Difference between revisions of "MATH 2551"

From Georgia Tech Student Wiki
m
 
(34 intermediate revisions by one other user not shown)
Line 1: Line 1:
  +
{{DISPLAYTITLE:MATH 2551 - Multivariable Calculus}}
−
==Overview==
  
  +
'''MATH 2551''' covers limits, differentiation, and integration of functions with more than one input and/or output. It is a requirement for engineering majors.
−
[https://math.gatech.edu/courses/math/2551 Course page]
  
   
  ⚫
== Topic List ==
−
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.
 
  +
* 3D Coordinates and Vectors
  +
** 3D Coordinates
  ⚫
** Vectors
  +
** The Dot Product
  +
** The Cross Product
  +
** Lines and Planes
  ⚫
** Cylinders and Quadric Surfaces
   
  ⚫
* Vector Functions
⚫
==== Topic List ====
  
  ⚫
** Domain, Limits, and Continuity
−
All topics exclusive to MATH 2551 are marked with an (*):
  
  +
** 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
⚫
# Vectors
  
  +
** Multivariable Functions
−
# 3D Geometry
  
  +
** Limits and Continuity
⚫
# Quadric Surfaces
  
  +
** Partial Derivatives
⚫
# Polar, Cylindrical, and Spherical Coordinate Systems
  
  +
** Chain Rule
⚫
# Vector-Valued Functions
  
  ⚫
** Directional Derivatives and Gradient
⚫
# Multivariable Limits and Continuity
  
  +
** Tangent Planes and Differentials
⚫
# Partial Derivatives, Directional Derivatives, and Gradients
  
  +
** Extreme Values
−
# Multivariable Function Analysis and Optimization
  
  +
** Lagrange Multipliers
⚫
# Double and Triple Integrals
  
  +
** Taylor Polynomials
⚫
# Line and Surface Integrals (*)
  
  +
** Partial Derivatives with Constrained Variables
−
# Green's, Gauss', and Stokes' Theorems (*)
  
   
  ⚫
* Double and Triple Integrals
−
====How it fits in the curriculum====
  
  +
** Double Integrals
−
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.
 
  +
** Double Integrals in Polar Coordinates
  +
** Triple Integrals
  +
** Applications
  ⚫
** Triple Integrals in Cylindrical and Spherical Coordinates
  +
** Integration by Substitution
   
  +
* Vector Fields and Integration*
−
==Current Registration Info==
  
  +
** Line Integrals of Scalar Fields*
−
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.
  
  +
** 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> Topic not covered in [[MATH 2550]]
−
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]].
  
   
  +
==Class Structure==
−
===[https://oscar.gatech.edu/bprod/bwckctlg.p_disp_course_detail?cat_term_in=202108&subj_code_in=MATH&crse_numb_in=2551 Prerequisites]===
  
  +
MATH 2551 is a core math class focused more on computation than pure theory. Typical problems can be quite lengthy, especially towards the end of the course.
−
All of the Following:
  
   
  +
== Prerequisite Knowledge ==
−
* D or higher in [[MATH 1552]] or a 4+ on AP Calculus BC.
  
−
* D or higher in [[MATH 1553 - Introduction to Linear Algebra|MATH 1553,]] [[MATH 1554 - Linear Algebra|MATH 1554]], or [[MATH 1564]].
  
⚫
===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===
 +
=== Single Variable Calculus ===
  +
[[Single Variable Calculus|Single variable 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 ===
−
* All College of Engineering Majors except Computer Engineering
  
  +
Although [[Linear Algebra|linear algebra]] 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.
−
* Applied Physics
  
−
* Biochemistry
  
−
* Chemistry
  
−
* Earth and Atmospheric Sciences
  
−
* Physics
  
   
−
==Resources==
 +
== Scheduling ==
  +
MATH 2551 is required by most engineering and science majors. It is also a prerequisite itself for many classes required by engineering and science majors. Due to its prerequisites, MATH 2551 is generally taken sometime between late freshmen year and early sophomore year.
  +
  ⚫
=== 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.
 
[[Category:Courses|^MATH^MATH]]
  
[[Category:Courses|^MATH^MATH]]
  +
<references />

Latest revision as of 14:13, 6 February 2022

MATH 2551 covers limits, differentiation, and integration of functions with more than one input and/or output. It is a requirement for engineering majors.

Topic List[edit | edit source]

  • 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
    • Integration 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

Class Structure[edit | edit source]

MATH 2551 is a core math class focused more on computation than pure theory. Typical problems can be quite lengthy, especially towards the end of the course.

Prerequisite Knowledge[edit | edit source]

Single Variable Calculus[edit | edit source]

Single variable 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[edit | edit source]

Although linear algebra 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.

Scheduling[edit | edit source]

MATH 2551 is required by most engineering and science majors. It is also a prerequisite itself for many classes required by engineering and science majors. Due to its prerequisites, MATH 2551 is generally taken sometime between late freshmen year and early sophomore year.

Equivalent Courses[edit | edit source]

  • 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.
Retrieved from "https://gt-student-wiki.org/mediawiki/index.php?title=MATH_2551&oldid=1697"