Calculus & Analysis [Archive] - Page 3

derivative of a complex function in terms of real and imaginary parts.
Derivative of an integration
Does the dirac delta function have a Laplace transform?
Relationship Between K-Cells and Intervals in Baby Rudin
Finding the derivative vs differentiating vs finding the differential of a fn/eqtn
Visualizing Vector Fields
Integrals over different domains
Proof that Every Compact Set is Bounded
Kronecker Delta and Dirac Delta
Chain rule explanation
are implicit and partial differentiations related?
Taylor Series/Newton Raphson Method question
a problem about integral
Analytic At Infinity?
Prelim problem: bizarre integral expression
approximate function
Do physicists know the Lebesgue integral?
Taylor Series/Newton Raphson Method question -Link Fixed
exponentials on TI-83
Optimization of a matrix with an objective function (for ML)
Proof that function exists
Question about simple analysis proof
fraction of integrals with different variables
Integration of function in a region
Geometric Meaning of a Vector Integral
Question about Taylor series and implicit function theorem.
Is that true ?
Differentiation Quesion
[Help]The proof of (a.c)b-(a.b)c=aX(bXc)?
Why is the unit square a 2-manifold?
del operator and divergence
Chain Rule and Multivariable Calculus Question
Question About Compact Sets
z-transform of a discrete convolution
Substitution in Laplace
Substitution changes limits of integration?
Lagrangian in Optimisation
first derivatives question
inverse Fourier transform and contour integral
Existence of meromorphic functions
Compactness and every infinite subset has a limit point
differentiable on interval implies monotonic on some neighborhood of every point
How to find primitive function?
Inverse Fourier Transformation of a Fourier Transformation
Integration with respect to the counting measure
Chain rule violated for arc length?
Transforming a summation into an anlytical expression
Prove of the complicated integral
Strange proof of Young's inequality
When can one Change order of derivatives?
function in terms of its partial derivatives
Fourier Transform of Bessel Function of the 1st Kind
Calculus of variation
Double integral over triangle with known nodes
How to visualize a line integral
A very basic question about continuous function
Partial integration of the function f = 1
Easy delta/epsilon proof of a multivariable limit
Prove of summation claim ??
Partial Derivative
3space graphs on Mathematica 8
Question regarding iteration and operations
Extending Bounded metric spaces to compact spaces
calculus 3 introduction to cross product
Question about directional derivatives and tangent planes...?
Difficult Definite Integral Question
Rigorous definition of derivative
The differences between autocorrelation and convolution
Imagining polar transformation
Constrained Optimization via Lagrange Multipliers
Does the vector triple-product identity hold for operators?
Question about Proof of Inverse Function
the precise definition of limits
What is the limit of x^lnx as x approaches 0+?
tangents, velocities and other rates of change
Variation question
It seems strange?+x+x.....(x times)=x^2 then x=2x(differentiate wrt x)?
Applying the FTC to an arbitrary solution of the Schrodinger equation
Multiple integral notation (or abuse of?)
How to implement a Lauricella function
Some Questions about Papa Rudin (RCA) Chapter 1
Differentiable Automorphisms of ℂ
How to integrate -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) dt
Differentiation
Is integration theory supposed to be this hard?
% rsd
Partial derivative of function w.r.t. the percent change of the variable
what is the integral of cos^3(x)tan^4(x)?
Converting infinite series into an integral - intuition
repeated applications of sinusoidal functions
Integration by Parts help
How to show integral identity involving gaussian over x
establishing inflection point
Supremum of function
Convex set and convex functions
Sobolev type norms and basis functions
Diverging Integral
Generating the Borel (sigma-)Algebra
Calculating <cos^2(theta)>
Confusion over line integrals, Green's Theoreom, Conservative fields
Limit of the greatest integer number
derivative of function = square of the function?
Expanding partial derivatives
Plotting 3D Vertical Planes
Regularity condition
Complex integral
epsilon-delta in problem solving
Contour integral with absolute value
diffrenetiating cos(yz^2)
I think this is a dominated convergence theorem question
Understanding Riemann Zeta functions for s=1/3
kinetic energy term in delta potential
(Deceptively?) Simple question about Taylor series expansions
Question about "del"
Recursive integral using integration by pars
Singularities classification in DE's
Velocity on the surface of a sphere
2D plot of a function WITH MATLAB
P(cos(x)^3)/(x^6+1) very hard
on nascent delta 'function'
Complex analysis question: can't find similar question on internet
Need keep in solove a system of differential equation
Arbitrary vector intersect sphere
Schwartz Distributions in N variables?
