# Courses

AER210H1 - Vector Calculus & Fluid Mechanics

**Credit Value:**0.50

**Hours:**38.4L/25.6T/6.4P

The first part of this course covers multiple integrals and vector calculus. Topics covered include: double and triple integrals, derivatives of definite integrals, surface area, cylindrical and spherical coordinates, general coordinate transformations (Jacobians), Taylor series in two variables, line and surface integrals, parametric surfaces, Green's theorem, the divergence and gradient theorems, Stokes's theorem. The second part of the course provides a general introduction to the principles of continuum fluid mechanics. The basic conservation laws are derived in both differential and integral form, and the link between the two is demonstrated. Applications covered include hydrostatics, incompressible and compressible frictionless flow, the speed of sound, the momentum theorem, viscous flows, and selected examples of real fluid flows.

**Prerequisite:**MAT195H1

**Corequisite:**MAT292H1

**Exclusion:**CHE211H1, CHE221H1, CME261H1, CME270H1, MAT291H1 or MIE312H1

**Recommended Preparation:**PHY180H1

**Total AUs:**54.40

AER301H1 - Dynamics

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Reference frames in relative translation and rotation, vector and matrix formulations. Dynamics of a single particle and of systems of particles. Lagrange's equations. D'Alembert's and Hamilton's principle. Orbital dynamics. Rigid body kinematics and dynamics, Lagrangian approach to vibrations of complex systems. Model analysis. Primary Reference: class notes. Reference Books: Greenwood, Principles of Dynamics; Goldstein, Classical Mechanics.

**Prerequisite:**AER210H1, MAT185H1 and PHY180H1

**Exclusion:**MIE301H1

**Total AUs:**44.80

AER302H1 - Aircraft Flight

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Basics of aircraft performance with an introduction to static stability and control. Topics covered include: Equations of Motion; Characteristics of the Atmosphere; Airspeed Measurement; Drag (induced drag, total airplane drag); Thurst and Power (piston engine characteristics, gas turbine performance); Climb (range payload); Tunrs; Pull-up; Takeoff; Landing (airborne distance, ground roll); Flight envelope (maneuvering envelope, gust load factors); Longitudinal and lateral static stability and control; Introduction to dynamic stability.

**Prerequisite:**AER307H1 and AER301H1

**Total AUs:**44.80

AER303H1 - Aerospace Laboratory I

**Credit Value:**0.15

**Hours:**12.8P

Students will perform a number of experiments in the subject areas associated with the Aerospace Option curriculum, and prepare formal laboratory reports.

**Corequisite:**AER307H1

**Total AUs:**6.40

AER304H1 - Aerospace Laboratory II

**Credit Value:**0.15

**Hours:**12.8P

Students will perform a number of experiments in the subject areas associated with the Aerospace Option curriculum, and prepare formal laboratory reports.

**Corequisite:**AER373H1

**Total AUs:**6.40

AER307H1 - Aerodynamics

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Review of fundamentals of fluid dynamics, potential-flow, Euler, and Navier-Stokes equations; incompressible flow over airfoils, incompressible flow over finite wings; compressibility effects; subsonic compressible flow over airfoils; supersonic flow; viscous flow; laminar layers and turbulent boundary layers and unsteady aerodynamics. Textbook: Anderson, J.D., Fundamentals of Aerodynamics, 3rd Edition, McGraw Hill, 2001.

**Prerequisite:**AER210H1 or MIE312H1

**Total AUs:**44.80

AER310H1 - Gasdynamics

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Basic introduction to compressible gasdynamics. Includes some fundamental thermodynamics, thermal and caloric equations of state, derivation of Euler's equations by control volume approach. Also, includes the theory of steady flows in ducts with area changes, adiabatic frictional flows, duct flows with heat transfer, normal and oblique shock waves, Prandtl-Meyer expansion wave, moving shock and rarefaction waves, shock tubes, and wind tunnels. The lectures are supplemented by problem sets. Reference book: Anderson, J.D., Modern Compressible Flow with Historical Perspective.

**Prerequisite:**AER307H1

**Total AUs:**44.80

AER315H1 - Combustion Processes

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Scope and history of combustion, and fossil fuels; thermodynamics and kinetics of combustion including heats of formation and reaction, adiabatic flame temperature, elementary and global reactions, equilibrium calculations of combustion products, and kinetics of pollutant formation mechanisms; propagation of laminar premixed flames and detonations, flammability limits, ignition and quenching; gaseous diffusion flames and droplet burning; introduction to combustion in practical devices such as rockets, gas turbines, reciprocating engines, and furnaces; environmental aspects of combustion.

