丁香园AV

Riemann sum, Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, applications of integration. First-order separable differential equations. Sequences and series, series tests, power series, convergence and applications of power series. Prerequisite: MATH 150 or 151; or MATH 154 or 157 with a grade of at least B. Students with credit for MATH 155 or 158 may not take this course for further credit. Quantitative.

Mathematical induction. Limits of real sequences and real functions. Continuity and its consequences. The mean value theorem. The fundamental theorem of calculus. Series. Prerequisite: MATH 152; or MATH 155 or 158 with a grade of B. Quantitative.

Rectangular, cylindrical and spherical coordinates. Vectors, lines, planes, cylinders, quadric surfaces. Vector functions, curves, motion in space. Differential and integral calculus of several variables. Vector fields, line integrals, fundamental theorem for line integrals, Green's theorem. Prerequisite: MATH 152; or MATH 155 or MATH 158 with a grade of at least B. Recommended: It is recommended that MATH 240 or 232 be taken before or concurrently with MATH 251. Quantitative.

Vector calculus, divergence, gradient and curl; line, surface and volume integrals; conservative fields, theorems of Gauss, Green and Stokes; general curvilinear coordinates and tensor notation. Introduction to orthogonality of functions, orthogonal polynomials and Fourier series. Prerequisite: MATH 240 or 232, and 251. MATH 240 or 232 may be taken concurrently. Students with credit for MATH 254 may not take MATH 252 for further credit. Quantitative.

Elementary experiments in optics, electricity, and mechanics that are designed to augment the general survey courses. Corequisite: PHYS 121 or 126 should be taken concurrently or may precede; or by permission of the department. Students with credit for PHYS 130 or 141 may not take PHYS 131 for further credit. Quantitative.

An intermediate mechanics course covering kinematics, dynamics, calculus of variations and Lagrange's equations, non-inertial reference frames, central forces and orbits, and rigid body motion. Prerequisite: PHYS 126 or 121 or 141, with a minimum grade of C-. Corequisite: MATH 251; MATH 232 or 240. Recommended: MATH 310 and PHYS 255. Quantitative.

Introductory physics laboratory with experiments chosen from mechanics, heat, optics, electricity, magnetism, properties of matter, atomic and nuclear physics, along with lectures on the use of computers for data acquisition and data analysis in the physics laboratory. Prerequisite: PHYS 141 or 131 or 130, with a minimum grade of C-. Recommended co-requisite: PHYS 255. Students with credit for PHYS 234 may not take this course for further credit. Quantitative.

Experiments chosen from among mechanics, heat, optics, electricity, magnetism, properties of matter, atomic and nuclear physics. Engineering Science students will do a selected set of experiments. Prerequisite: PHYS 231 or ENSC 220, with a minimum grade of C-. Quantitative.

The physics of vibrations and waves. Topics include periodic motion, including free and forced oscillations, coupled oscillators, normal modes, and waves in one and higher dimensions. Prerequisite: PHYS 126 or 121 or 141 with a minimum C- grade; or PHYS 101 and 102 with a grade of B or better. Corequisite: MATH 251; MATH 232 or 240. Recommended concurrent: PHYS 211 and MATH 310. Quantitative.

Special relativity, including relativistic kinematics and dynamics; tests of relativity; matter waves and early quantum models; wave mechanics and its application to molecular, atomic and subatomic systems. Prerequisite: PHYS 255, with a minimum grade of C-. Quantitative.

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Corequisite: MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Quantitative. Prerequisite: COREQ-MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Equivalent Courses: STAT102 STAT103 STAT201 STAT203 STAT301. Quantitative.

An elementary introduction to computing science and computer programming, suitable for students with little or no programming background. Students will learn fundamental concepts and terminology of computing science, acquire elementary skills for programming in a high-level language and be exposed to diverse fields within, and applications of computing science. Topics will include: pseudocode, data types and control structures, fundamental algorithms, computability and complexity, computer architecture, and history of computing science. Treatment is informal and programming is presented as a problem-solving tool. Students should consult with the self-evaluation on the School of Computing Science website to decide whether they should follow the CMPT 120/125 course sequence or enrol in CMPT 126. Prerequisite: BC Math 12 or equivalent is recommended. Students with credit for CMPT 102, 125, 126, 128 or CMPT 200 or higher may not take this course for further credit. Quantitative/Breadth-Science.

A rigorous introduction to computing science and computer programming, suitable for students who already have some backgrounds in computing science and programming. Intended for students who will major in computing science or a related program. Topics include: fundamental algorithms; elements of empirical and theoretical algorithmics; abstract data types and elementary data structures; basic object-oriented programming and software design; computation and computability; specification and program correctness; and history of computing science. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157) and CMPT 120. Students with credit for CMPT 126, 128, 135 or CMPT 200 or higher may not take for further credit. Quantitative.