Integration of O() terms of the Taylor series
Is it possible to obtain identical results from cont. and discrete Fourier transform?
Proof: Norms converge imply Coordinates converge
Vectors differentiation formulas for Dot and Box Product! how?
Looking for an analytic mapping theorem
distance between two parallel planes
I need to find the gradient of this norm
Existence of a function vs being well-defined?
Integral involving power , exp and exp(power)
Multivariate Calculus Text Recommendation
Basic calculus notation help.
Using IFT to find inverse.
Finding the function from an indeterminate form.
Finding the function from an indeterminate form.
Laplacian Operator
A book for Intuitive understanding of Calculus
dx>0 or dx<0 ??
Integral of double exponential matrices
Can you have a formula for every degree of polynomial?
fourier series & orthogonality
Confusing variable change calculation...
Question about complex analysis
Understanding the Integral
Question about Fubini's Theorem
Indefinitte Integral of Vector Valued Function
Kepler's First Law of Planetary Motion
Is this valid?
solve linear equations using simplex method
hankel transform of (dirac delta)/k and of 1
gradient of r
Involving Landau's 'big oh' notation
Implicit function Theorem
Integration of functions mapping into a vector space
Integration of Composite Functions.
Why do you Tack on The Negative For this Integral
Can u-substitution be described as a Jacobian?
trying to find the quotient of infinite sums
Trying to find integral using laplace method
Proof of Definite Integral??
calculate this sum
The dual nature of Nabla ?
Derivative of a vector function
Trigonometric Substitution
Multivariable confluence hypergeometric function
integration problem
Find dy/dx of x^2 − (y^2) x = (3x − 3)y
Average Value of a Function
When to use shells, when to use disks?
Proof - Legendre polynomials
Lp weak convergence
Lim of An=(n+1)^(1/3) - n^(1/3)
@what pt. does y=e^(32x) have max curvature?
Confusion in understanding Taylors theorem.
derivative of an integral...
Lim of An=n^2*exp(-sqrt(n))
Derivation of least squares containing vectors
Inner product-preserving map that isn't unitary?
Alt. approach to Taylor series of derivative of arcsin(x)?
Differentiating with respect to a constant
When exactly does the tabular method for integration by parts fail?
Riemann zeta function - one identity
contradiction of statement regarding monotonicity
Reduction formulas for integral of sin and cos
finding a monotone function in a weakly open ball
elliptic integral
Partial Fraction Decomp with a constant
integral of a vector valued function
Whats the method for determining if a functional has a local or global extremum
zeta function the the orime counting function
Uniqueness of Limits of Sequences
continuous and differentiable function
Integration of f(dx)
triangle integral ∫∫dxdyf(x*y) how to reduce to one dimension?
cylindrical coordinates
Calculate angle of attack
Tricky Complex Series
Sum of infs?
Functional Analysis: Open normed subspace
Integral x^2(1-x^2)
The limit of an "almost uniformly Cauchy" sequence of measurable functions
Equivalence of Completeness Properties
Convergence in Galilean space-time
connectivity
Epsilon Delta Limit.
Finding the dimensions of a rectangular box
Center of circle from two points and a tangent angle
Complex Radius of Convergence (without limsup formula)
About the chain rule.. what's wrong with me?
Prove that a normed space is not Banach
Can some one give me a proof for this
line integral of a scalar field
Computing integrals on the half line
integrate mixture of multivariate normal distributions
Is this solution right or not ??? Need yr backing
Continuous functions
Partial Derivatives of Vectors and Gradients
analytic continuation of an integral involving the mittag-leffler function
Closed Curves on the Riemann Sphere
mathematica partial differentiation weirdness
Can anyone construct a 3-variable function with this property?
Substitution Method on indefinite integral
Expanding in powers of 1/z (Laurent series)
2 particles in a 3d corkscrew over surface of a sphere
how to evaluate this limit
Second derivative
Definite integrals with -infinity low bound
Advice on data fitting
Visualizing integration
Total variation
Why z^(-1/2) cannot be expanded in Laurent series with center z=0?
