MATH 300B - Advanced Boundary Value Problems

1.5 units (fi 6)(EITH/SP/SU, 3-0-0)

Derivation of the classical partial differential equations of applied mathematics, solutions using separation of variables. Fourier expansions and their applications to boundary value problems. Introduction to Fourier Transforms. Emphasis on building an appropriate mathematical model from a physical problem, solving the mathematical problem, and carefully interpreting the mathematical results in the context of the original physical problem. Prerequisites: MATH 201 and 209. Notes: (1) Open only to students in Engineering, Specialization Physics, and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 300 and 337. (3) Course cannot be taken for credit if credit has been obtained in ECE 341.

MATH 100 - Calculus for Engineering I

3 units (fi 6)(EITHER, 3-0-1)

Review of numbers, inequalities, functions, analytic geometry; limits, continuity; derivatives and applications, Taylor polynomials; log, exp, and inverse trig functions. Integration, fundamental theorem of calculus substitution, trapezoidal and Simpson's rules. Prerequisites: Mathematics 30-1 and Mathematics 31. Notes: (1) Credit can be obtained in at most one of MATH 100, 113, 114, 117, 134, 144, 154, or SCI 100. (2) Students in all sections of this course will write a common final examination. (3) Restricted to Engineering students. Non-Engineering students who take this course will receive 3 units.

MATH 309 - Mathematical Methods for Electrical Engineers

3 units (fi 6)(1 TRM S/S, 3-0-0)

Complex numbers, analytic functions, Cauchy-Riemann equation, Cauchy Theorem, power series and Laurent expansions, residues, inverse Laplace transform. Complex inner product spaces, orthogonal expansions, Gram-Schmidt orthogonalization completeness, Fourier expansions applied to signals, Parseval's relation and Bessel's inequality. Prerequisite: MATH 209. Notes: (1) Restricted to Engineering students. (2) This course may not be taken for credit if credit has already been obtained in MATH 311 or 411.

MATH 101 - Calculus for Engineering II

3 units (fi 6)(EITHER, 3-0-1)

Area between curves, techniques of integration. Applications of integration to planar areas and lengths, volumes and masses. First order ordinary differential equations: separable, linear, direction fields, Euler's method, applications. Infinite series, power series, Taylor expansions with remainder terms. Polar coordinates. Rectangular, spherical and cylindrical coordinates in 3-dimensional space. Parametric curves in the plane and space: graphing, arc length, curvature; normal binormal, tangent plane in 3- dimensional space. Volumes and surface areas of rotation. Prerequisite: MATH 100. Notes: (1) Credit can be obtained in at most one of MATH 101, 115, 118, 136, 146, 156 or SCI 100. (2) Students in all sections of this course will write a common final examination. (3) Restricted to Engineering students. Non-Engineering students who take this course will receive 3 units.

MATH 371 - Mathematical Modelling in the Life Sciences

3 units (fi 6)(EITHER, 3-0-0)

Model development, computation, and analysis for problems in the life sciences. Models include differential equations, difference equations and stochastic formulations. Model evaluation and prediction. Applications are chosen from epidemiology, ecology, population biology, physiology and medicine. Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217. Note: No previous computing experience is needed.