ACM 101C: Partial Differential Equations, Dr. Yong
Content: Partial Differential Equations. Solution methods via separation of variables, transform methods, method of characteristics. Analysis via traveling waves solutions, self similar solutions, dispersion relation, group velocity. Perturbation methods, regular perturbation problems, singular perturbation problems, multiple scales.
Books: Strauss, WA, "Partial Differential Equations: An Introduction", Wiley 1992
Kevorkian, J, "Partial Differential Equations, Analytical Solution Techniques", Springer 1999

ACM 112: Numerical PDEs, Dr. Zhou
Content: Numerical Partial Differential Equations. Finite Difference Schemes, Lax-Friedrichs, Leap Frog, Lax-Wendroff, Crank-Nicholson. Consistency, Stability and Convergence of schemes, Lax-Richtmeyer equivalence theorem, CFL condition and Von Neumann stability analysis. Numerical Schemes for Conservation Laws, Godunov Scheme for Riemann problems. Introduction to the Finite Element method. 
Books: Leveque, RJ, "Numerical Methods for Conservation Laws", Springer 1992
Strickwerda, JC, "Finite Difference Schemes and Partial Differential Equations", Chapman & Hall 1989

ACM 116: Applied Probability, Dr. Candes
Content: Stochastic processes. Gaussian Process, Poisson Process, Markov Chains, Brownian Motion. 
Books: Ross, S, "Introduction to Probability Models", Academic Press 2000
Feller, W, "An Introduction to Probability Theory and its Applications", Wiley 1971

AE 101C: Fluid Mechanics, Dr. Dimotakis
Content: Potential Theory applied to airfoils. Viscous flows: Full Navier Stokes equations, Couette and Poiseuille flow, Stokes flow. Dimensional Analysis and Similarity. Boundary Layers: laminar BL approximation, contact volume analysis, method of Thwaites, BL with  heat transfer. 
Books: Class Notes
 

ACM 101B: Ordinary Differential Equations, Dr. Yong
Content: Ordinary Differential Equations. System of first order equations, phase space analysis, equilibrium points and stability analysis. Local analysis of stability, Lyapunov functions, Floquet theory, Center Manifold theory. Perturbation methods, regularly and singularly perturbed problems, boundary layers and multiple scales.
Books: John, "Linear and Nonlinear oscillators"

ACM 105: Real Analysis, Dr. Novikov
Content: Measure Theory: Riemann and Lebesgue integration, measurable functions, Fatou's lemma, Monotone convergence, Dominated Convergence theorems, Fubini's and Tonelli's theorems, Radon-Nikodym theorem. Functional analysis: Banach spaces, Riesz-Fisher theorem, Riesz Representation theorem, Hahn-Banach theorem, extension theorem, open mapping theorem, closed graph theorem, Banach-Steinhaus theorem, weak topologies and Banach-Alaoglu theorem. Sobolev spaces: mollifiers, distributions, Sobolev Embedding theorem, Sobolev inequality, interpolation inequality, generalized Holder inequality. Compact Operators: trace, Fredholm alternative. 
Books: Royden, HL, "Real Analysis", Prentice Hall 1988

ACM 111: Numerical ODEs, Dr. Zhou
Content: Approximation theory: polynomial interpolation in Lagrangian and Newton form, uniform polynomial approximation, orthogonal polynomials, trigonometric polynomials, cubic splines, wavelets. Numerical differentiation and integration, Gaussian and adaptive quadrature. Numerical solution of ODEs, Taylor schemes, Runge-Kutta methods, multi-steps methods of Adams-Bashforth and Adams-Moulton, predictor-corrector methods. Study of convergence, stability and consistency. Boundary value problems.  
Books: Class Notes

AE 101B: Fluid Mechanics, Dr. Dimotakis
Content: Gas Dynamics: fanno flow, Rayleigh flow. Shocks: Rankine-Hugoniot jump conditions, normal shock relations, Prandtl-Meyer relations, oblique shocks, method of characteristics. Potential Theory: method of singularities, multipole expansion, application to thin airfoil theory. 
Books: Class Notes
 

ACM 101A: Complex Analysis, Dr. Yong
Content: Review of Complex Analysis. Complex integration. Asymptotic expansion of integrals, Laplace's Method, Stationary phase, method of steepest descent. Riemann Hilbert Problems and integral equations. 
Books: Ablowitz, MJ, Fokas "Complex Variables", Cambridge 1997

ACM 104: Linear Algebra, Dr. Novikov
Content: Linear equations and matrices. Eigenvalue problems, Jordan form, singular value decomposition. Applications.
Books: Strang, G "Linear Algebra and Its Applications", International Thomson Publishing, 1988
Franklin, JN, "Matrix Theory", Dover 2000

ACM 110: Numerical Linear Algebra
Content: Singular Value Decomposition, Choleski and LU factorization. Conditioning and Stability. QR factorization via Gram-Schmidt, Modified Gram-Schmidt, Householder transformation and Givens rotation. QR algorithm. Iterative methods for linear systems: Jacobi, Gauss-Seidel, SOR. Projection methods for linear system and for eigenvalue problems. Krylov space methods: Arnoldi iteration, GMRES, Lanczos iteration, Conjugate Gradient and Preconditioned CG. 
Books: Trefethen, LN, Bau, D, "Numerical Linear Algebra", SIAM 1997

AE 101A: Fluid Mechanics
Content: Lagrangian and Euler coordinate systems. Conservation of Mass. Reynolds transport theorem. Conservation of momentum. Bernoulli's equation. Thermodynamics: first and second law, equation of state, isentropic process, energy equation. Gas Dynamics: steady adiabatic ideal flow. 
Books: Class Notes, suggested book: White, FM, "Fluid Mechanics", McGraw Hill 1979.