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# Class Notes for Mathematics at Northeastern University

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##### MATH 1231 Lecture 31: Average of Function and Rate of Change 24HRPremium

MATH 1231 Lecture 31 Average of Function and Rate of Change Example 1: Determine the average value of each of the following functions on the given interval. (a)

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture 36: Review and Quiz 24HRPremium

MATH 1231 Lecture 36 : Review and Quiz Important sums for the quiz: Question: b dx f(x) dx f(b) f(a) d= a Solution: 55 dx ln(x) ln(x)dxd+5= d+5 22 = n(x)l+5 ln(5) ln(2)= +5 +5 = n107l Question: x ddx (t) dt f(x)f= a Soluti...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture 30: Review and Quiz 24HRPremium

MATH 1231 Lecture 30 Review and Quiz Please note the below important problems for the quiz: Question 1: b dx f(x) dx f(b) f(a) d= a Solution: 55 dx ln(x) ln(x)dxd+5= d+5 22 = n (x)l+5 ln (5) ln (2)= +5 +5 = n 107l Question...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 28: Presentation Of A Group 24HRPremium

MATH 1231 Lecture 28 Fundamental Theorem of Calculus The quiz corrected papers were distributed. There was also a group presentation on the final project by the students for 20 minutes. Point 1: If we have the following Th...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture 27: Review and Quiz 24HRPremium

MATH 1231 Lecture 27 Review and Quiz There was a brief review on the formulas discussed so far on the Intervals estimation. List of Anti derivatives The Fundamental Theorem of Calculus states the relation between differen...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture 26: Intervals continued 24HRPremium

MATH 1231 Lecture 26 Intervals continued Approximating Definite Integrals Not all integrals can be computed. A perfect example is the following definite integral. We now need to talk a little bit about estimating values ...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture 25: Interval Estimation continued 24HRPremium

MATH 1231 Lecture 25 Interval Estimation continued 2 Let a function , f(x) = 10 x X belongs to a set of numbers between 0 and 2 inclusive. X [0,2] Let the following be the points: L(Left point) R (Right Point)M(Middle P...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture 24: Region Area Estimate by Counting 24HRPremium

MATH 1231 Lecture 24 Region Area Estimate by Counting Area of a rectangle is length X breadth. 2 If we consider it to be in general it is X 2 So we take a graph Y= X So we have a kind of triangle but the diagonal is not st...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 23: Umber, Product Rule 24HRPremium

MATH 1231 Lecture 23 Integrals Continued. Formulae Recapitulation: f(x) dx g(x) C= + Here the derivative, g(x) = function, f(x) x ( ) dx lnx c1= + e x dx xc=e+ x 2 dx x 33 c= + New Formulae: ln x dx xlnx x c= + Here ln(x) ...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 22: Differentiable Function, Antiderivative 24HRPremium

MATH 1231 Lecture 22 Anti Derivative or Integral Definition: In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative i...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 21: Ope 24HRPremium

MATH 1231 Lecture 21 Functions Flow Continued Concave upward is when the slope increases. Concave downward is when the slope decreases. Usually our task is to find where a curve is concave upward or concave downward:

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 19: Inflection, Inflection Point, Product Rule 24HRPremium

MATH 1231 Lecture 19 Understanding Functions Flow On Derivative tests Few Problems of the midterm were discussed: Problem 6: x^2 lnx We need to find the derivative of e t Let y be a function=e 2 So we have T=xlnx Dydx = ...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 18: Second Derivative 24HRPremium

MATH 1231 Lecture 19 Mid Term Review Please note below the Structure of Mid Term: 4 multiple choice questions 5 points each 1 limit definition of derivative question 10 points 4 calculation of derivatives questions 5 ...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 17: Minimax 24HRPremium

MATH 1231 Lecture 17 Second Derivative Test Critical Point: y = f(x) No derivative f(x) = 0 Let x be a relative maxmin point of a function o Therefore: f(x) = 0 o 3 f(x) = x , x =0 (neither max nor min at this point) If f(...

