Upcoming Courses
ES APPM 411-1: Differential Equations in Mathematical Physics – Fall 2022
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green’s functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.
ES APPM 420-1: Asymptotic and Perturbation Methods in Applied Mathematics – Fall 2022
Asymptotic expansions of integrals. Regular and singular perturbation methods for ordinary and partial differential equations. Boundary layer theory. Matched asymptotic expansions. Homogenization. Two-time and uniform expansions. Wave propagation and WKBJ method. Turning point theory. Nonlinear oscillations. Bifurcation and stability theory.
ES APPM 312-0: Complex Variables – Spring 2023
Imaginary numbers and complex variables, analytic functions, calculus of complex functions, contour integration with application to transform inversion, conformal mapping. May be taken independently of 311-1,2.
Past Courses
GEN ENG 205-4: Engineering Analysis IV
Solution methods for ordinary differential equations, including exact, numerical, and qualitative methods. Applications and modeling principles; solution techniques
ES APPM 206-4: Honors Engineering Analysis IV
Honors version of GEN ENG 205-4
MATH 220-1,2: Single-Variable Differential and Integral Calculus
Limits. Differentiation. Linear approximation and related rates. Extreme value theorem, mean value the orem, and curve-sketching. Optimization. Definite integrals, antiderivatives, and the fundamental theorem of calculus. Transcendental and inverse functions. Areas and volumes. Techniques of integration, numerical integration, and improper integrals. First-order linear and separable ordinary differential equations.
MATH 228-1,2: Multivariable Differential and Integral Calculus for Engineering
Vectors, vector functions, partial derivatives, Taylor polynomials, and optimization. Emphasis on engineer ing applications. Multiple integration: double integrals, triple integrals, and change of variables. Vector calculus: vector fields, line integrals, surface integrals, curl and divergence, Green’s theorem, Stokes’ theorem, and the divergence theorem.
ES APPM 311-1,2: Methods of Applied Mathematics
Ordinary differential equations; Sturm-Liouville theory, properties of special functions, solution methods including Laplace transforms. Fourier series: eigenvalue problems and expansions in orthogonal functions. Partial differential equations: classification, separation of variables, solution by series and transform methods.
ES APPM 312-0: Complex Variables
Imaginary numbers and complex variables, analytic functions, calculus of complex functions, contour integration with application to transform inversion, conformal mapping
ES APPM 411-1,2,3: Differential Equations in Mathematical Physics
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green’s functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.
ES APPM 420-1,2,3: Asymptotic and Perturbation Methods in Applied Mathematics Asymptotic
Expansions of integrals. Regular and singular perturbation methods for ordinary and partial differential equations. Boundary layer theory. Matched asymptotic expansions. Homogenization. Two time and uniform expansions. Wave propagation and WKBJ method. Turning point theory. Nonlinear oscillations. Bifurcation and stability theory.
ES APPM 424-1,2: Mathematical Topics in Combustion
Fundamentals of chemically reacting flows. Premixed and diffusion flames. Instabilities in flames. Turbulent combustion. Detonation waves. Ignition and explosion. Combustion synthesis of materials
ES APPM 440-0: Integral Equations and Applications
Integral equations in various scientific theories and their relation to differential equations. Methods of solving linear problems with Hilbert-Schmidt, Cauchy, and Wiener-Hopf type kernels; applications. Nonlinear problems, bifurcation phenomena.