Cauchy theorem Study guides, Revision notes & Summaries
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Math 475: Partial Differential Equations
- Exam (elaborations) • 19 pages • 2023
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Math 475: Partial Differential Equations 
Shereen Elaidi 
Fall 2019 Term 
Contents 
1 Introduction 2 
1.1 Domains and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.1.1 What are the main boundary conditions? . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Classification of PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
2 Diffusion 4 
2.1 Derivation and Setting Up (n = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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AU MATH 376 STUDY GUIDE ORDINARY DIFFERENTIAL EQUATIONS NEW UPDATED SOLUTION FOR THE COMING 2022-2023 EXAM Athabasca University
- Exam (elaborations) • 263 pages • 2022
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AU MATH 376 STUDY GUIDE ORDINARY DIFFERENTIAL EQUATIONS NEW UPDATED SOLUTION FOR THE COMING 2022-2023 EXAM Athabasca University 
Contents 
Introduction	1 
Some Preliminary Remarks	2 
Part I: First-order Differential Equations	9 
1	Introducing Ordinary Differential Equations	11 
1.1	Solutions: Complete, General, Particular, Partial	12 
1.2	Methods for Solving Ordinary Differential Equations	14 
1.3	The Fundamental Theorem	15 
1.4	Direction Fields	18 
2	Directly Integrable Ordinary Differential 
...
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Department of Mathematics
- Exam (elaborations) • 13 pages • 2023
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Department of 
Mathematics 
Courses of Study: 
Minor 
Major (B.A.) 
Combined B.A./M.A 
Master of Arts 
Doctor of Philosophy 
Objectives 
Undergraduate Major 
As our society becomes more technological, it is more affected by 
mathematics. Quite sophisticated mathematics is now central to 
the natural sciences, to ecological issues, to economics, and to 
our commercial and technical life. A student who takes such 
general level courses as MATH 5, 8, 10, 15, or 20 will better 
understand the world ...
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Exam (elaborations) TEST BANK FOR Understanding Analysis 2nd Edition By Stephen Abbott (Instructors' Solution Manual)
- Exam (elaborations) • 156 pages • 2021
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1 The Real Numbers 1 
1.1 Discussion: The Irrationality of 
p 
2 . . . . . . . . . . . . . . . . . 1 
1.2 Some Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . 1 
1.3 The Axiom of Completeness . . . . . . . . . . . . . . . . . . . . . 6 
1.4 Consequences of Completeness . . . . . . . . . . . . . . . . . . . 8 
1.5 Cantor’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 14 
2 Sequences and Series 19 
2.1 Discussion: Rearrangements of Infinite Series . . . . . . . ....
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Orthogonality- Chapter 6 Exam with Solutions
- Exam (elaborations) • 3 pages • 2024
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What is the formula for computing the distance between these two points: (x1,y1), (x2,y2)? - √( (x1-x2)² + (y1-y2)² ) 
 
What is the formula of the length of vector X = [x,y,z]: denoted by |X|? - |X| = √( x² + y² + z² ) 
 
What is the formula for dot product of the following vectors: X = [x1, ..., xn] and Y = [y1, ..., yn]? (Definition 6.1) 
 
Dot product symbol we'll use: . - X.Y = x1*y1 + ... + xn*yn 
 
What is the formula for the law of cosines? - |X-Y|² = |X|² + |Y|² - 2|X||...
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TestBank for Introduction to Econometrics 3e Stock Watson SM completed Instructors Guide Completed for Exam preparation and Review
- Exam (elaborations) • 117 pages • 2022
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TestBank for Introduction to Econometrics 3e Stock Watson SM 
For Instructors 
Solutions to End-of-Chapter Exercises©2011 Pearson Education, Inc. Publishing as Addison Wesley 
Chapter 2 
Review of Probability 
2.1. (a) Probability distribution function for Y 
Outcome (number of heads) Y 0 Y 1 Y 2 
Probability 0.25 0.50 0.25 
(b) Cumulative probability distribution function for Y 
Outcome (number of heads) Y 0 0 Y 1 1 Y 2 Y 2 
Probability 0 0.25 0.75 1.0 
(c) ...
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Complete Statistics Summary
- Summary • 16 pages • 2023
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A complete summary of the weekly course material for statistics for econometrics students. The course is taught in the first year and this summary explains thoroughly what needs to be understood each week, including examples.
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Exam (elaborations) TEST BANK FOR Understanding Analysis 2nd Edition By Stephen Abbott (Instructors' Solution Manual)
- Exam (elaborations) • 156 pages • 2021
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Exam (elaborations) TEST BANK FOR Understanding Analysis 2nd Edition By Stephen Abbott (Instructors' Solution Manual) 
Contents 
Author’s note v 
1 The Real Numbers 1 
1.1 Discussion: The Irrationality of 
p 
2 . . . . . . . . . . . . . . . . . 1 
1.2 Some Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . 1 
1.3 The Axiom of Completeness . . . . . . . . . . . . . . . . . . . . . 6 
1.4 Consequences of Completeness . . . . . . . . . . . . . . . . . . . 8 
1.5 Cantor’s Theore...
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Sequences and series
- Summary • 10 pages • 2023
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Notes on sequences and series from book 'Understanding Analysis by Abott'. This includes topics like convergence of a sequence, infinite series, convergence of series, monotone convergence theorem, harmonic series, bolzano weistrass theorem,cauchy sequence, conditional convergence etc. It also contains tests like ratio test, p series test, abel's test, dirichlet's test, comparison test, alternating series test and more. There are many theorems included but the proof are not provided.
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Sequences
- Lecture notes • 3 pages • 2023
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Introduce sequences and its epsilon proof. Then explain sequences with the algebraic limit theorem and the order limit theorem. Write proof for the theorem that a sequence converges if and only if that sequence is a Cauchy sequence.
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