Path integrals Study guides, Class notes & Summaries
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MAT2615 EXAM PACK 2023
- Exam (elaborations) • 108 pages • 2023
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INTRODUCTION 
Dear Student 
Welcome to MAT2615. We trust that you will find the mathematics studied in this module interesting 
and useful, and that you will enjoy doing it. 
THIS TUTORIAL LETTER CONTAINS INFORMATION TO FACILITATE YOUR STUDIES. PLEASE 
READ IT CAREFULLY AND KEEP IT FOR FUTURE REFERENCE. 
The delivery mode for this module is “blended”, which means that only some study material will be 
printed and posted to you. All study material which may include additional material will be...
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CALCULUS FINAL EXAM QUESTIONS WITH VERIFIED ANSWERS
- Exam (elaborations) • 10 pages • 2024
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evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 
 
consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 
 
find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - ANSWER-26/3 J 
 
an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...
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CALCULUS FINAL EXAM QUESTIONS WITH VERIFIED ANSWERS
- Exam (elaborations) • 4 pages • 2024
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evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 
 
consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 
 
find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - ANSWER-26/3 J 
 
an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...
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CALCULUS AND ITS APPLICATIONS 10TH EDITION BY Marvin L.Bittinger Indiana University Purdue University Indianapolis, David J.Ellenbogen Community College of Vermont and Scott A.Surgent Arizona State University
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Contents 
Preface vii 
Prerequisite Skills 
Diagnostic Test xix 
CHAPTER R 
Functions, Graphs, and Models 1 
R.1 Graphs and Equations 2 
R.2 Functions and Models 13 
R.3 Finding Domain and Range 24 
R.4 Slope and Linear Functions 33 
R.5 Nonlinear Functions and Models 50 
R.6 Mathematical Modeling and Curve Fitting 68 
Chapter Summary 79 
Chapter Review Exercises 85 
Chapter Test 88 
Extended Technology Application 
Average Price of a Movie Ticket 90 
CHAPTER 1 
Differentiation 93 
1.1 Limits: A...
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Advanced engineering Mathematics
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1.	Definition of the Com- plex Line integral 2.	Complex line integral sum form 3.	What is the line inte- gral of f(z) over the curve C by limit form? 4.	What is the line inte- gral of f(z) over the curve C by integral form? 5.	What is the meaning of complex line in- tegrals consist of fi- nitely many smooth curves? 6.	Three basic proper- ties of complex inte- gration 7.	What is linearity of in- tegration? 8.	What is sense rever- sal property? 1 . C has to be a smooth curve and f(z) h...
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Lecture notes Mathematics II (MATH2011A) - Calculus_Chapter_4
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This document clearly describes, with detailed notes and examples, how to evaluate/solve the following: 
~ Path Integrals in Scalar Fields 
~ Path Integrals in Vector Fields 
~ Double and Repeated Integrals 
~ Enclosed Volumes 
~ Change of variables in Double Integrals 
~ Green's Theorem - Corollary 1 
as taught by the University of Witwatersrand 
 
As a student, I am always searching for a great set of notes that I can rely on to ensure that I can achieve the best of my abilities. With this c...
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Exam (elaborations) TEST BANK FOR Functions of One Complex Variable I By Andreas Kleefeld
- Exam (elaborations) • 166 pages • 2021
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Exam (elaborations) TEST BANK FOR Functions of One Complex Variable I By Andreas Kleefeld 
Solutions Manual for 
Functions of One Complex Variable I, Second Edition1 
© Copyright by Andreas Kleefeld, 2009 
All Rights Reserved2 
1by John B. Conway 
2Last updated on January, 7th 2013 
Contents 
1 The Complex Number System 1 
1.1 The real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 
1.2 The field of complex numbers . . . . . . . . . . . . . . . . . . . ...
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CALCULUS FINAL EXAM fully solved & updated
- Exam (elaborations) • 17 pages • 2024
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evaluate the integral 2/1, ln(x)/x dx - answer-(ln2)^2/2 
 
consider the function f(x)=x^4-4x^3. which of the following is NOT true - answer-f has a local extrema at x=0 and x=3 
 
find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - answer-26/3 J 
 
an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...
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Exam (elaborations) TEST BANK FOR An Introduction to Modern Astrophysics By Carroll B.W. and Ostlie D.A. (Solution manual)
- Exam (elaborations) • 226 pages • 2021
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Exam (elaborations) TEST BANK FOR An Introduction to Modern Astrophysics By Carroll B.W. and Ostlie D.A. (Solution manual) 
CHAPTER 1 
The Celestial Sphere 
1.1 From Fig. 1.7, Earth makes S=P˚ orbits about the Sun during the time required for another planet to make 
S=P orbits. If that other planet is a superior planet then Earth must make one extra trip around the Sun to 
overtake it, hence 
S 
P˚ 
D S 
P 
C 1: 
Similarly, for an inferior planet, that planet must make the extra trip, or 
S 
...
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Numerical_Analysis_By_Richard_L._Burden.pdf
- Exam (elaborations) • 850 pages • 2022
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x Preface 
reasonable prices for most common computer systems. Although there are significant dif- 
ferences among the packages, both in perfolillance and price, all can perfOIm standard 
algebra and calculus operations. Having a symbolic computation package available can be 
very useful in the study of approximation techniques. The results in most of our examples 
and exercises have been generated using problems for which exact values can be deter- 
mined, since this penllits the perfonnance of...
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