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by: Braeden Lind

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# Calculus II MA 241

Braeden Lind
NCS
GPA 3.93

Allyson Alston

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COURSE
PROF.
Allyson Alston
TYPE
Study Guide
PAGES
6
WORDS
KARMA
50 ?

## Popular in Mathematics (M)

This 6 page Study Guide was uploaded by Braeden Lind on Thursday October 15, 2015. The Study Guide belongs to MA 241 at North Carolina State University taught by Allyson Alston in Fall. Since its upload, it has received 32 views. For similar materials see /class/223686/ma-241-north-carolina-state-university in Mathematics (M) at North Carolina State University.

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Date Created: 10/15/15
MA 241004 Fall 2006 Test 1 Study Guide General Info 0 Test Date Monday September 18 2006 0 Covers Chapter 5 Sections 110 excluding8 and Chapter 6 Sections 14 0 You are allowed to have a nongraphing nonprogrammable calculator however one is not required You will not be allowed to use your cell phones calculator Review the examples done in class on webassign and those on the review sheet Sections 5154 Review 0 Difference between indefinite and definite integral 0 Basic rules of integration 0 Approximate area ofa region using midpoints ofsubintervals o How to do position velocity and acceleration problems 0 Fundamental Theorem of Calculus m 0 When to use the substitution rule 0 Solve both definite and indefinite integrals usingthe substitution rule Section 56 0 When to use integration by parts 0 Solve both definite and indefinite integrals using integration by parts 0 Solve problems that require using integration by parts more than once andor require both 0 integration by parts and substitution Section 57 o How to use trigonometric identities o How to find indefinite integrals of trigfunctions using substitution 0 Trig Identities will be given Section 57 and Appendix G o KnowApply the steps for rewriting a rational function using partial fraction decomposition 0 Find the definite or indefinite integral of a rational function using partial fraction decomposition Section 59 o Midpoint Rule and how to apply it o Trapezoidal Rule and howto apply it o Simpson s Rule and how to apply it Section 510 0 Difference between convergent and divergent o How to evaluate Type L and Type 2 improper integrals o How to use the Comparison Theorem Section 61 0 Know the definition for finding the area between two curves 0 Be prepared to sketch the region by hand before calculating the area 0 Don t forget that some regions are best considered by in integrating in terms ofy Section 62 0 Know how to calculate the volume of a solid usingthe disk or washer method Your axis of revolution could be the xaxis the yaxis xc oryc Section 63 0 Know the formulas for arc length when given parametric equations or regular functions and how to use them Section 64 o How to calculate the average value of a function on a given integral MA 241004 Fall 2006 Test 2 Study Guide General Info 0 Test Date Monday October 9 2006 0 Covers Section 65 Sections 7173 0 You should have a nongraphing nonprogrammable calculator You will not be allowed to use your cell phones calculator Review the examples done in class on webassign and those on the review sheet Section 65 o How to set up and evaluate work problems involving a spring 0 Hooke s Law 0 Limits of Integration are distances from natural length 0 How to set up and evaluate work problems involving pumping water out of a tank 0 Find the moments and centers of mass ofa system 0 Find the center of mass of a plate Section 71 0 Understand definitions of differential equations order solution both general and particular initial value problem initial condition 0 Be able to identify constant solutions of a DE as well as verify a solution is a solution Section 72 0 Know what a directionslope field 0 Be able to sketch a direction field 0 Be able to identify various direction fields 0 Euler s Method know the equations involved Section 73 0 Know what it means to be a separable equation and how to solve 0 Know how to find a particular solution when given an initial condition 0 How to setup and evaluate mixing problems MA 241 005 Spring 2006 Test 3 Study Guide General Info Test Date Wednesday March 29 2006 Test 3 will cover Chapter 7 Sections 39 and Section 81 You are allowed to have a nongraphing nonprogrammable calculator however one will not be required You will not be allowed to use your cell phone s calculator Review the examples done in class on webassign and those on the review sheet Section 7 3 Separable Equations Determine if a DB can be solved using separation ofvariables Hint This is the only type of first order problem we did in class Solve a DB using separation ofvariables Make sure you include the arbitrary constant of integration at the right time and solve for the function if possible Solve an initial value DE using separation ofvariables Note that your solution will not have an arbitrary constant Section 7 4 Exponential Growth and Decay Know the natural growth or decay DE and general solution Know how to solve population growth radioactive decay and continuously compounded interest problems Find the halflife