A programming course which will provide the science student with a working knowledge of a scientific programming language and an introduction to computing concepts, structured programming, and modular design. The student will also gain knowledge in the use of programming environments including the use of numerical algorithm packages. Corequisite: MATH 152 or 155 (or 158). Students with credit for CMPT 120, 125, 126, 130, 135, or 128 may not take CMPT 102 for further credit. Quantitative.

A rigorous introduction to computing science and computer programming, suitable for students who already have substantial programming background. This course provides a condensed version of the two-course sequence of CMPT 120/125, with the primary focus on computing science and object oriented programming. Topics include: fundamental algorithms and problem solving; abstract data types and elementary data structures; basic object-oriented programming and software design; elements of empirical and theoretical algorithmics; computation and computability; specification and program correctness; and history of computing science. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157). Students with credit for CMPT 120, 125, 128, 130, 135 or higher may not take CMPT 126 for further credit. Quantitative/Breadth-Science.

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Topics as for Math 151 with a more extensive review of functions, their properties and their graphs. Recommended for students with no previous knowledge of Calculus. In addition to regularly scheduled lectures, students enrolled in this course are encouraged to come for assistance to the Calculus Workshop (Burnaby), or Math Open Lab (Surrey). Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B+, or MATH 100 with a grade of at least B-, or achieving a satisfactory grade on the 丁香园AV Calculus Readiness Test. Students with credit for either MATH 151, 154 or 157 may not take MATH 150 for further credit. Quantitative.

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Logarithmic and exponential functions, trigonometric functions, inverse functions. Limits, continuity, and derivatives. Techniques of differentiation, including logarithmic and implicit differentiation. The Mean Value Theorem. Applications of Differentiation including extrema, curve sketching, related rates, Newton's method. Antiderivatives and applications. Conic sections, polar coordinates, parametric curves. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least A, or MATH 100 with a grade of at least B, or achieving a satisfactory grade on the 丁香园AV Calculus Readiness Test. Students with credit for either MATH 150, 154 or 157 may not take MATH 151 for further credit. Quantitative.

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 240 make not take this course for further credit. Quantitative.

Linear equations, matrices, determinants. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphais and includes proofs of the basic theorems. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 232 cannot take this course for further credit. Quantitative.

A general calculus-based introduction to mechanics. Topics include translational and rotational motion, momentum, energy, gravitation, and selected topics in modern physics. Prerequisite: BC Principles of Physics 12 or PHYS 100 or equivalent, with a minimum grade of C-. This prerequisite may be waived, at the discretion of the department, as determined by the student's performance on a regularly scheduled PHYS 100 final exam. Please consult the physics advisor for further details. Corequisite: MATH 150 or 151 or 154 must precede or be taken concurrently. Students with credit for PHYS 101, 125 or 140 may not take this course for further credit. Quantitative/Breadth-Science.

Newtonian mechanics and special relativity for students with good preparation in physics and mathematics. Topics include Newtonian particle mechanics, angular momentum, torque, conservation laws, gravitation, and special relativity. Prerequisite: Greater than 85% in both BC Pre-Calculus 12 & BC Physics 12, or a grade of A in PHYS 100, or equivalent. Co-requisite: MATH 150 or 151 or 154 must precede or be taken concurrently. Students with credit for PHYS 101, 120 or PHYS 140 may not take PHYS 125 for further credit. Quantitative.

A general calculus-based introduction to mechanics taught in an integrated lecture-laboratory environment. Topics include translational and rotational motion, momentum, energy, gravitation, and selected topics in modern physics. Prerequisite: BC Principles of Physics 12, or equivalent, with a minimum grade of C-. Corequisite: MATH 150 or 151 or 154 must precede or be taken concurrently. Students with credit for PHYS 125 or 120 or 101 may not take this course for further credit. Quantitative/Breadth-Science.

A general calculus-based introduction to electricity, magnetism and optics. Topics include electricity, magnetism, simple circuits, optics and topics from applied physics. Prerequisite: PHYS 120 or 125 or 140 (or PHYS 101 with a grade of A or B). Corequisite: MATH 152 or 155 must precede or be taken concurrently. Students with credit for PHYS 102, 126 or 141 may not take this course for further credit. Quantitative/Breadth-Science.

Electricity, magnetism, and the electromagnetic character of light for students with good preparation in physics and mathematics. Topics include waves, simple electrical circuits, electricity, magnetism, the unifications of electromagnetism in relativity, light as an electromagnetic wave, and photons. Prerequisite: PHYS 125 or a grade of A or better in PHYS 120 or 140. Corequisite: MATH 152 or 155 must precede or be taken concurrently. Students with credit in PHYS 102, 121 or 141 may not take this course for further credit. Quantitative.