**Prerequisite:**CHE260H1

**Exclusion:**MIE516H1

**Total AUs:**44.80

AER336H1 - Scientific Computing

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Introduces numerical methods for scientific computation which are relevant to the solution of a wide range of engineering problems. Topics addressed include interpolation, integration, linear systems, least-squares fitting, nonlinear equations and optimization, initial value problems, and partial differential equations. The assignments require programming of numerical algorithms.

**Prerequisite:**ESC103H1 and MAT185H1

**Total AUs:**44.80

AER372H1 - Control Systems

**Credit Value:**0.50

**Hours:**38.4L/12.8T/19.2P

An introduction to dynamic systems and control. Models of physical systems. Stability and feedback control theory. Analysis and synthesis of linear feedback systems by "classical" and state space techniques. Introduction to nonlinear and optimal control systems. Digital computer control. Multivariable feedback system design.

**Prerequisite:**MAT185H1 and MAT292H1

**Exclusion:**CHE322H1, ECE356H1 or MIE404H1

**Total AUs:**54.40

AER373H1 - Mechanics of Solids and Structures

**Credit Value:**0.50

**Hours:**38.4L/12.8T

An Introduction to Solid and Structural Mechanics. Continuum Mechanics: Stress, strain and constitutive relations for continuous systems, Equilibrium equations, Force and Flexibility methods, Introduction to Cartesian Tensors. Variational Principles: Virtual Work, Complementary Virtual Work, Strain Energy and Work, Principle of Stationary Value of the Total Potential Energy, Complementary Potential Energy, Reissner's Principle, Calculus of Variations, Hamilton's Principle. Beam and Plate theory. Dynamics of discrete and continuous systems.

**Prerequisite:**CIV102H1

**Total AUs:**44.80

AER406H1 - Aircraft Design

**Credit Value:**0.50

**Hours:**38.4T

Teams of 3 or 4 students design, build, and fly a remotely piloted aircraft. The aircraft is designed and built to maximize a flight score, which is a complex function of many factors - payload fraction, payload type, flight time, takeoff distance, etc. Teams are provided with identical motors, batteries, radio equipment, and flight instrumentation. Weekly sessions consist of a combination of lectures and one-on-one meetings with the tutors and professor to discuss each teams' progress. Evaluations are based on the weekly reports, preliminary and final design presentations and reports, an as-built report, and measured flight performance.

**Prerequisite:**AER302H1, AER307H1 and AER373H1

**Total AUs:**51.28

AER407H1 - Space Systems Design

**Credit Value:**0.50

**Hours:**38.4P

Introduction to the conceptual and preliminary design phases for a space system currently of interest in the Aerospace industry. A team of visiting engineers provide material on typical space systems design methodology and share their experiences working on current space initiatives through workshops and mock design reviews. Aspects of operations, systems, electrical, mechanical, software, and controls are covered. The class is divided into project teams to design a space system in response to a Request for Proposals (RFP) formulated by the industrial team. Emphasis is placed on standard top-down design practices and the tradeoffs which occur during the design process. Past projects include satellites such as Radarsat, interplanetary probes such as a solar sailer to Mars, a Mars surface rover and dextrous space robotic systems.

**Prerequisite:**AER301H1, AER372H1

**Total AUs:**51.28

AER501H1 - Computational Structural Mechanics and Design Optimization

**Hours:**38.4L/12.8T

Introduction to the Finite Element Method and Structural Optimization. Review of linear elasticity: stress, strain and material constitutive laws, Variational Principles. The Finite Element technique: problem formulation - methods of Ritz and Galerkin, element properties - C0 and C1 formulations, static and dynamic problems: applications to bar, beam, membrane and plate problems. Structural Optimization: Overview of problems, Optimal Design problem formulation, solution strategies - gradient search techniques, Sensitivity analysis for static and dynamic problems, Optimization problems using commercial finite element codes. Text: Shames & Dym, Energy and Finite Element Methods in Structural Mechanics.

**Prerequisite:**AER373H1

**Total AUs:**44.80

AER503H1 - Aeroelasticity

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Static aeroelastic phenomena are studied, including divergence of 2D sections and slender 3D wings, as well as control reversal of 3D wings. Various methods of solution are considered such as closed form, discrete element, and the Rayleigh-Ritz approach. A study of vibration and flutter of wings and control surfaces is presented with particular emphasis on those parameters that affect flutter speed. Classical, k, and p-k methods for flutter estimation are presented.

