L1  Using MATLAB® to evaluate and plot expressions 
pp. 125. MATLAB® Tutorial

Linear Algebra Linear Systems of Algebraic Equations Review of Scalar, Vector, and Matrix Operations Elimination Methods for Solving Linear Systems Existence and Uniqueness of Solutions

L2  Solving systems of linear equations  pp. 2532 and 3656. 
Linear Algebra Existence and Uniqueness of Solutions Matrix Inversion Matrix Factorization Matrix Norm and Rank Submatricies and Matrix Partitions Example. Modeling a Separation System Sparse and Banded Matricies

L3 
Matrix factorization Modularization

Condition Number Heath, Michael T. Scientific Computing: An Introductory Survey. 2nd ed. New York, NY: McGrawHill Companies, Inc., 2002, pp. 56 and 5265. ISBN: 9780072399103. Recktenwald, Gerald W. Introduction to Numerical Methods with MATLAB®: Implementations and Applications. Upper Saddle River, NJ: PrenticeHall, 2000, pp. 402410. ISBN: 9780201308600.
 
L4  When algorithms run into problems: Numerical error, illconditioning, and tolerances  pp. 6177. 
Nonlinear Algebraic Systems Existence and Uniqueness of Solutions to a Nonlinear Algebraic Equation Iterative Methods and Use of Taylor Series Newton's Method for a Single Equation The Secant Method Bracketing and Bisection Methods Finding Complex Solutions Systems of Multiple Nonlinear Algebraic Equations Newton's Method for Multiple Nonlinear Equations

L5  Introduction to systems of nonlinear equations  pp. 7785 and 8899. 
Nonlinear Algebraic Equations Estimating the Jacobian and QuasiNewton Methods Robust Reducedstep Newton's Method The Trust  Region Newton Method Solving Nonlinear Algebraic Systems in MATLAB® Homotopy Example. Steadystate Modeling of a Condensation Polymerization Reactor Bifurcation Analysis

L6  Modern methods for solving nonlinear equations  pp. 104113. 
Matrix Eigenvalue Analysis Orthogonal Matrices Eigenvalues and Eigenvectors Defined Eigenvalues / Eigenvectors of a 2×2 Real Matrix Multiplicity and Formulas for the Trace and Determinant Eigenvalues and the Existence/uniqueness Properties of Linear Systems Estimating Eigenvalues; Gershgorin's Theorem

L7  Introduction to eigenvalues and eigenvectors  pp. 117123 and 148149. 
Matrix Eigenvalue Analysis Eigenvector Matrix Decomposition and Basis Sets Computing Roots of a Polynomial

L8  Constructing and using the eigenvector basis  pp. 123126 and 137141. 
Matrix Eigenvalue Analysis Numerical Calculation of Eigenvalues and Eigenvectors in MATLAB® Eigenvalue Problems in Quantum Mechanics

L9  Function space vs. real space methods for partial differential equations (PDEs)  pp. 141149. 
Matrix Eigenvalue Analysis Singular Value Decomposition Computing the Roots of a Polynomial

L10  Function space  pp. 126134. 
Matrix Eigenvalue Analysis Computing Extremal Eigenvalues The QR Method for Computing all Eigenvalues

L11 
Numerical calculation of eigenvalues and eigenvectors Singular value decomposition (SVD)
 
Initial Value Problems Initial Value Problems of Ordinary Differential Equations (ODEIVPs) Polynomial Interpolation Newtoncotes Integration Linear ODE Systems and Dynamic Stability

Q1  Quiz 1  pp. 154163 and 169176. 
Initial Value Problems Initial Value Problems of Ordinary Differential Equations (ODEIVPs) Polynomial Interpolation Newtoncotes Integration Linear ODE Systems and Dynamic Stability

L12  Ordinary differential equation  initial value problems (ODEIVP) and numerical integration  pp. 176194. 
Initial Value Problems Overview of ODEIVP Solvers in MATLAB® Accuracy and Stability of Singlestep Methods Stiff Stability of BDF Methods

L13  Stiffness. MATLAB® ordinary differential equation (ODE) solvers  pp. 195203. 
Initial Value Problems DifferentialAlgebraic Equation (DAE) Systems

L14 
Implicit ordinary differential equation (ODE) solvers Shooting
 pp. 212231. 
Numerical Optimization Local Methods for Unconstrained Optimization Problems The Simplex Method Gradient Methods Newton Line Search Methods Trustregion Newton Method Newton Methods for Large Problems Unconstrained Minimizer fminunc in MATLAB® Example. Fitting a Kinetic Rate Law to Timedependent Data

