites]===
  
===[https://oscar.gatech.edu/bprod/bwckctlg.p_disp_course_detail?cat_term_in=202108&subj_code_in=MATH&crse_numb_in=2551 Prerequisites]===

Revision as of 11:49, 13 June 2021

MATH 2551 is a 4 credit core math class in multivariable calculus. MATH 2551 covers all topics in MATH 2550 and includes an extra unit on vector fields and integration.

Content

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

* Vector Fields and Integration is not covered in MATH 2550

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 applied to 2D and 3D regions in multiple coordinate systems.

Linear Algebra

While linear algebra, covered in MATH 1553, 1554, and 1564, is listed as a prerequisite for MATH 2551, topics that require prerequisite knowledge of linear algebra are rarely seen in MATH 2551, with the exception of the matrix determinant. However, linear algebra may provide a theoretical background for concepts such as vectors and determinants.

Relation to the Overall Curriculum

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

Current Registration Info

MATH 2551 is a linked course, as it has a studio. You must register for a lecture section (marked with a single letter A, B, C, etc.), and its corresponding studio section (e.g. if you are in Section C, you must register for studio sections that start with C, like C01, C04, etc.). You must register for both of these at the same time.

And while it isn't a prerequisite, you will use some Multivariable Calculus concepts (such as vector valued functions and Green's theorem) in PHYS 2212.

Course page

Prerequisites

All of the Following:

Equivalent Courses

MATH 2561 is an honors version, and goes over the topics in MATH 2551 at a much higher level (along with a few extra topics).

Majors That Require This Class

  • All College of Engineering Majors except Computer Engineering
  • Applied Physics
  • Biochemistry
  • Chemistry
  • Earth and Atmospheric Sciences
  • Physics

Resources

Retrieved from "https://gt-student-wiki.org/mediawiki/index.php?title=MATH_2551&oldid=650"