Chapter 1. Programming in MATLAB (Lecture notes download; MATLAB codes download) Texts: Gilat, MATLAB: An Introduction with Applications, 4th ed., Wiley; Moore, MATLAB for Engineers, 4th ed., Pearson
1.1. Basics of MATLAB
1.2. MATLAB variables and build-in functions
1.3. MATLAB script files
1.4. MATLAB arrays
1.5. MATLAB two-dimensional and three?dimensional plots
1.6. MATLAB used-defined functions
1.7. MATLAB relational operators, conditional statements, and selection structures I
1.8. MATLAB relational operators, conditional statements, and selection structures II
1.9. MATLAB loops
1.10. Summary
Chapter 2. Linear algebra (Lecture notes download; MATLAB codes download) Text: Gilat, MATLAB: An Introduction with Applications, 4th ed., Wiley
2.1. Systems of linear equations (SLEs). Matrix operations
2.2. Solutions of SLEs by the Gauss elimination
2.3. Two?dimensional arrays and operations with matrices in MATLAB
2.4. Determinant and matrix inverse
2.5. Solution of SLEs in MATLAB
2.6. Summary
Chapter 3. Numerical analysis I (Lecture notes download; MATLAB codes download) Text: Gilat, MATLAB: An Introduction with Applications, 4th ed., Wiley
3.1. Root finding: Bisection method
3.2. Root finding: Newton-Raphson method
3.3. Interpolation
3.4. Curve fitting: Least square method
3.5. Curve fitting in MATLAB
3.6. Summary
Chapter 4. Numerical analysis II (Lecture notes download; MATLAB codes download) Text: Gilat, MATLAB: An Introduction with Applications, 4th ed., Wiley
4.1. Numerical differentiation
4.2. Numerical integration
4.3. Ordinary differential equations (ODEs). First-order ODEs
4.4. Numerical methods for initial value problems (individual ODEs)
4.5. Second- and higher order ODEs. Systems of ODEs
4.6. Numerical methods for initial value problems (systems of ODEs)
4.7. Numerical solution of IVPs with build-in MATLAB solvers
4.8. Summary
Chapter 5. Engineering economics (Lecture notes download; MATLAB codes download) Text: White, Case, and Pratt, Principles of Engineering Economic Analysis, 5th ed., Wiley
5.1. Introduction
5.2. Time value of money
5.3. Planning horizon and minimum attractive rate of return
5.4. Present worth analysis
5.5. Summary
Chapter 1. First-order ordinary differential equations (Lecture notes download) Texts: Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, Chapter 1
1.1. Prerequisites. Formulation of engineering problems in terms of ODEs
1.2. Ordinary differential equations. Basic concepts
1.3. First-order ODEs. Initial value problem
1.4. Separable ODEs
1.5. Linear ODEs
1.6. Exact ODEs
1.7. ODEs that reduce to exact ODEs. Integrating factors
1.8. Relaxation and equilibrium
Chapter 2. Second-order ordinary differential equations (Lecture notes download) Texts: Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, Chapter 2
2.1. Second-order ODEs. Initial and boundary value problems
2.2. Second-order linear homogeneous ODEs
2.3. Second-order linear homogeneous ODEs with constant coefficients
2.4. Euler-Cauchy equations
2.5. Second-order linear nonhomogeneous ODEs. Method of undetermined coefficients
2.6. Second-order linear nonhomogeneous ODEs. Method of variation of parameters
2.7. Free oscillations in mechanical systems
2.8. Forced oscillations and resonance in mechanical systems
Chapter 3. ODEs of higher orders and systems of ODEs (Lecture notes download) Texts: Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, Chapters 3 and 4
3.1. Higher order ODEs and systems of ODEs. Basic concepts
3.2. Higher order linear ODEs
3.3. Autonomous systems of ODEs, their phase portraits, and stability
3.4. Prerequisites. Matrix eigenvalue problem
3.5. Phase portraits of two?dimensional systems of linear ODEs
3.6. Local analysis of non?linear systems. Linearization
3.7. Chaotic motion. Double pendulum
Chapter 4. Numerical methods for ODEs (Lecture notes download) Texts: Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, Chapter 21
4.1. Numerical methods for solution of IVP for ODEs. Basic concepts
4.2. Euler method
4.3. Convergence, approximation, and stability
4.4. Methods of higher orders of approximation
4.5. Runge-Kutta methods
4.6. Numerical solution of IVP for systems of ODEs
4.7. Explicit, implicit and predictor?corrector methods
4.8. Linear multistep methods (LMMs). Adams family of LMMs (optional)
Chapter 5. Fourier Analysis (Lecture notes download) Texts: Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, Chapter 11