**Prerequisite:**AER307H1 and AER501H1

**Total AUs:**44.80

AER506H1 - Spacecraft Dynamics and Control

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Planar "central force" motion; elliptical orbits; energy and the major diameter; speed in terms of position; angular momentum and the conic parameter; Kepler's laws. Applications to the solar system; applications to Earth satellites. Launch sequence; attaining orbit; plane changes; reaching final orbit; simple theory of satellite lifetime. Simple (planar) theory of atmospheric entry. Geostationary satellite; adjustment of perigee and apogee; east-west stationkeeping. Attitude motion equations for a torque-free rigid body; simple spins and their stability; effect of internal energy dissipation; axisymmetric spinning bodies. Spin-stabilized satellites; long-term effects; sample flight data. Dual-spin satellites; basic stability criteria; example-CTS. "active" attitude control; reaction wheels; momentum wheels; controlmoment gyros; simple attitude control systems.

**Prerequisite:**AER301H1 and AER372H1

**Total AUs:**44.80

AER507H1 - Introduction to Fusion Energy

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Nuclear reactions between light elements provide the energy source for the sun and stars. On earth, such reactions could form the basis of an essentially inexhaustible energy resource. In order for the fusion reactions to proceed at a rate suitable for the generation of electricity, the fuels (usually hydrogen) must be heated to temperatures near 100 million Kelvin. At these temperatures, the fuel will exist in the plasma state. This course will cover: (i) the basic physics of fusion, including reaction cross-sections, particle energy distributions, Lawson criterion and radiation balance, (ii) plasma properties including plasma waves, plasma transport, heating and stability, and (iii) fusion plasma confinement methods (magnetic and inertial). Topics will be related to current experimental research in the field.

**Total AUs:**44.80

AER510H1 - Aerospace Propulsion

**Credit Value:**0.50

**Hours:**38.4L/12.8T

Scope and history of jet and rocket propulsion; fundamentals of air-breathing and rocket propulsion; fluid mechanics and thermodynamics of propulsion including boundary layer mechanics and combustion; principles of aircraft jet engines, engine components and performance; principles of rocket propulsion, rocket performance, and chemical rockets; environmental impact of aircraft jet engines.

**Prerequisite:**AER310H1

**Total AUs:**44.80

AER525H1 - Robotics

**Credit Value:**0.50

**Hours:**38.4L/12.8T/19.2P

The course addresses fundamentals of analytical robotics as well as design and control of industrial robots and their instrumentation. Topics include forward, inverse, and differential kinematics, screw representation, statics, inverse and forward dynamics, motion and force control of robot manipulators, actuation schemes, task-based and workspace design, mobile manipulation, and sensors and instrumentation in robotic systems. A series of experiments in the Robotics Laboratory will illustrate the course subjects.

**Prerequisite:**AER301H1 and AER372H1

**Exclusion:**ECE470H1

**Total AUs:**54.40

APM446H1 - Applied Nonlinear Equations

**Credit Value:**0.50

**Hours:**36L

Partial differential equations appearing in physics, material sciences, biology, geometry, and engineering. Nonlinear evolution equations. Existence and long-time behaviour of solutions. Existence of static, traveling wave, self-similar, topological and localized solutions. Stability. Formation of singularities and pattern formation. Fixed point theorems, spectral analysis, bifurcation theory. Equations considered in this course may include: Allen-Cahn equation (material science), Ginzburg-Landau equation (condensed matter physics), Cahn-Hilliard (material science, biology), nonlinear Schroedinger equation (quantum and plasma physics, water waves, etc). mean curvature flow (geometry, material sciences), Fisher-Kolmogorov-Petrovskii-Piskunov (combustion theory, biology), Keller-Segel equations (biology), and Chern-Simmons equations (particle and condensed matter physics).

Joint undergraduate/graduate course - APM446H1/MAT1508H

**Prerequisite:**APM346H1/MAT351Y1

**Total AUs:**38.40

APM466H1 - Mathematical Theory of Finance

**Credit Value:**0.50

**Hours:**36L

Introduction to the basic mathematical techniques in pricing theory and risk management: Stochastic calculus, single-period finance, financial derivatives (tree-approximation and Black-Scholes model for equity derivatives, American derivatives, numerical methods, lattice models for interest-rate derivatives), value at risk, credit risk, portfolio theory.