Separating Variables in Integration
Integration of functions of Complex Variables
Gradient WRT a point.
Is 1/x ~ 0?
Question about tables in mathematica
Writing shear and moment equations for a simple beam problem?
Young functions
Contour integral of dz/(z-w)^n
Help with 1 step in proof of d/dx sin x = cos x
Small proof on monotonic functions
Why is integral of 1/z over unit circle not zero?
Can the existence of nonstandard hyperreal extensions be proved?
Parametrize y = sin(x) with i^ j^ components
wikiversity: The necessities in DSP
Gradient vs. Directional Derivative
Using u-sub for inetgral(x^4sinxdx)
Need some advice regarding apostol calculus volume 1
min eigenvalue of a perturbed matrix
Integration by substitution (and esp. Weierstrass' substitution)
Extrema in Several Variables: A different way?
Rolles Theorem, showing two distinct points.
Finding the limit of a recurrence equation.
Any formulas for arctan(a/b)?
Lebesgue outer measure
Fourier Transform of a discrete function
Limit involving dirac delta distributions
Find upper limit of improper integral -- Numerical Integration
Is there someway to find the exact area of a blob using integrals?
partial derivative of a single variable function
convexity and continuity
What is the topic full of inequalities of 1/(n+1) and integrals?
Helly's theorem and piecewise constant function
What type of expansion is this?
Any good resources that help you practice setting up an integral from scratch?
A double integral
solution of exp(lambda)*Gamma(0,lambda)
A way to count the uncountable Cantor Set.
Gaussian integral trouble
Improper integral of odd integrand
Can anyone help me with this integral problem?
Base-b expansion of a number?
Using L'hopital's rule in exponential function
Need help evaulating a few limits
Need help with a proof on closure
Equation re-arrangement
question about derivative definition
How to tell if U(n) is cyclic?
Extending radius of convergence by analytic continuation
Why is there a dx/dx in the Implicit Differentiation rule?
a very intriguing integral
Quick math question!
evalution of a complex integral
fourier transformation
Help me to clear my confusion, this is regarding nth derivative of e^ax cos(bx+c)
A question on the paragraph before 7.23 of Rudin's Real and complex analysis
converges sequence dual element
Drawing curves in Spherical coordinate
W. W. Hansen's Trick to Evaluating Integrals
Subtraction of Power Series
I'm confused about the consistency of partial derivatives
Problem on limits from chemistry
what is meaning of pai decimal expansion
Integrating a Laurent Series
Clarification on Jacobians please
what is the derivation of fokker planck equation?
Euler-Lagrange as a Sparse matrix
Help with Spivak's treatment of epsilon-N sequence definition...
The "importance" of Limits
Interactive Query and Analysis Computation
Good App for Calculus
Study Strategy for Baby Rudin
path dependent function with a defined path
relationship between differential and the operator
Cross Product Proof #1
Is every empty set function continuous?
Calculate Ellipse based on 4 points
Cauchy Sequences
Help me simplify this
Direct Proof
Time for Gravity to force two objects in a vacuum together
Holomorphic Maps on D(0,1)
Supremum and Infimum
Gradient Confusion
vector calculus velocity question
Mittag-Leffler(Arfken)
Secant line in Fermat's Theorem
Simplex method - algebraic form or tabular form
Need Recommendation(s) for Calc Book(s)
complex analysis
Help me im stuck at this Laplace transform..
Integral help
Help Understanding Stewart Chain Rule Proof [Picture Provided]
complex analysis/linear fractional transformation
Variational Calc boundary question
filling a tank flow rate problem
Is math valid in step 5 of Simple Derivation of the Lorentz Transformation
Gaussianity of solution to stochastic differential equations (SDE)
Surface integral problem from H.M. Schey's book
complex analysis
stability of a FEM solution to NS equations
Help with integral
Surface Integral, flux. Boundary and orientation
new proof of rolles theorom
Help with problem about triple integral
The major problem of 5.1 Definition in Baby Rudin
norms in sequence spaces.
Proof for part 2 of fundamental theorem of calculus
Why is Harmonic Series Convergent
derivative wrt one variable of an integral wrt another
Complex anaylsis, winding number question.
definite integral help
Function must be a bijection for its inverse to exist?