Mathematics
MATH 1231
Ruoran Zhang
##### MATH 1231 Lecture Notes - Lecture 15: Marginal Cost, Farad, Junkers F.13 24HRPremium

MATH 1231 Lecture 15 Linearization for the function Linearization for the function f at x0: We are considering a static point x0 and another point x0+h on the Xaxis. Note that h is very small. P and P are very close as h i...

Mathematics
MATH 1231
Ruoran Zhang
##### Statistics - Reference Guides

This Guide provides an easy to follow summary of all basic principles that are the foundation to Statistics and Probabilities. Using a combination of charts and sample equations, the key concepts are developed and the esse...

Econometrics
ETC2430
All Professors
##### Calculus Derivatives - Reference Guides

This advanced Calculus Guide provides assistance to the user through its articulation of key Derivatives principles. Helpful tips to solve exponential and logarithmic functions are featured.

All Professors
##### Permachart - Marketing Reference Guide: Becquerel, Hyperbolic Function, International Standard Book Number

l e a r n • r e f e r e n c e • r e v i e w permacharts TM CCalculus Integrals II INTEGRALS INVOLVING a+bu & p+qu ...

All Professors
##### College Mathematics - Reference Guides

This comprehensive Guide provides concrete reference materials in three math fundamentals – Algebra, Calculus, and Trigonometry. Helpful sample equations and rules are the backbone to this Guide

All Professors
##### Permachart - Marketing Reference Guide: Inflection Point, Inflection, Farad

l e a r n • r e f e r e n c e • r e v i e w permacharts TM Differential Calculus Differential Calculus ...

All Professors
##### Permachart - Marketing Reference Guide: Iterated Integral, Centroid, Multiple Integral

permacht asrTM integral Calculus theorems types of iNtegrals averaGe value Theorem ...

All Professors
##### Laplace Transforms - Reference Guides

This useful Math Guide is a specific reference for techniques to convert ordinary differential equations to algebraic equations. Helpful charts and summaries are used to convey information such as exponential, square root,...

All Professors
##### Permachart - Marketing Reference Guide: Charge Pump, Diode, Electrolytic Capacitor

l e a r n • r e f e r e n c e • r e v i e w permacharts TM CConductors & Semiconductors BASICS TERMS Conductor Valence and conduction bands for electr...

Electrical Engineering
4400:307
All Professors
##### Permachart - Marketing Reference Guide: Steradian, Luminous Intensity, Si Base Unit

l e a r n • r e f e r e n c e • r e v i e w permacharts TM Metric System ...

Basic Engineering
BE 1101
All Professors
##### Intermediate Algebra - Reference Guides

This more advanced Guide builds upon the reference material set out in the Introductory Algebra Guide. Linear equations, polynomial equations and complex numbers are readily explained; clear and easy to follow emphasis is ...

MATH
MATH 504
All Professors
##### Introductory Algebra - Reference Guides

This Guide provides a concise and very readable summary of all key Algebraic principles. Special attention is directed to terminology, laws, and operations, with practical examples developed as illustration of these princi...

MATH
MATH 504
All Professors
##### Permachart - Marketing Reference Guide: Circumscribed Circle, Trapezoidal Rule, Quadrilateral

permacharts TM Geometry Geometry QUADRILATERALS CIRCLES & CONICS...

MATH
MATH 501
All Professors
##### Permachart - Marketing Reference Guide: Cubic Yard, Nautical Mile, Fluid Ounce

l e a r n • r e f e r e n c e • r e v i e w permacharts TM Weights & Measures THE U.S./IMPERIAL SYSTEM OF MEASUREMENTS ...

Physics
PHYS 24300
All Professors
##### Vectors & Matrices - Reference Guides

Vectors are an important area of study that develops naturally from a basic understanding of physics and is subsets – statics, dynamics, and mechanics. This practical Guide provides assistance in an often complex disciplin...

Physics
PHYS 24300
All Professors
##### Permachart - Marketing Reference Guide: Luminous Flux, Magnetic Flux, Magnetic Flux Quantum

permacharts TM F u n d a m e n t a lP h y s ic a lC o n s t a n t s General Constants Quantity...

Physics
PHYS 24300
All Professors
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