A general calculus-based introduction to electricity, magnetism and optics taught in an integrated lecture-laboratory environment. Topics include electricity, magnetism, simple circuits, optics and topics from applied physics. Prerequisite: PHYS 140, with a minimum grade of C-. Corequisite: MATH 152 or 155 must precede or be taken concurrently. Students with credit for PHYS 126 or 121 or 102 may not take this course for further credit. Quantitative/Breadth-Science.

A presentation of the problems commonly arising in numerical analysis and scientific computing and the basic methods for their solutions. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240, and computing experience. Quantitative.

First-order differential equations, second- and higher-order linear equations, series solutions, introduction to Laplace transform, systems and numerical methods, applications in the physical, biological and social sciences. Prerequisite: MATH 152; or MATH 155/158 with a grade of at least B, MATH 232 or 240. Quantitative.

Sequences and series of functions, topology of sets in Euclidean space, introduction to metric spaces, functions of several variables. Prerequisite: MATH 242 and 251. Quantitative.

Functions of a complex variable, differentiability, contour integrals, Cauchy's theorem, Taylor and Laurent expansions, method of residues. Prerequisite: MATH 251. Students with credit for MATH 424 may not take this course for further credit. Quantitative.

First-order linear equations, the method of characteristics. The wave equation. Harmonic functions, the maximum principle, Green's functions. The heat equation. Distributions and transforms. Higher dimensional eigenvalue problems. An introduction to nonlinear equations. Burgers' equation and shock waves. Prerequisite: MATH 310 and one of MATH 314, 320, 322, PHYS 384. An alternative to the above prerequisite is both of MATH 254 and MATH 310, both with grades of at least A-. Quantitative.

Convergence in Euclidean spaces, Fourier series and their convergence, Legendre polynomials, Hermite and Laguerre polynomials. Prerequisite: MATH 232 or 240 and one of MATH 314, 320, 322, PHYS 384. Students with credit for MATH 420 or MATH 719 may not complete this course for further credit. Quantitative.

Conformal mapping, Cauchy Integral Formula, Analytic Continuation, Riemann Mapping Theorem, Argument Principle. Prerequisite: MATH 320 and either MATH 322 or 254, or permission of the instructor. Quantitative.

Metric spaces, normed vector spaces, measure and integration, an introduction to functional analysis. Prerequisite: MATH 320. Quantitative.

Formulation, analysis and numerical solution of continuous mathematical models. Applications may be selected from topics in physics, biology, engineering and economics. Prerequisite: MATH 310 and one of MATH 314, MACM 316, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Students with credit for MATH 361 or MATH 761 may not complete this course for further credit. Quantitative.

Incompressible fluid flow phenomena: kinematics and equations of motion, viscous flow and boundary layer theory, potential flow, water waves. Aerodynamics. Prerequisite: one of MATH 314, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Quantitative.

The topics included in this course will vary from term to term depending on faculty availability and student interest. Prerequisite: Will be specified according to the particular topic or topics offered under this course number.

A first course in computer algebra also called symbolic computation. It covers data-structures and algorithms for mathematical objects, including polynomials, general mathematical formulae, long integer arithmetic, polynomial greatest common divisors, the Risch integration algorithm. Other topics include symbolic differentiation, simplification of formulae, and polynomial factorization. Students will learn Maple for use on assignments. Prerequisite: CMPT 307 or MATH 332 or MATH 340. Quantitative.

The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Prerequisite: MATH 310 and MACM 316. Quantitative.

Stability and bifurcation in continuous and discrete dynamical systems, with applications. The study of the local and global behaviour of linear and nonlinear systems, including equilibria and periodic orbits, phase plane analysis, conservative systems, limit cycles, the Poincare-Bendixson theorem, Hopf bifurcation and an introduction to chaos. Prerequisite: MATH 310. Quantitative.

Development and application of Maxwell's equations in vector differential form. Notation and theorems of vector calculus; electric charge, fields, potentials, capacitance and field energy; conductors; methods for solving electrostatic problems; electric fields in matter; electrical current and the magnetic field; Ampere's law and the vector potential; magnetic fields in matter; electromotive force, electrical resistance, Faraday's law and inductance; Maxwell's correction to Ampere's law and electromagnetic waves. Prerequisite: PHYS 130 or 131 or 141; MATH 252 or 254; MATH 310, with a minimum grade of C-. Students with credit for PHYS 221 may not take this course for further credit. Quantitative.

Experiments in optics and modern physics, including diffraction, interference, spectroscopy, lasers and holography. Engineering Science students will do a selected set of experiments. Prerequisite: PHYS 233 and 285, or equivalent, with a minimum grade of C-. Students with credit for PHYS 332 may not take this course for further credit. Writing/Quantitative.

