Integrals Study guides, Class notes & Summaries
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MAT1512 Assignment 9 2021 (Oct/Nov 2020 exam)
- Other • 24 pages • 2021
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UNISA MAT1512 Calculus A Assignment NINE of 2021 solutions. October November 2020 past paper. 
Where possible, alternative methods are used. 
Topics covered: 
Limits at a finite point. 
Limits at plus/minus. 
Limits from the left/right hand side. 
Continuity. 
Curve sketching. 
Integrals. 
Integration. 
Simplify then integrate. 
u-substitution. 
Definite/indefinite integrals. 
Area in between curve. 
Initial value Ordinary differential equations. 
Differentiation. 
Derivatives. 
Derivative from ...
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COMPLETE - Elaborated Test Bank for Differential Equations-Theory,Technique and Practice 3Ed. by Steven G. Krantz.ALL Chapters (1-13)included with 133 pages of questions
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COMPLETE - Elaborated Test Bank for Differential Equations-Theory,Technique and Practice 3Ed. by Steven G. Krantz.ALL Chapters (1-13)included with 133 pages of questions. 
Differential Equations-Theory,Technique and Practice 3Ed. by Steven G. Krantz 
 
1. What Is a Differential Equation? 
1.1 Introductory Remarks 
1.2 A Taste of Ordinary Differential Equations 
1.3 The Nature of Solutions 
 
2. Solving First-Order Equations 
2.1 Separable Equations 
2.2 First-Order Linear Equations 
2.3 Exact E...
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Math 215: Final Exam 2024 with 100% correct answers
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what is the equation for finding the mass of a function on a line integral? correct answersm=∫a→b p[x(t),y(t),z(t)]∙[x'(t)²+y'(t)²+z'(t)²]^(1/2) dt 
 
how do you find moment about the x-axis correct answersMyz=∫a→b x∙p(x,y,z) ds 
 
NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. use t limits to solve 
 
how do you find moment about the y-axis correct answersMxz=∫a→b y∙p(x,y,z) ds 
 
NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. us...
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COMPLETE - Elaborated Test Bank for Differential Equations-Theory,Technique and Practice 3Ed. by Steven G. Krantz.ALL Chapters (1-13)included with 133 pages of questions
- Exam (elaborations) • 140 pages • 2023
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COMPLETE - Elaborated Test Bank for Differential Equations-Theory,Technique and Practice 3Ed. by Steven G. Krantz.ALL Chapters (1-13)included with 133 pages of questions. 
Differential Equations-Theory,Technique and Practice 3Ed. by Steven G. Krantz 
 
1. What Is a Differential Equation? 
1.1 Introductory Remarks 
1.2 A Taste of Ordinary Differential Equations 
1.3 The Nature of Solutions 
 
2. Solving First-Order Equations 
2.1 Separable Equations 
2.2 First-Order Linear Equations 
2.3 Exact E...
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Math 2024/2025-Introduction to Multivariable Calculus (Written by Dr. Hon-Ming HO). Lecture Notes 15: Double and Iterated Integrals over Rectangular Regions. 2024 UPDATE.
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Before we introduce double integration, let us recall the fact that for functions of a single variable, integration is the reverse process of differentiation. Also see examples below. 
Functions of a Single Real Variable 
 	Functions of Two Real Variables 	Functions of Two Real Variables 
 
 
differentiation. 
 
 
6)	where ≠ −1 . 
 
7)	One of the antiderivatives of 
	Thus we have 	. 
 
 
8)	The general form of antiderivativ denoted by 
 
where 	
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Department of Mathematics
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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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Student Solutions Manual for Mathematical Methods for Physics and Engineering
- Exam (elaborations) • 546 pages • 2024
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Preface page ix 
1 Preliminary algebra 1 
2 Preliminary calculus 17 
3 Complex numbers and hyperbolic functions 39 
4 Series and limits 55 
5 Partial differentiation 71 
6 Multiple integrals 90 
7 Vector algebra 104 
8 Matrices and vector spaces 119 
9 Normal modes 145 
10 Vector calculus 156 
11 Line, surface and volume integrals 176 
v 
CONTENTS 
12 Fourier series 193 
13 Integral transforms 211 
14 First-order ODEs 228 
15 Higher-order ODEs 246 
16 Series solutions of ODEs 269 
17 Eigenfuncti...
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70 Solved Integrals
- Exam (elaborations) • 34 pages • 2022
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70 Solved Integrals
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AP CALCULUS REVIEW
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AP CALCULUS REVIEW FOR 2017/18.
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Elliptic Curves - P. Stevenhagen, Leiden University 2008
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Elliptic Curves 
P. Stevenhagen, Leiden University 2008 
 
1. Elliptic integrals 
2. Elliptic functions 
3. Complex elliptic curves
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