The area under a discontinuous & integrable function
Complex function general form
Left Inverse vs Right Inverse
Scale Factors and Jacobians
Sequence of complex numbers
about least upper bound and ordered set
Parametric definition for a complex integral
Interpretation of "dx" as the differential of x for Indefinite Integrals
integration constant question
Derivative as a Fraction
on the integration by parts infinitely many times
Scalar function satisfying div f=F
Nonsensical (lack of) relation between area and arc-length of polar curves
If replace the (1-x) by (a-x) in the Beta integral what the result will be?
MVDT Proof in economics
Question about one part of the Ratio Test proof
Roots and Weights in Lie algebras
Conversion of equation which preserves motion
About definition of 'Bounded above' and 'Least Upper Bound Property'
Help! Exam in one hour! Find equation of plane?
xyxx
Antiderrivative of e^(-x)*sin(x)*x^n
Real integrals with complex coefficients
An Infinite Product of (1+n^-2)
question from reading Div Grad Curl and All That
Meromorphic Functions on Riemann surfaces
#Upper bounds of a given set
complex identity
Integral of a function
integration and differentiation
proof of a theorem (y^n=x)
laplacian positive and subharmonic
Convergent sequence property and proving divergence
An Interesting Limit.
Basic calculus question
GPS, irregular area under graph project
Line integral - term
linear fractional transformation
Discretizing an integral
show the function doesnt exist
Comparison theorem.
Quick question about dense sets
Quick Linear Integration Question
Rouche's theorem
Does the following have a solution?
Conformal mapping between two half space
Ohda!: Definition of Order in Baby Rudin
Fourier Series and the first term
Definition of the residual spectrum
Meaning of (A dot nabla)B
Can L’hospital rule work for finding limits of complex functions
How to control a graph of f(x) = y
Basic limit question ( f(x) = x^2 )
Improper Integration
Need guidance on where to start on the study of the variational principle
Estimating Error in a Quadrature
Polynomial/Integration question?
Why surface area of sphere differ when find in two ways using the same approximation?
line integral
A new Method of Differentiation (PURE ALGEBRA), what do you think?
what is the trigonometric identity used to simplify this expression?
Generalized geometric series
Convergence of complex log series on the boundary
Is this proof (about limits) acceptable?
Some questions concerning asymptotic expansions of integrals
x not differentiable at x=0
3D splines, reference text
Sum of two closed sets are measurable
Sum of sets with positive measure contains interval
Nonelementary integral
Convex functions
Finding the volume of the cone using cylindrical polar coordinates?
difference between functional and function?
Total derivative of integral seen as a functional, how?
normal and exponential-normal (?) distribution
simple proof of uniform continuity
Integral using Euler's formula.
General function in two variables
function with f(0)=0,f'(0)=+inf,f(inf)=<1
help with chain rule
Level Sets and Degenerate Critical Points
Help with an integral
integration with sqrt in denominator
Doubt with a theorem that if f is cont. at interval it has max
convergence radius of a perturbation series
entire function
Laplace transform is holomorphic on half plane
biholomorphic mapping
Partial derivatives (question I am grading).
higher order differentials: dZ, d^2Z, d^3Z
derivation of imaginary exponential function
Derivative wrt Complex Conjugate
How to integrate this conundrum?
Integral of dx/(sqrt(d^2+x^2))
on a divergent integral
How to get fourier transform from fourier series
Napier's Constant Limit Definition
Directional Derivatives and Limits
Analogy for Curl with Torque: Correct?
separation of heat equation
Simple question about simple functions
Product of Diagonals of Regular Polygon?
he power series of arctan
Understanding what integrating in polar gives you
double modulus sign?
What's dt in finding normal vector for curvature
How is T the tangent to a vector
Parametric equation confusion of d2y/dx2
Finding the domain of integration in spherical coordinate of a shifted cylinder
Exponential Growth and Logarithmic Growth
Limits/continuity - finding largest delta
find a formula for a higher degree antiderivative
Fourier series
Using the limit comparison test
Determining Convergence of ((sin(n))^4)/(1+n^2)
Proving convergence of 1/log(n)
Congruence as explained by Apostol in Calculus Volume 1.
