## CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)

Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite:
CME 102/
ENGR 155A.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

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

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.Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext). Recommended:
CME100.

Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)

## ENGR 155B: Linear Algebra and Partial Differential Equations for Engineers (CME 104)

Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite:
CME 102/
ENGR 155A.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

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