Engineering Mathematics with Maple

Part 1 Introduction: goals; about MAPLE; basic algebra and calculus operations; two-dimensional graphics; three-dimensional graphics. Part 2 Vector Algebra: laboratory goals; building vectors; vector products; determining direction cosines; applications. Part 3 Manipulating discrete data: laboratory goals; arrays; reading lists of data; plotting multidimensional data. Part 4 Matrices: laboratory goals; products, transposes and inverses; powers, eigenvalues and eigenvectors; transition probabibilities; application to cryptography. Part 5 Linear and nonlinear equations: laboratory goals; linear equations; nonlinear equations; graphical and numerical solutions. Part 6 First-order ODEs: laboratory goals; first-order linear ODEs; homogeneous equations; special first-order equations. Part 7 Second-order constant-coefficient ODEs: laboratory goals; general solutions; using initial conditions; damped motion; forced motion. Part 8 Laplace transforms: laboratory goals; simple transforms; application to differential equations; a circuit analysis problem. Part 9 Systems of ODEs: laboratory goals; homogeneous linear systems; nonhomogeneous linear systems; chemical mixing. Part 10 Numerical solutions of ODEs: laboratory goals; second order equations; manipulating multiple solutions; systems of ODEs. Part 11 Variable coefficient ODEs: laboratory goals; Cauchy-Euler equations; other special equations; applications. Part 12 Fourier systems: laboratory goals; Fourier sine series; Fourier cosine series; Fourier series. Part 13 The heat equation: laboratory goals; one-dimensional solution; asymmetric initial temperature; displaying heat flow dynamical; discussion. Part 14 The vibrating bar: laboratory goals; vibrating car; separation of variables; the hinged-hinged bar; the hinged-clamped bar; examining many eigenvalues. Part 15 The vibrating annulus: laboratory goals; description of the annulus; separation of variables solution; determination of the eigenvalues; sketching the eigenmodes. Part 16 Approximating eigenvalues: laboratory goals; motivation; using difference equations; generating the coefficient matrix; application to vibrating string. Part 17 Vector differentiation: laboratory goals; other vector differentiation operators; establishing vector identities. Part 18 Vector functions of a single variable: laboratory goals; three-dimensional particle motion; the TNB coordinate system; curvature and torsion. Part 19 Vector integration: laboratory goals; the divergence theorem; Stoke's theorem. Part 20 Multi-variable optimization: laboratory goals; description of the trough; locating critical points; the second derivative test; discussion. Part 21 Visualizing fields: laboratory goals; gradient fields; divergence of a vector field. Part 22 Complex arithmetic: laboratory goals; manipulating complex numbers; complex functions. Part 23 Taylor and Laurent series: laboratory goals; Taylor series; Laurent series. (Part contents).