Gradient Flow - Definition and Sources
Fourier transform in higher dimensions
Continuity and Compactness
Unbounded Sequences w.r Divergence
Implicit differentiation - major confusion
Intuitively understanding div(curl F) = 0
Deriving the divergence in cylindrical coordinates using the Jacobian
Why can't holomorphic functions be extended to a closed disc?
Why use a Direction Vector?
Kline Calculus Problems - Simple Derivatives and Marginal Cost
numerical integration, use given random distribution as integration points
Orthogonal complement of gradient field?
curl of gradient
Discrete Fourier Transform of Even Function
limsup and bounded above
Major problem in differentiation from first principles
Steepest descent approximation
Analysis question about continuity and vanishing functions
how do you get to v=d/t?
Why can you cancel out the dx in u-substitution?
Iteration functions for Fixed Point method
a gamma integral
Root-finding Algorithm Question
Bessel Function FROM Kepler Equation?
fourier transform integration problem
iteration
Limits of integration for regions between polar curves
3d trajectory of system of wheels
Convergence in the L^2 norm
Splitting Infinite Series into Real and Imaginary Parts
How to define the domain of a 2-variable function as this?
Inverse of a Definite Integral or integral transform
Convergence/Divergence of a Series
Fourier series and Euclidean spaces
Fourier series on a general interval [a, a + T]
A hard integration.
Finite Integral, not sure why
Functional differentiability: Frechet, but not Hadamard?
Probability density function
Converting sums to integrals
Local minimum of z=(x^2+y^2)^(1/2)
Constrained gradient? (optimization theory)
Derivative at infinity on the Riemann sphere
How to find equations of two lines given a conic equation?
Total differential of general function mapping
Help understanding the First Fundamental Theorem of Calculus
A question regarding the order of a pole
constrained minimum problem
Setting up the correct limit for an area (double) integral
Different uses of the double integral?
Problems with Lagrange Multipliers
Continously differentiable f: R^n --> R^m not 1-1?
Help getting started with this integral
Oscillation of a point x in [c, d] <N => oscillation of subintervals of partition <N
summation
Length of Sine Curve
solving a transcendental equation
Riemann integrals and step functions
I'm trying to understand why e works this way
The polarization identity in Hilbert space
Operators and Dual Spaces
Paramaterizing a curve
Laplace transform of frequency differentiation
Interesting integral formula (please help)
wierd sum of squares compilation to a single vector norm
Clarification on the output of partial derivatives
solving or approximating a special class of fourier transforms
Finding the x-int
Partial Derivatives of Power Functions
Where is this function differentiable?
Half wave fourier series help !!!
Identity for the cross of a curl?
How do you integrate this?
How to undo or inverse a Curl?
Some expressions with Del (nabla) operator in spherical coordinates
Why does cantors theorem not prove the interval (0,1) in Q uncountable?
How to find the sum of this series
what is the exact definition of a function?
Physical Meaning of T's in Laplace equations
Error estimate
Calculating the final velocity?
sum of series with normal CDF
Differential Forms and Vector Calculus
Holder's inequality for integrals
Direct product between vectorspaces
Difficult Double Integrals
Limits in an area integral
Double Integral of exp(y)/y
Double integral of cos(x/y)
integral of spherical bessel function (first kind), first order
Trying to remember what Theorem this is.
How does this integral come out to be zero?
Difficulty in finding upper limit of x
Checking method and answer of Triple Integral
First and Second Derivatives
Using limits to find tangents
Approximating Areas Under Curves
Total Derivatives of fxns from R^n to R^m
Dimensions?
Spherical coordinates?
Triple Integral question
Parametrization question for my Intro. to Higher Math Class..
functional derivative
Difficulty to find this limit
Difference Between lim(n->inf.) n and Infinity
Numerical computation of double integral
The n body problem
Determining an Analytic Function from its Real Part
Taylor expansion for f(x,y) about (x0,y0) ?
Gauss theorem
Integrating the differential rate equation
Numerical Matrix Exponential
A question about differential equations
partial fraction
How to get Euler angles
contour integration: why is this integral non-zero
Question on Ring.....Help Please!
Question on functions
Just took calc 3 "semifinal"
Limit demonstration of sequence
Determining Tangent Slope w/Point Not On Curve
Help with a trig to sum identity.
Series expression
Area under a curve?
Formula involving double integral over a disc?
Laurent Series Convergence
Partial fraction decomposition with complex function
Laplace inversion
Spivak correction?