5.1. Fourier analysis. Motivation: Analysis of complex periodic and non-smooth functions
5.2. Periodic functions. Basic trigonometric function. Trigonometric sum and series
5.3. Orthogonal system of functions. Trigonometric system of functions
5.4. Fourier and generalized Fourier series
5.5. Fourier expansions for functions satisfying the Dirichlet conditions
5.6. Complex Fourier series
5.7. Fourier series of even and odd periodic functions
5.8. Fourier series of non?periodic function given at finite interval. Half?range series
5.9. Parseval's identity
5.10. Application of the Fourier series: Solving ODEs, forced mechanical oscillations
5.11. Application of the generalized Fourier series: The Sturm?Liouville problem. Solving the heat conduction equation by the separation of variables
5.12. Application of the Fourier series: Frequency spectrum analysis
5.13. Fourier transform
5.14. Various forms of the Fourier transform
5.15. Applications of the Fourier transform
5.16. Discrete Fourier transform (DFT). Fast Fourier transform (FFT)
Chapter 6. Vector Calculus (Lecture notes download) Texts: Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, Chapters 9 and 10
6.1. Vector physical quantities
6.2. Vector calculus: Motivation and applications
6.3. Linear vector space. Dot, cross, and triple products
6.4. Scalar and vector fields and their derivatives
6.5. Curves
6.6. Surfaces
6.7. Line integrals of scalar and vector fields
6.8. Gradient, divergence, and curl
6.9. Path-independent line integrals
6.10. Double integrals
6.11. Triple integrals
6.12. Surface integrals of scalar and vector fields
6.13. Green's theorem for a plane
6.14. Stokes's theorem
6.15. Gauss divergence theorem
Chapter 1. Elementary kinetic theory of gases (Lecture notes download)
1.1. Introduction. Molecular description of gases
1.2. Molecular quantities and macroscopic gas parameters
1.3. Gas laws
1.4. Collision frequency. Free molecular, transitional, and continuum flow regimes
1.5. Transfer of molecular quantities
1.6. Transfer equation
1.7. Diffusion, viscous drag, and heat conduction
1.8. Appendix: Probability and Bernoulli trial
Chapter 2. Molecular models (Lecture notes download)
2.1. Degrees of freedom. Molecular models. Simple gas
2.2. Model of Hard Sphere (HS) molecules
2.3. Interatomic potentials
2.4. Mechanics of a binary collisions
2.5. Collision cross sections
2.6. Variable Hard Sphere (VHS) model
Chapter 3. Kinetic theory of dilute gases (Lecture notes download)
3.1. Distribution function
3.2. Macroscopic gas parameters
3.3. Kinetic equation
3.4. Boltzmann collision term. Boltzmann kinetic equation
3.5. Boltzmann H-theorem
3.6. Statistical equilibrium. Maxwell-Boltzmann distribution function. Entropy
3.7. Gas-surface interaction. Kinetic boundary condition
3.8. Models of diffuse, specular, and specular-diffuse scattering
3.9. Formulation of problems in RGD. Boltzmann equation in reduced units
3.10. Macroscopic gas dynamics equations. Stress tensor and heat flux vector
Chapter 4. Elements of statistics (Lecture notes download)
4.1. Motivation: Deterministic vs. stochastic phenomena
4.2. Random events and their probability
4.3. Random variable and its cumulative distribution function
4.4. Discrete random variable, its mean and standard deviation
4.5. Discrete variables with uniform and Poisson distributions
4.6. Continuous random variable, its mean and standard deviation
4.7. Uniform and normal distributions
4.8. Functions of random variables and random vectors
4.9. Central limit theorem
Chapter 5. Monte Carlo method (Lecture notes download; C++ code download)
5.1. Central problem of the Monte Carlo method
5.2. Random and pseudo-random numbers
5.3. Sampling of discrete random variables
5.4. Sampling of continuous random variables
5.5. Sampling of random events
Chapter 6. Direct Simulations Monte Carlo (DSMC) method (Lecture notes download; C++ code download)
6.1. Basic concepts of the Direct Simulation Monte Carlo method
6.2. Skeleton of a DSMC-based code simulations of two-dimensional flows
6.3. Particle motion, indexing, and sampling of macroscopic gas parameters
6.4. 2D test problem: Flow past a thin wing at an attack angle
6.5. Initial and boundary conditions for the 2D test problem
6.6. Sampling of binary collisions
6.7. Numerical parameters of the DSMC method