×

Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

by: Jack Pullman

48

1

3

Intro to Multivariable Calculus Test 1 Study Guide MATH 2204

Marketplace > Virginia Polytechnic Institute and State University > Math > MATH 2204 > Intro to Multivariable Calculus Test 1 Study Guide
Jack Pullman
Virginia Tech
GPA 4.0

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

These notes cover everything on the first test, from chapter 12, section 1 to chapter 14, section 4
COURSE
Introduction to Multivariable Calculus
PROF.
Peter Wapperom
TYPE
Study Guide
PAGES
3
WORDS
CONCEPTS
multivariable calculus, polar coordinates, three dimensional coordinate systems, vector calculus, dot product, cross product, partial derivatives, domains, range, linearization, Linear Approximations
KARMA
50 ?

Popular in Math

This 3 page Study Guide was uploaded by Jack Pullman on Wednesday September 21, 2016. The Study Guide belongs to MATH 2204 at Virginia Polytechnic Institute and State University taught by Peter Wapperom in Fall 2016. Since its upload, it has received 48 views. For similar materials see Introduction to Multivariable Calculus in Math at Virginia Polytechnic Institute and State University.

×

Reviews for Intro to Multivariable Calculus Test 1 Study Guide

×

×

What is Karma?

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/21/16
Intro to Multivariable Calculus Test 1 Study Guide Wednesday, September 21, 2016 9:39 AM • Basic single variable calculus ○ Differentiationof basic lines ○ Product, quotient, and chain rule ○ Equations for 2D lines  Lines:  Parabolas:  Hyperbolas:  Ellipses:  Trig functions:  Logarithmic functions: ○ Limits: • Chapter 12: Vectors and the Geometryof Space ○ 12.1: Three Dimensional Coordinate Systems  Coordinate axes: (x, y, z, etc….)  Points: (  Coordinate planes: xy planes, xz plane, yz plane  Projectionon coordinate plane: The shadow a vector would leave on a plane if a flashlight was shined over a vector at the plane  Surfaces: An equation in x, y, and z that relates them in three dimensions  Distance between points: d =  Equation of a sphere: ○ 12.2: Vectors  Definition of a vector:a line segment with a direction and length  Notation:  Scalar multiplication: c  Vector addition:  Vectors between 2 points:  Length of a vector:  Unit vector = vector with each componentdivided by vectorlength  Newton's 2nd law: F = ma; vector componentsof tension ○ 12.3: The Dot Product  Dot product definition:  Geometricinterpretation:  Angle and perpendicular vectors:when dot product is 0, angle is 90 degrees  Vector projection of b on a:  Scalar projection of b on a:  Work: ○ 12.4: The Cross Product  Geometricinterpretation:a vectororthogonal to the plane created by 2 given vectors  Area of a parallelogram:  Torque: ○ 12.5: Equations of Lines and Planes  Vector equation of a line  Parametricequation of a line:  Parametricequation of a line:  Parallel lines and parallel planes: if normal vectors are parallel, so are planes, if vectors are scalar multiples of each other, they are parallel  Intersection of a line and a plane: a point at subbing parametric equations into plane equation  Intersection of two planes: cross normal vectorsfor vector coefficientof t and add to point you found  Distance from point to plane: create a vector between desired point and a point on the plane, scalar projection of that vectoron the normal vector ○ 12.6: Cylinders and Quadric Surfaces  Sketching surfaces using cross sections: set one dimension to zero and treat as two dimensional to find the trace  Cylinders and quadric surfaces: □ Ellipsoid: □ Cone: □ Cylinder: □ Hyperboloid of one sheet: □ Hyperboloid if two sheets: □ Elliptic paraboloid: □ Hyperbolic paraboloid: • Chapter 14: Partial Derivatives ○ 14.1: Functions of Several Variables  Evaluating functions: several inputs, one output  Domain:all points where function is defined  Range: all possible outputs  Graphing: in three dimensions is a surface  Level curves: a curve along which ○ 14.2: Limits and Continuity  Two path test for nonexistence of a limit: If you can get two different values for Limit L as it approaches a point from different paths, the limit Does Not Exist  Limit exists: if you can't disprove it  Cancel commonfactors: to simplify such that limit is a real number  Polar coordinates:check for factors in terms of  Function is continuous if: ○ 14.3: Partial Derivatives  Notation of partial derivatives:  Computationof partial derivatives:like taking a normal derivative in single variable calculus, but treat variables other than the one in respect to as constants  Approximationof partial derivatives:  Mixed derivativetheorem:if f is sufficiently smooth,  Geometricinterpretation:plane made by two tangent lines to surface at a point with partials in x and y  Implicit differentiation:take partial derivative of both sides and solve when function is not defined in terms of variable dependent on variable in question ○ 14.4: Tangent Planes and Linear Approximation  Tangent planes:  Linearization:  Linear approximation:create linearization using easy values then plug in harder values Total differential:  Total differential:

×

50 Karma

×

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over \$500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Bentley McCaw University of Florida

Forbes

"Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

Refund Policy

STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com