Multivariable calc Study guides, Class notes & Summaries
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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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Multivariable Calculus with Questions and Correct Answers
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how do you integrate cosx, sinx, and tanx - cos(x)=sin(x) 
sin(x)=-cos(x) 
tan(x)=ln(sec(x)) or -ln(cos(x)) 
how do you differentiate cosx, sinx and tanx - cos(x)=-sin(x) 
sin(x)=cos(x) 
tan(x)=sec^2(x) 
how do you differentiate cosh sinh and tanh - cosh(x)=sinh(x) 
sinh(x)=cosh(x) 
tanh(x)=sech^2(x) 
how do you integrate cosh sinh and tanh - cosh(x)=sinh(x) 
sinh(x)=cosh(x) 
tanh(x)=ln(cosh(x))
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Multivariable Calculus Notes: Partial Derivatives
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Lecture notes for MIT OpenCourseware's Math 18.02 taught by Prof. Denis Auroux. Includes vector math and partial derivatives.
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Multivariable Calculus Q&A
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Multivariable Calculus Q&A
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Multivariable Calculus with Questions and Correct Answers
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Vector Equation of the Line - 
Part Equation of the Line - 
Translation - 
Projection/Orthogonal of a Vector on Another One - 
Dot Product (The Purpose) - 
Cross Product (The Purpose/Properties) - 
Cosine Theorem (Proof) - 
Def. Plane (Four points belong to a same plane?) - Vector
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MATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICE
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MATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICEMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICEMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICE
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MATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICE
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vMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICEMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICEMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICE
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Multivariable Calculus (Questions with Detailed Solutions)
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Detailed written solutions to past exams for the Kings College London Calculus II module.
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Multivariable Calculus Notes: Differential and Integral Package
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Notes for MIT OpenCourseware's MATH 18.02 taught by Professor Denis Auroux including both differential and integral calculus.
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MATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICE
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MATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICEMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICEMATH 230 MIDTERM 1 MULTIVARIABLE DIFFERENTIAL CALCULUS OFFICIAL PRACTICE
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