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## CME 102:Ordinary Differential Equations for Engineers (ENGR 155A)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields. Prerequisite: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test: https://exploredegreesnextyear.stanford.edu/undergraduatedegreesandprograms/#aptextt),), or Math 19-21. Recommended: CME100.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## CME 106:Introduction to Probability and Statistics for Engineers (ENGR 155C)

Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite: CME 100/ENGR154 or MATH 51 or 52.
Terms: Win, Sum | Units: 4 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR | Grading: Letter or Credit/No Credit

## CME 108:Introduction to Scientific Computing (MATH 114)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites: MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of CS 106A or higher).
Terms: Win, Sum | Units: 3 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR | Grading: Letter or Credit/No Credit

## CME 232:Introduction to Computational Mechanics (ME 332)

Provides an introductory overview of modern computational methods for problems arising primarily in mechanics of solids and is intended for students from various engineering disciplines. The course reviews the basic theory of linear solid mechanics and introduces students to the important concept of variational forms, including the principle of minimum potential energy and the principles of virtual work. Specific model problems that will be considered include deformation of bars, beams and membranes, plates, and problems in plane elasticity (plane stress, plane strain, axisymmetric elasticity). The variational forms of these problems are used as the starting point for developing the finite element method (FEM) and boundary element method (BEM) approaches ­ providing an important connection between mechanics and computational methods.
Terms: Sum | Units: 3 | Grading: Letter (ABCD/NP)
Instructors: ; Pinsky, P. (PI)

## CME 263:Introduction to Linear Dynamical Systems (EE 263)

Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in EE 103 or MATH 104; ordinary differential equations and Laplace transforms as in EE 102B or CME 102.
Terms: Aut, Sum | Units: 3 | Grading: Letter or Credit/No Credit

## CME 291:Master's Research

Terms: Aut, Win, Spr, Sum | Units: 1-6 | Repeatable for credit | Grading: Letter or Credit/No Credit

## CME 364A:Convex Optimization I (CS 334A, EE 364A)

Convex sets, functions, and optimization problems. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Least-squares, linear and quadratic programs, semidefinite programming, and geometric programming. Numerical algorithms for smooth and equality constrained problems; interior-point methods for inequality constrained problems. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Prerequisite: linear algebra such as EE263, basic probability.
Terms: Win, Sum | Units: 3 | Grading: Letter or Credit/No Credit

## CME 390:Curricular Practical Training

Educational opportunities in high technology research and development labs in applied mathematics. Qualified ICME students engage in internship work and integrate that work into their academic program. Students register during the quarter they are employed and complete a research report outlining their work activity, problems investigated, results, and follow-on projects they expect to perform. May be repeated three times for credit.
Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable for credit | Grading: Satisfactory/No Credit

## CME 399:Special Research Topics in Computational and Mathematical Engineering

Graduate-level research work not related to report, thesis, or dissertation. May be repeated for credit.
Terms: Aut, Win, Spr, Sum | Units: 1-15 | Repeatable for credit | Grading: Letter or Credit/No Credit

## CME 400:Ph.D. Research

Terms: Aut, Win, Spr, Sum | Units: 1-15 | Repeatable for credit | Grading: Satisfactory/No Credit

## CME 801:TGR Project

Terms: Aut, Win, Spr, Sum | Units: 0 | Repeatable for credit | Grading: TGR

## CME 802:TGR Dissertation

Terms: Aut, Win, Spr, Sum | Units: 0 | Repeatable for credit | Grading: TGR