Back to basics II
Integrating Areas between curves
What method to use to calculate volume...
An odd trig identity, I WANT PROOF!
Manipulation of an analytic function
Converge series
A possible solution to the infinite summation of sin(x)
Directional Derivatives, Complex Variables and the exsistence of a complex derivative
Finding singularities
Do Alternating Series Have Limits?
Differentiability of composite functions
integral of an exponential that has a polynomial
A difficult integral with exp and erf squared
Finding if a point belongs to a line in space.
Limit proof on Sequence Convergence
Limit proof on monotonic sequences
Bilinear limit
Area and Volume integral using polar coordinates
log(z) : singularity, series and pole
Value of second derivative at a given point?
log expansion
Complex Fourier Series
Inverse of jacubian
Probelm in calculating a First Variation
Simple partial differential equation
Integral of xcos(xy) over a rectangle
Integrating the generator lines of an elliptical orbit
holomorphic function on the unit disc
double integral on one function of x and another of y
Alternating Series Question
Gauss theorem for tensors
Arc length and definite integral
Question about relation between powers and distance
Line/Curve Integral Question
Measure theory - Help
Noob Integral Question, Indeterminate form of ...?
Chinese integration shortcut?
Proofing the derivatives of e^x from the limit approach
I don't understand uniform continuity :(
Is my proof of this sequence's divergence good enough?
Derivative of a function with variable also in the integrand
Shortcut to taylor series of f, given taylor series of g
Degenerate Laurent Series
Naive regular perturbation
Integral help
Maxima minima of function of several variables...
Does Fourier series of x^2 converge?
Property of the dirac delta function
Surface of revolutions
quick chain rule q
Mean of vector field using info at surface
Complex Analysis Residue Query
Septim
Complex line integral
Find a function f such that f(xy)≠f(yx) at (0,0).
A little confusion over x and y values
derivative of transformation of basis in R^n
Help required for Directional derivatives
Proving gradient points in the direction of maximum increase
Help in evaluating the chain rule?
Problem on integrating dirac delta function
Would someone clarify this for me please? (from Rudin's analysis)
Divergence of the sum of the reciprocals of the primes
Integrating ln(x+1)/(x^2+1) using recursive integration by parts
What does [itex]\zeta(s)/s[/itex] converge to as [itex]\Im(s)\rightarrow\infty[/itex]
Finding a point in a plane.
Help in equation of a plane?
4 dimensional curl.
Polar Coordinates - Areas
Minimum distance of a point on a line from the origin?
Continuity in multi-variable calculus
Setting up a path for a line integral
Merging 2D bezier curves into a 3D one
help with a mellin-type integral
Does this method have a name? Function Approximation by Polynomial Sum
Lebesgue integral
Significance of parabola in a line integral?
Trouble with line integral
Using lagrange mutilpliers when lamda has two values
Fourier Transform of Ohno Potential
Examples of Measures in context of probability
Question on complex integration involving Bessel Function and essential Singularities
finding angle of rotation relating two vectors to a third
Quality of Widder's Advanced Calc. and Edwards's Adv. Calc. of Several Variables
Epsilon-delta definition of limit
condition for inflection point
f has a primitive on D ⊂ ℂ ⇒ ∫f = 0 along any closed curve in D?
Adjusted Cost Formula. Purpose of 0.5 power?
Trouble with the unit normal vector for stokes theorem
Product of Dense sets
Circumference of ellipse
Parameterizing z-value of Cylinder in Line Integral Projection (Using Stokes Theorem)
Applications of Green's theorem to physics
Derivative and Integral notation
Converting Trigonometric Ratios to Degree
Infinitely differentiable function
summation regarding ith roots
Symmetry and Nother's Theorem
Complex conjugate of a derivative wrt z
Analytic proof of the Lindemann - Weierstrass Theorem
Does this derivative have a name?
Indefinite integrals. Arriving at different results.
question about calculus and education
How is the tangent and area inverse?
Partial Vs. Complete differentials when dealing with non-independent variables
Infinitely differentiable functions
If a quantity is small, is the derivative of that quantity small?
Continuously smooth functions and Lp space
Delta Dirac Function
covariance of small angle quaternion
Indefinite integral. Different results depending upon what substitutions you use.
Integral of two-variable function
How to study mathematical analysis?