Site Navigation
Welcome
Important Notice and Disclaimer
Fee Payment Deadlines
Academic Schedule
Undergraduate Degrees with a Major
Combined Degrees
Minor Programs
Student Services
Undergraduate Admissions
Academic Regulations
Tuition and General Fees
International Foundations Program
Faculty of Arts
Cumming School of Medicine
Faculty of Environmental Design
Faculty of Graduate Studies
Haskayne School of Business
Faculty of Kinesiology
Faculty of Law
Faculty of Nursing
Qatar Faculty
Schulich School of Engineering
Faculty of Science
Faculty of Social Work
Faculty of Veterinary Medicine
Werklund School of Education
Co-operative Education/Internship
Continuing Education
Awards and Financial Assistance
COURSES OF INSTRUCTION
How to Use
Courses of Instruction by Faculty
Course Descriptions
A
Academic Writing ACWR
Accounting ACCT
Actuarial Science ACSC
African Studies AFST
American Sign Language ASL
Anthropology ANTH
Applied Mathematics AMAT
Arabic Language and Muslim Cultures ALMC
Archaeology ARKY
Architectural Studies ARST
Art ART
Art History ARHI
Arts ARTS
Arts and Science Honours Academy ASHA
Astronomy ASTR
Astrophysics ASPH
Athletic Therapy ATTH
B
C
D
E
F
G
H
I
J, K
L
M
N, O
P
R
S
T, U
V, W, Z
About the University of Calgary
Where
Who's Who
Glossary of Terms
Contact Us
Archives
Summary of Revisions
 University of Calgary Calendar 2015-2016 COURSES OF INSTRUCTION Course Descriptions A Applied Mathematics AMAT
Applied Mathematics AMAT
AMAT 311 411 413 415 425 433 481 491 493 501 503 505 507 509 581 583
 

Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Department Head – M. Bauer

Note: For listings of related courses, see Actuarial Science, Mathematics, Pure Mathematics and Statistics.

Note: Effective Fall 2014, Mathematics 265, 267, 367, Mathematics 275, 277, 375 and 377 replaced respectively Mathematics 251, 253, 353, Applied Mathematics 217, 219, 307 and 309 and serves as prerequisites for appropriate courses. In some special cases, Mathematics 267 replaces Mathematics 349 or 353. For these and other deviations from the general rule, see individual course entries for details. Mathematics 267 supplemented by Mathematics 177 will be accepted as equivalent to Mathematics 277.
 
