 Chapter 1.2: Heat Equation
 Chapter 1.3: Heat Equation
 Chapter 1.4: Heat Equation
 Chapter 1.5: Heat Equation
 Chapter 10.2: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 Chapter 10.3: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 Chapter 10.4: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 Chapter 10.5: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 Chapter 10.6: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 Chapter 10.7: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 Chapter 11.2: Greens Functions for Wave and Heat Equations
 Chapter 11.3: Greens Functions for Wave and Heat Equations
 Chapter 12.2: The Method of Characteristics for Linear and Quasilinear Wave Equations
 Chapter 12.3: The Method of Characteristics for Linear and Quasilinear Wave Equations
 Chapter 12.4: The Method of Characteristics for Linear and Quasilinear Wave Equations
 Chapter 12.5: The Method of Characteristics for Linear and Quasilinear Wave Equations
 Chapter 12.6: The Method of Characteristics for Linear and Quasilinear Wave Equations
 Chapter 12.7: The Method of Characteristics for Linear and Quasilinear Wave Equations
 Chapter 13.2: Laplace Transform Solution of Partial Differential Equations
 Chapter 13.3: Laplace Transform Solution of Partial Differential Equations
 Chapter 13.4: Laplace Transform Solution of Partial Differential Equations
 Chapter 13.5: Laplace Transform Solution of Partial Differential Equations
 Chapter 13.6: Laplace Transform Solution of Partial Differential Equations
 Chapter 13.7: Laplace Transform Solution of Partial Differential Equations
 Chapter 13.8: Laplace Transform Solution of Partial Differential Equations
 Chapter 14.1: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.2: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.3: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.4: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.5: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.6: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.7: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.8: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 14.9: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 Chapter 2.2: Method of Separation of Variables
 Chapter 2.3: Method of Separation of Variables
 Chapter 2.4: Method of Separation of Variables
 Chapter 2.5: Method of Separation of Variables
 Chapter 3.2: Fourier Series
 Chapter 3.3: Fourier Series
 Chapter 3.4: Fourier Series
 Chapter 3.5: Fourier Series
 Chapter 3.6: Fourier Series
 Chapter 4.2: Fourier Series
 Chapter 4.3: Fourier Series
 Chapter 4.4: Fourier Series
 Chapter 4.5: Fourier Series
 Chapter 4.6: Fourier Series
 Chapter 5.1: SturmLiouville Eigenvalue Problems
 Chapter 5.3: SturmLiouville Eigenvalue Problems
 Chapter 5.4: SturmLiouville Eigenvalue Problems
 Chapter 5.5: SturmLiouville Eigenvalue Problems
 Chapter 5.6: SturmLiouville Eigenvalue Problems
 Chapter 5.7: SturmLiouville Eigenvalue Problems
 Chapter 5.8: SturmLiouville Eigenvalue Problems
 Chapter 5.9: SturmLiouville Eigenvalue Problems
 Chapter 6.2: Finite Difference Numerical Methods for Partial Differential Equations
 Chapter 6.3: Finite Difference Numerical Methods for Partial Differential Equations
 Chapter 6.4: Finite Difference Numerical Methods for Partial Differential Equations
 Chapter 6.5: Finite Difference Numerical Methods for Partial Differential Equations
 Chapter 6.6: Finite Difference Numerical Methods for Partial Differential Equations
 Chapter 6.7: Finite Difference Numerical Methods for Partial Differential Equations
 Chapter 7.1: HigherDimensional Partial Differential Equations
 Chapter 7.2: HigherDimensional Partial Differential Equations
 Chapter 7.3: HigherDimensional Partial Differential Equations
 Chapter 7.4: HigherDimensional Partial Differential Equations
 Chapter 7.5: HigherDimensional Partial Differential Equations
 Chapter 7.6: HigherDimensional Partial Differential Equations
 Chapter 7.7: HigherDimensional Partial Differential Equations
 Chapter 7.8: HigherDimensional Partial Differential Equations
 Chapter 7.9: HigherDimensional Partial Differential Equations
 Chapter 8.2: Nonhomogeneous Problems
 Chapter 8.3: Nonhomogeneous Problems
 Chapter 8.4: Nonhomogeneous Problems
 Chapter 8.5: Nonhomogeneous Problems
 Chapter 8.6: Nonhomogeneous Problems
 Chapter 9.2: Greens Functions for TimeIndependent Problems
 Chapter 9.3: Greens Functions for TimeIndependent Problems
 Chapter 9.4: Greens Functions for TimeIndependent Problems
 Chapter 9.5: Greens Functions for TimeIndependent Problems
 Chapter 9.6: Greens Functions for TimeIndependent Problems
Applied Partial Differential Equations with Fourier Series and Boundary Value Problems 5th Edition  Solutions by Chapter
Full solutions for Applied Partial Differential Equations with Fourier Series and Boundary Value Problems  5th Edition
ISBN: 9780321797056
Applied Partial Differential Equations with Fourier Series and Boundary Value Problems  5th Edition  Solutions by Chapter
Get Full SolutionsThis expansive textbook survival guide covers the following chapters: 81. The full stepbystep solution to problem in Applied Partial Differential Equations with Fourier Series and Boundary Value Problems were answered by , our top Math solution expert on 01/25/18, 04:21PM. This textbook survival guide was created for the textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, edition: 5. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems was written by and is associated to the ISBN: 9780321797056. Since problems from 81 chapters in Applied Partial Differential Equations with Fourier Series and Boundary Value Problems have been answered, more than 6886 students have viewed full stepbystep answer.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Solvable system Ax = b.
The right side b is in the column space of A.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.