Heat, temperature, heat transfer, kinetic theory, laws of thermodynamics, entropy, heat engines, applications of thermodynamics to special systems, phase transitions. Prerequisite: PHYS 126 or 121, MATH 251, with a minimum grade of C-. Quantitative.

Applications of mathematical methods in physics, differential equations of physics, eigenvalue problems, solutions to wave equations. Prerequisite: MATH 252 or 254; MATH 310; PHYS 255 or ENSC 380, with a minimum grade of C-. Corequisite: PHYS 211. Quantitative.

Wave mechanics and the Schroedinger equation, the harmonic oscillator, introduction to Dirac notation, angular momentum and spin, the hydrogen atom, atomic structure, time-independent perturbation theory, atomic spectra, and applications. Prerequisite: MATH 252 or 254; PHYS 285 or ENSC 380 or CHEM 260, with a minimum grade of C-. Corequisite: PHYS 211; MATH 310. Quantitative.

Central forces, rigid body motion, small oscillations. Lagrangian and Hamiltonian formulations of mechanics. Prerequisite: PHYS 384, with a minimum grade of C- or permission of the department. Non-physics majors may enter with MATH 252, 310 and PHYS 211, with a minimum grade of C-. Quantitative.

Foundations of quantum mechanics, time-dependent perturbation theory, radiation, variational methods, scattering theory, advanced topics, and applications. Prerequisite: PHYS 385 and either PHYS 384 or MATH 314 and 419, with a minimum grade of C-. Quantitative.

A continuation of PHYS 321: properties of electromagnetic waves and their interaction with matter. Transmission lines and waveguides; antennas, radiation and scattering; propagation of electromagnetic waves in free space and in matter; reflection and refraction at boundaries; polarization, interference and diffraction. Prerequisite: PHYS 321; PHYS 255 or ENSC 380, with a minimum grade of C-. Students with credit for PHYS 324 or 425 may not take PHYS 421 for further credit. Quantitative.

Postulates of statistical mechanics, partition functions, applications to gases, paramagnetism and equilibrium. Quantum statistics and applications. Prerequisite: PHYS 344 or CHEM 360, with a minimum grade of C-. Recommended: PHYS 385. Quantitative.

Characteristics of stars and their evolution, thermodynamics of stellar interior, origin of the elements, galaxies, cosmology, and origin of the planets. Prerequisite: PHYS 211 and either CHEM 120 or 121, with a minimum grade of C-. Quantitative.

Computer based approaches to the solution of complex physical problems. A partial list of topics includes: Monte-Carlo and molecular dynamics techniques applied to thermal properties of materials; dynamical behavior of conservative and dissipative systems, including chaotic motion; methods for ground state determination and optimization, including Newton-Raphson, simulated annealing, neural nets, and genetic algorithms; the analysis of numerical data; and the use of relevant numerical libraries. Prerequisite: MATH 310, PHYS 211, CMPT 101 or 102, with a minimum grade of C-. Recommended: PHYS 344 or equivalent. Quantitative.

Undergraduate research and preparation of an honours thesis. The research project may be in experimental or theoretical physics. Prospective students must obtain agreement of a faculty member willing to supervise the project, and submit the project to the physics department for approval at least two months prior to enrolling for the course. The research must be done during the term in which the student is enrolled for the course, and may not be part of a co-op practicum. The course will be graded on the basis of the honours thesis, which must be submitted before the end of the term. Prerequisite: All students interested in taking this course must consult with their faculty supervisor regarding prerequisites; normally requires PHYS 431, with a minimum grade of C-.

Optical physics, including geometrical and physical optics, waves in anisotropic media, coherence, image formation and Fourier optics, guided wave optics and selected advanced topics such as lasers, nonlinear optics, photonics and quantum optics. Prerequisite: PHYS 321 or 221, with a minimum grade of C-. Corequisite: PHYS 385. Quantitative.

Crystal structure, lattice vibrations and thermal properties of solids, free electron model, band theory, and applications. Prerequisite: PHYS 385, with a minimum grade of C-. Quantitative.

Physics of elementary particles. Symmetries, strong interactions, electromagnetic interactions, weak interaction. Prerequisite: PHYS 385 or CHEM 464, with a minimum grade of C- or permission of the department. Recommended: PHYS 380. Students with credit for NUSC 485 may not take this course for further credit. Quantitative.

Gravity and space-time, Einstein's equations and their solution, tests of relativity, black holes, stellar equilibrium and collapse, and cosmological models. Prerequisite: PHYS 285 or MATH 471; PHYS 384, with a minimum grade of C-. Quantitative.