Senior Courses
 
Applied Mathematics 311       Differential Equations I
Classification of ordinary differential equations, first and second order equations with applications, series solutions about regular points and singular points, special functions, Laplace transform.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): Mathematics 253 or 267 or 277 or 283 or Applied Mathematics 219.
Antirequisite(s): Credit for more than one of Applied Mathematics 311 and Mathematics 375 or Applied Mathematics 307 will not be allowed.
back to top
Applied Mathematics 411       Differential Equations II
Existence and uniqueness theorems, comparison and oscillation theorems, Green's functions, Sturm-Liouville problems, systems of equations, phase portraits, stability.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): One of Mathematics 375, Applied Mathematics 311 or 307; and one of Mathematics 331, 353, 367, 377, 381, Applied Mathematics 309.
Notes: It is recommended that students complete Mathematics 335 or 355 or Pure Mathematics 435 or 455 before taking this course.
back to top
Applied Mathematics 413       Introduction to Partial Differential Equations
Orthogonal sets of functions, Fourier series, solution of potential equation, heat equation and wave equation. Numerical solution of partial differential equations.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): One of Mathematics 353, 367, 375, 381, Applied Mathematics 307 or 309 or 311, Mathematics 331.
Antirequisite(s): Credit for both Applied Mathematics 413 and 415 will not be allowed for the Actuarial Science, Applied Mathematics, General Mathematics, Pure Mathematics, Statistics programs, and the Natural Sciences program with a Concentration in General Mathematics.
back to top
Applied Mathematics 415       Mathematical Methods
Mathematical analysis of linear systems. Fourier and Laplace transforms, applications and numerical methods. Functions of a complex variable and applications.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): One of Applied Mathematics 311, 307, Mathematics 331, 353, 367, 375, 381, or Applied Mathematics 309.
Antirequisite(s): Credit will be not be allowed for more than one of Applied Mathematics 415 and 413 for the Actuarial Science, Applied Mathematics, General Mathematics, Pure Mathematics, Statistics, and the Natural Sciences program with a Concentration in General Mathematics.
Notes: Credit in an introductory Computer Science course prior to taking Applied Mathematics 415 is highly recommended.
back to top
Applied Mathematics 425       Introduction to Optimization
Examples of optimization problems. Quadratic forms, minimum energy and distance. Least squares, generalized inverse. Location and classification of critical points. Variational treatment of eigenvalues. Lagrange multipliers. Linear programming.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): Mathematics 311 or 313; and one of Mathematics 331 or 353 or 367 or 377 or 381 or Applied Mathematics 309.
back to top
Applied Mathematics 433       Mathematical Methods in Physics
Fourier analysis. Laplace Transforms. Partial differential equations. Complex analysis. Residue integrals.  Extensive physical applications.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): Applied Mathematics 307 or 311 or Mathematics 375; and one of Applied Mathematics 309 or Mathematics 353 or 367 or 377 or 381 or 331; and Mathematics 211 or 213.
Antirequisite(s): Credit will be not be allowed for Applied Mathematics 433 for the Actuarial Science, Applied Mathematics, General Mathematics, Pure Mathematics, Statistics programs, and the Natural Sciences program with a Concentration in General Mathematics.
back to top
Applied Mathematics 481       Introduction to Mathematical Finance
This course is an introduction to the fundamental concepts of mathematical finance in an elementary setting. Topics include: risk, return, no arbitrage principle; basic financial derivatives: options, forwards and future contracts; risk free assets, time value of money, zero coupon bonds; risky assets, binomial tree model, fundamental theorem of asset pricing; portfolio management and capital asset pricing model; no arbitrage pricing of financial derivatives; hedging.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): Mathematics 321 or Statistics 321.
back to top
Applied Mathematics 491       Numerical Analysis I
Interpolation and approximation, numerical integration, numerical methods for the solution of non-linear equations, systems of linear equations and the eigenvalue problem.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): Mathematics 311 or 313 and 381 or 367 or 377 or 349 and 353 or Applied Mathematics 309; and Computer Science 231 or 217.
Antirequisite(s): Not open to students with credit in Computer Science 491.
back to top
Applied Mathematics 493       Numerical Analysis II
Numerical differentiation, numerical solution of ordinary and partial differential equations.
Course Hours: 3 units; H(3-1T)
Prerequisite(s): Applied Mathematics 311, 413, and 491 or Computer Science 491.
back to top
Applied Mathematics 501       Seminar in Applied Mathematics
Topics will be chosen according to the interests of instructors and students and could include analysis of optimization algorithms, approximation theory, control theory, differential equations, mathematical physics.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Consent of the Department.
MAY BE REPEATED FOR CREDIT
back to top
Applied Mathematics 503       The Mathematics of Wavelets, Signal and Image Processing
Continuous and discrete Fourier transforms, the Fast Fourier Transform, wavelet transforms, multiresolution analysis and orthogonal wavelet bases, and applications.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Applied Mathematics 491 or Computer Science 491.
back to top
Applied Mathematics 505       Calculus on Manifolds
Integral and differential calculus on manifolds including tensor fields, covariant differentiation, Lie differentiation, differential forms, Frobenius' theorem, Stokes' theorem, flows of vector fields.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Pure Mathematics 445 or 545; and one of Mathematics 375 or Applied Mathematics 311 or 307.
back to top
Applied Mathematics 507       Introduction to Relativity Theory
Mathematical theories of space and time. Special Relativity. Electro-dynamics. General Relativity.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Applied Mathematics 505.
back to top
Applied Mathematics 509       Analytical Dynamics
Symplectic geometry, Hamilton's equation, Hamilton-Jacobi theory, constraints and reduction.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Applied Mathematics 505.
back to top
Applied Mathematics 581       Stochastic Calculus for Finance
Martingales in discrete and continuous time, risk-neutral valuations, discrete- and continuous-time (B,S)-security markets, Cox-Ross-Rubinstein formula, Wiener and Poisson processes, Ito formula, stochastic differential equations, Girsanov’s theorem, Black-Scholes and Merton formulas, stopping times and American options, stochastic interest rates and their derivatives, energy and commodity models and derivatives, value-at-risk and risk management.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Applied Mathematics 481.
Antirequisite(s): Credit for both Applied Mathematics 581 and 681 will not be allowed.
back to top
Applied Mathematics 583       Computational Finance
Review of financial asset price and option valuation models; model calibration; tree-based methods; finite-difference methods; Monte Carlo simulation; Fourier methods.
Course Hours: 3 units; H(3-0)
Prerequisite(s): Applied Mathematics 481 and 491.
Antirequisite(s): Credit for both Applied Mathematics 583 and 683 will not be allowed.
back to top