 4.6.1: In 112, use the Laplace transform to solve the given system of diff...
 4.6.2: In 112, use the Laplace transform to solve the given system of diff...
 4.6.3: In 112, use the Laplace transform to solve the given system of diff...
 4.6.4: In 112, use the Laplace transform to solve the given system of diff...
 4.6.5: In 112, use the Laplace transform to solve the given system of diff...
 4.6.6: In 112, use the Laplace transform to solve the given system of diff...
 4.6.7: In 112, use the Laplace transform to solve the given system of diff...
 4.6.8: In 112, use the Laplace transform to solve the given system of diff...
 4.6.9: In 112, use the Laplace transform to solve the given system of diff...
 4.6.10: In 112, use the Laplace transform to solve the given system of diff...
 4.6.11: In 112, use the Laplace transform to solve the given system of diff...
 4.6.12: In 112, use the Laplace transform to solve the given system of diff...
 4.6.13: Solve system (1) when k1 3, k2 2, m1 1, m2 1 and x1(0) 0, x 1(0) 1,...
 4.6.14: Derive the system of differential equations describing the straight...
 4.6.15: (a) Show that the system of differential equations for the currents...
 4.6.16: (a) In in Exercises 2.9 you were asked to show that the currents i2...
 4.6.17: Solve the system given in (17) of Section 2.9 when R1 6 , R2 5 , L1...
 4.6.18: Solve (5) when E 60 V, L 1 2 h, R 50 , C 104 f, i1(0) 0, and i2(0) 0.
 4.6.19: Solve (5) when E 60 V, L 2 h, R 50 , C 104 f, i1(0) 0, and i2(0) 0....
 4.6.20: (a) Show that the system of differential equations for the charge o...
 4.6.21: Range of a ProjectileNo Air Resistance If you worked in Exercises 3...
 4.6.22: Range of a ProjectileWith Linear Air Resistance In The Paris Guns p...
 4.6.23: m d2 x dt 2 b dx dt m d2 y dt 2 mg 2 b dy dt, (11) where b 0 is a c...
Solutions for Chapter 4.6: Systems of Linear Differential Equations
Full solutions for Advanced Engineering Mathematics  6th Edition
ISBN: 9781284105902
Solutions for Chapter 4.6: Systems of Linear Differential Equations
Get Full SolutionsSince 23 problems in chapter 4.6: Systems of Linear Differential Equations have been answered, more than 36877 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 6. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781284105902. Chapter 4.6: Systems of Linear Differential Equations includes 23 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column space C (A) =
space of all combinations of the columns of A.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Iterative method.
A sequence of steps intended to approach the desired solution.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Outer product uv T
= column times row = rank one matrix.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).