whiffee / engineering_math_worked_problems_with_mathematica Goto Github PK

engineering_math_worked_problems_with_Mathematica

Exercises from the 10th and final edition of a popular engineering math text. A collection of 1364 mostly odd-numbered exercises. Worked at a mediocre skill level in Mathematica 10. Browse PDFs at the website link icon provided in the About panel, or download notebooks from branches.

The chapter contents:

CHAPTER 1 First-Order ODEs 1.1 Basic Concepts. Modeling 1.2 Geometric Meaning of ƒ'(x, y). Direction Fields, Euler’s Method 1.3 Separable ODEs. Modeling 1.4 Exact ODEs. Integrating Factors 1.5 Linear ODEs. Bernoulli Equation. Population Dynamics 1.6 Orthogonal Trajectories 1.7 Existence and Uniqueness of Solutions for Initial Value Problems

CHAPTER 2 Second-Order Linear ODEs 2.1 Homogeneous Linear ODEs of Second Order 2.2 Homogeneous Linear ODEs with Constant Coefficients 2.3 Differential Operators 2.4 Modeling of Free Oscillations of a Mass–Spring System 2.5 Euler–Cauchy Equations 2.6 Existence and Uniqueness of Solutions. Wronskian 2.7 Nonhomogeneous ODEs 2.8 Modeling- Forced Oscillations. Resonance 2.9 Modeling- Electric Circuits 2.10 Solution by Variation of Parameters

CHAPTER 3 Higher Order Linear ODEs 3.1 Homogeneous Linear ODEs 3.2 Homogeneous Linear ODEs with Constant Coefficients 3.3 Nonhomogeneous Linear ODEs

CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 4.1 Systems of ODEs as Models in Engineering Applications 4.3 Constant-Coefficient Systems. Phase Plane Method 4.4 Criteria for Critical Points. Stability 4.5 Qualitative Methods for Nonlinear Systems 4.6 Nonhomogeneous Linear Systems of ODEs

CHAPTER 5 Series Solutions of ODEs. Special Functions 5.1 Power Series Method 5.2 Legendre’s Equation. Legendre Polynomials Pn(x) 5.3 Extended Power Series Method- Frobenius Method 5.4 Bessel’s Equation. Bessel Functions Jv(x) 5.5 Bessel Functions of the Yv(x). General Solution

CHAPTER 6 Laplace Transforms 6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) 6.2 Transforms of Derivatives and Integrals. ODEs 6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting) 6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions 6.5 Convolution. Integral Equations 6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients 6.7 Systems of ODEs

CHAPTER 7 Linear Algebra-- Matrices, Vectors, Dets 7.1 Matrices, Vectors - Addition and Scalar Multiplication 7.2 Matrix Multiplication 7.3 Linear Systems of Equations. Gauss Elimination 7.4 Linear Independence. Rank of a Matrix. Vector Space 7.7 Determinants. Cramer’s Rule 7.8 Inverse of a Matrix. Gauss–Jordan Elimination 7.9 Vector Spaces, Inner Product Spaces. Linear Transformations

CHAPTER 8 Linear Algebra - Matrix Eigenvalue Problems 8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors 8.2 Some Applications of Eigenvalue Problems 8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices 8.4 Eigenbases. Diagonalization. Quadratic Forms 8.5 Complex Matrices and Forms

CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 9.1 Vectors in 2-Space and 3-Space 9.2 Inner Product (Dot Product) 9.3 Vector Product (Cross Product) 9.4 Vector and Scalar Functions and Their Fields. Vector Calculus- Derivatives 9.5 Curves. Arc Length. Curvature. Torsion 9.7 Gradient of a Scalar Field. Directional Derivative 9.8 Divergence of a Vector Field 9.9 Curl of a Vector Field

CHAPTER 10 Vector Integral Calculus. Integral Theorems 10.1 Line Integrals 10.2 Path Independence of Line Integrals 10.3 Calculus Review- Double Integrals. 10.4 Green’s Theorem in the Plane 10.5 Surfaces for Surface Integrals 10.6 Surface Integrals 10.7 Triple Integrals. Divergence Theorem of Gauss 10.8 Further Applications of the Divergence Theorem 10.9 Stokes’s Theorem

CHAPTER 11 Fourier Analysis 11.1 Fourier Series 11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions 11.3 Forced Oscillations 11.4 Approximation by Trigonometric Polynomials 11.5 Sturm–Liouville Problems. Orthogonal Functions 11.6 Orthogonal Series. Generalized Fourier Series 11.7 Fourier Integral 11.8 Fourier Cosine and Sine Transforms 11.9 Fourier Transform. Discrete and Fast Fourier Transforms