L15 
Differential algebraic equations (DAEs) Introduction: Optimization
 pp. 231246. 
Numerical Optimization Lagrangian Methods for Constrained Optimization Constrained Minimizer fmincon in MATLAB®

L16  Unconstrained optimization  pp. 258270. 
Boundary Value Problems (BVPs) BVPs from Conservation Principles Realspace vs. Functionspace BVP Methods The Finite Difference Method Applied to a 2D BVP Extending the Finite Difference Method Chemical Reaction and Diffusion in a Spherical Catalyst Pellet

L17  Constrained optimization  pp. 270279. 
Boundary Value Problems Finite Differences for a Convection/diffusion Equation

L18 
Optimization Sensitivity analysis Introduction: Boundary value problems (BVPs)
 pp. 282299. 
Boundary Value Problems Numerical Issues for Discretized PDEs with More Than Two Spatial Dimensions The MATLAB® 1D Parabolic and Elliptic Solver pdepe Finite Differences in Complex Geometries The Finite Volume Method

L19  Boundary value problems (BVPs) lecture 2  pp. 299311. 
Boundary Value Problems The Finite Element Method (FEM) FEM in MATLAB® Further Study in the Numerical Solution of BVPs

L20  Boundary value problems (BVPs) lecture 3: Finite differences, method of lines, and finite elements   
L21  TA tutorial on BVPs, FEMLAB®   
L22  Introduction: Models vs. Data  pp. 372389 and 325338. 
Bayesian Statistics and Parameter Estimation General Problem Formulation Example. Fitting Kinetic Parameters of a Chemical Reaction Singleresponse Linear Regression The Bayesian View of Statistical Inference The Least Squares Method Reconsidered Probability Theory and Stochastic Simulation Important Probability Distributions
 Bernoulli Trials
 The Random Walk Problem
 The Binomial Distribution
 The Gaussian (Normal) Distribution
 The Central Limit Theorem of Statistics
 The Gaussian Distribution With Nonzero Mean
 The Poisson Distribution
Random Vectors and Multivariate Distributions
 The Boltzmann Distribution
 The Maxwell Distribution

L23  Models vs. Data lecture 2: Bayesian view  pp. 389403. 
Bayesian Statistics and Parameter Estimation Selecting a Prior for Singleresponse Data Confidence Intervals From the Approximate Posterior Density

L24  Uncertainties in model predictions  pp. 403431. 
Bayesian Statistics and Parameter Estimation MCMC Techniques in Bayesian Analysis MCMC Computation of Posterior Predictions Applying Eigenvalue Analysis to Experimental Design Bayesian Multi Response Regression Analysis of Composite Data Sets Bayesian Testing and Model Criticism

L25  Conclude models vs. data   
L26  TA led review   
Q2  Quiz 2 (lectures 1  21)  
Probability Theory and Stochastic Simulation Markov Chains and Processes; Monte Carlo Methods Markov Chains Monte Carlo Simulation in Statistical Mechanics Monte Carlo Integration Simulated Annealing

L27 
Models vs. Data recapitulation Monte carlo and molecular dynamics
  
L28  Guest lecture on Monte Carlo / molecular dynamics: Frederick Bernardin  pp. 363364. 
Probability Theory and Stochastic Simulation Genetic Programming

L29 
Global optimization Multiple minima
  
L30 
Modeling intrinsically stochastic processes multiscale modeling
 pp. 338353. 
Probability Theory and Stochastic Simulation Brownian Dynamics and Stochastic Differential Equations (SDEs)

L31  Fluctuationdissipation theorem   
L32  Kinetic Monte Carlo and turbulence modeling   
L33 
Operator splitting Strang splitting

Strang Splitting Schwer, Douglas A., Pisi Lu, William H. Green, Jr., and Viriato Semião. "A Consistentsplitting Approach to Computing Stiff Steadystate Reacting Flows With Adaptive Chemistry." Combust Theory Modelling 7 (2003): 383399.
 
L34 
Fourier transforms Fast fourier transform (FFT)
 pp. 436452. 
Fourier Analysis Fourier Series and Transforms in One Dimension 1D Fourier Transforms in MATLAB® Convolution and Correlation Fourier Transforms in Multiple Dimensions

L35  Summary: Problem solving   
L36  TA led final review   