of a given substance Section 7 5 The Logistic Equation Know the form of the logistic differential equation and the solution to the logistic equation Section 7 7 Second Order Linear Equations Know the difference between homogeneous and nonhomogeneous linear equations Find the auxiliary or characteristic equation for a given secondorder linear DE with constant coefficienm Find the roots of the characteristic equation by factoring or the quadratic formula Know the 3 types of general solutions Find the particular solution for an initialvalueboundary value problem secondorder linear DE Section 7 8 V Linear Equations Solve a secondorder nonhomogeneous linear DE with constant coefficients using the method of undetermined coefficienm Know the possible functions Gx can be 0 Find the complementary solution 0 Find the particular solution 0 State the solution Section 7 9 quot 39 of SecondOrder Differential Fnuatinn Know the second order linear and homogeneous differential equation mx cx kx 0 where m is the mass of the spring 0 is the damping constant and k is the constant found using Hooke s law Be able to determine if overdamping critical damping or underdamping is produced for a given problem Section 81 Sequences Be able to list terms of a sequence Be able to determine if a sequence converges or diverges Know the limit laws for convergent sequences Know the limim of functions and thus the sequences Know when the sequence rn is convergent Be able to determine if a sequence is increasing decreasing and monotonic Be able to determine if a sequence is bounded Know and be able to apply the Monotonic Sequence Theorem MA 241005 Spring 2006 Test 1 Study Guide General Info Test Date Wednesday February 1 2006 Test 1 will cover Chapter 5 isections 13910 excluding 58 0 Most of the test will come from Sections 55510 excluding 58 You are allowed to have a nongraphing on39programmable calculator for this test You will not be allowed to use your cell phone s calculator Review the examples done in class on webassign and those on the review sheet Sections 5154 Review You should knowi 0 Difference between indefinite and definite integral 0 Basic rules of integration 0 Approximate area of a region using midpoints of subintervals o How to do position velocity and acceleration problems 0 Fundamental Theorem of Calculus Section 55 Review You should knowi 0 When to use the substitution rule 0 Solve both definite and indefinite integrals using the substitution rule Mm You should knowi 0 When to use integration by parts 0 Solve both definite and indefinite integrals using integration by parts 0 Solve problems that require using integration by parts more than once andor require both integration by parts and substitution Section 57 Review You should knowi o How to use trigonometric identities o How to find inde nite integrals of trig functions using substitution I Trig Identities will be given Section 57 and Appendix G Review You should knowi o KnowApply the steps for rewriting a rational function using partial fraction decomposition 0 Find the definite or indefinite integral of a rational function using partial fraction decomposition w You should knowi o Midpoint Rule and how to apply it o Trapezoidal Rule and how to apply it o Simpson s Rule and how to apply it Section 510 You should knowi 0 Difference between convergent and divergent o How to evaluate Type 1 and Type 2 improper integrals o How to use the Comparison Theorem MA 241005 Spring 2006 Test 3 Study Guide General Info 0 Test Date Monday February 27 2006 0 Test 2 will cover Chapter 6 7 Sections 15 and Chapter 7 7 Sections 1 amp 2 0 You are allowed to have a nongraphing nonprogrammable calculator however one will is not required You will not be allowed to use your cell phone s calculator Review the examples done in class on webassign and those on the review sheet Section 61 0 Know the de nition for nding the area between two curves 0 Be prepared to sketch the region by hand before calculating the area 0 Don t forget that some regions are best considered by in integrating in terms ofy Section 62 Know how to calculate the volume of a solid using the disk or washer method Your aXis of revolution could be the xaXis the yaXis xc or yc Section 63 0 Know the formulas for arc length when given parametric equations or regular functions and how to use them Section 64 0 How to calculate the average value of a function on a given integral Section 65 0 Be able to solve work problems especially problems dealing with spring and emptying a liquid out of a tank Section 71 0 Know general de nitions of the following you won t have to write the de nitions but you will need to know what they are when used in a sentence 0 Order 0 Equilibrium solution 0 General solution 0 Particular solution 0 Initial value problem Section 72 0 Direction Fields or Slope Fields 0 Given a directional eld plot a particular solution when provided initial conditions 0 Determine equilibrium solutions 0 Euler s Method 0 Know the formula and how to use it when given a rst order initial value problem 0 Approximate values for a solution using Euler s Method Review integration techniques from Chapter 5 you may have to use them for various integrals

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