CHAPTER 12 Partial Differential Equations (PDEs) 12.1 Basic Concepts of PDEs 12.3 Solution by Separating Variables. Use of Fourier Series 12.4 D’Alembert’s Solution of the Wave Equation. Characteristics 12.6 Heat Equation- Sol'n by Fourier Series. Steady 2D Heat, Dirichlet Problems 12.7 Heat Equation- Modeling Long Bars. Sol'n by Fourier Integrals and Transforms 12.9 Rectangular Membrane. Double Fourier Series 12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series 12.11 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential 12.12 Solution of PDEs by Laplace Transforms

CHAPTER 13 Complex Numbers and Functions. Complex Differentiation 13.1 Complex Numbers and Their Geometric Representation 13.2 Polar Form of Complex Numbers. Powers and Roots 13.3 Derivative. Analytic Function 13.4 Cauchy–Riemann Equations. Laplace’s Equation 13.5 Exponential Function 13.6 Trigonometric and Hyperbolic Functions. Euler’s Formula 13.7 Logarithm. General Power. Principal Value

CHAPTER 14 Complex Integration 14.1 Line Integral in the Complex Plane 14.2 Cauchy’s Integral Theorem 14.3 Cauchy’s Integral Formula 14.4 Derivatives of Analytic Functions

CHAPTER 15 Power Series, Taylor Series 15.1 Sequences, Series, Convergence Tests 15.2 Power Series 15.3 Functions Given by Power Series 15.4 Taylor and Maclaurin Series 15.5 Uniform Convergence

CHAPTER 16 Laurent Series. Residue Integration 16.1 Laurent Series 16.2 Singularities and Zeros. Infinity 16.3 Residue Integration Method 16.4 Residue Integration of Real Integrals

CHAPTER 17 Conformal Mapping 17.1 Geometry of Analytic Functions- Conformal Mapping 17.2 Linear Fractional Transformations (Möbius Transformations) 17.3 Special Linear Fractional Transformations 17.4 Conformal Mapping by Other Functions 17.5 Riemann Surfaces

CHAPTER 18 Complex Analysis and Potential Theory 18.1 Electrostatic Fields 18.2 Use of Conformal Mapping. Modeling 18.3 Heat Problems 18.4 Fluid Flow 18.5 Poisson’s Integral Formula for Potentials 18.6 Harmonic Functions. Uniqueness for Dirichlet Problem

CHAPTER 19 Numerics in General 19.1 Introduction 19.2 Solution of Equations by Iteration 19.3 Interpolation 19.4 Spline Interpolation 19.5 Numeric Integration and Differentiation

CHAPTER 20 Numeric Linear Algebra 20.1 Linear Systems- Gauss Elimination 20.2 Linear Systems- LU-Factorization, Matrix Inversion 20.3 Linear Systems- Solution by Iteration 20.4 Linear Systems- Ill-Conditioning, Norms 20.5 Least Squares Method 20.7 Inclusion of Matrix Eigenvalues 20.8 Power Method for Eigenvalues 20.9 Tridiagonalization and QR-Factorization

CHAPTER 21 Numerics for ODEs and PDEs 21.1 Methods for First-Order ODEs 21.2 Multistep Methods 21.3 Methods for Systems and Higher Order ODEs 21.4 Methods for Elliptic PDEs 21.5 Neumann and Mixed Problems. Irregular Boundary 21.6 Methods for Parabolic PDEs 21.7 Method for Hyperbolic PDEs

CHAPTER 22 Linear Programming 22.1 Unconstrained Optimization. Method of Steepest Descent 22.2 Linear Programming 22.3 Simplex Method 22.4 Simplex Method -- Difficulties

CHAPTER 23 Graphs, Optimization 23.1 Graphs and Digraphs 23.2 Shortest Path Problems. Complexity 23.3 Bellman's Principle. Dijkstra's Algorithm 23.4 Shortest Spanning Trees -- Greedy Algorithm 23.5 Shortest Spanning Trees -- Prim's Algorithm 23.6 Flows in Networks 23.7 Maximum Flow -- Ford-Fulkerson Algorithm 23.8 Bipartite Graphs. Assignment Problems

CHAPTER 24 Probability, Statistics 24.1 Data Representation. Average. Spread 24.2 Experiments, Outcomes, Events 24.3 Probability 24.4 Permutations and Combinations 24.5 Random Variables. Probability Distributions 24.6 Mean and Variance of a Distribution 24.7 Binomial, Poisson, and Hypergeometric Distributions 24.8 Normal Distribution 24.9 Distributions of Several Random Variables

CHAPTER 25 Mathematical Statistics 25.2 Point Estimation of Parameters 25.3 Confidence Intervals 25.4 Testing Hypotheses. Decisions 25.5 Quality Control 25.6 Acceptance Sampling 25.7 Goodness of Fit. Chi-squared Test 25.8 Nonparametric Tests 25.9 Regression. Fitting Straight Lines. Correlation