Joint undergraduate/graduate course - APM466H1/MAT1856H

**Prerequisite:**APM346H1, STA347H1

**Corequisite:**STA457H1

**Total AUs:**38.40

APS100H1 - Orientation to Engineering

**Credit Value:**0.25

**Hours:**12.8L/12.8T

This course is designed to help students transition into first-year engineering studies and to develop and apply a greater understanding of the academic learning environment, the field of engineering, and how the fundamental mathematics and sciences are used in an engineering context. Topics covered include: study skills, time management, problem solving, successful teamwork, effective communications, exam preparation, stress management and wellness, undergraduate research, extra- and co-curricular involvement, engineering disciplines and career opportunities, and applications of math and science in engineering.

**Total AUs:**19.20

APS105H1 - Computer Fundamentals

**Credit Value:**0.50

**Hours:**38.4L/12.8T/25.6P

An introduction to computer systems and problem solving using computers. Topics include: the representation of information, programming techniques, programming style, basic loop structures, functions, arrays, strings, pointer-based data structures and searching and sorting algorithms. The laboratories reinforce the lecture topics and develops essential programming skills.

**Total AUs:**57.60

APS106H1 - Fundamentals of Computer Programming

**Credit Value:**0.50

**Hours:**38.4L/12.8T/25.6P

An introduction to computer systems and software. Topics include the representation of information, algorithms, programming languages, operating systems and software engineering. Emphasis is on the design of algorithms and their implementation in software. Students will develop a competency in the Python programming language. Laboratory exercises will explore the concepts of both Structure-based and Object-Oriented programming using examples drawn from mathematics and engineering applications.

**Total AUs:**57.60

APS110H1 - Engineering Chemistry and Materials Science

**Credit Value:**0.50

**Hours:**38.4L/12.8T/12.8P

This course is structured around the principle of the structure-property relationship. This relationship refers to an understanding of the microstructure of a solid, that is, the nature of the bonds between atoms and the spatial arrangement of atoms, which permits the explanation of observed behaviour. Observed materials behaviour includes mechanical, electrical, magnetic, optical, and corrosive behaviour. Topics covered in this course include: structure of the atom, models of the atom, electronic configuration, the electromagnetic spectrum, band theory, atomic bonding, optical transparency of solids, magnetic properties, molecular bonding, hybridized orbitals, crystal systems, lattices and structures, crystallographic notation, imperfections in solids, reaction rates, activation energy, solid-state diffusion, materials thermodynamics, free energy, and phase equilibrium.

**Total AUs:**51.20

APS111H1 - Engineering Strategies & Practice I

**Credit Value:**0.50

**Hours:**38.4L/12.8T/12.8P

This course introduces and provides a framework for the design process. Students are introduced to communication as an integral component of engineering practice. The course is a vehicle for understanding problem solving and developing communications skills. This first course in the two Engineering Strategies and Practice course sequence introduces students to the process of engineering design, to strategies for successful team work, and to design for human factors, society and the environment. Students write team and individual technical reports.

**Total AUs:**51.20

APS112H1 - Engineering Strategies & Practice II

**Credit Value:**0.50

**Hours:**25.6L/25.6P

This course introduces and provides a framework for the design process, problem solving and project management. Students are introduced to communication as an integral component of engineering practice. The course is a vehicle for practicing team skills and developing communications skills. Building on the first course, this second course in the two Engineering Strategies and Practice course sequence introduces students to project management and to the design process in greater depth. Students work in teams on a term length design project. Students will write a series of technical reports and give a team based design project presentation.

**Total AUs:**38.40

APS150H1 - Ethics in Engineering

**Credit Value:**0.05

**Hours:**12.8T

An introduction to professional ethics and the Academic Code of Conduct. Topics include: the theory of ethics, professional code of ethics, ethics in the profession, proper use of intellectual property in the professional and in academic settings, plagiarism, the Academic Code of Conduct, and application of ethics in practice.

**Total AUs:**6.40

APS160H1 - Mechanics

**Credit Value:**0.50

The principles of statics are applied to composition and resolution of forces, moments and couples. The equilibrium states of structures are examined. Throughout, the free body diagram concept is emphasized. Vector algebra is used where it is most useful, and stress blocks are introduced. Shear force diagrams, bending moment diagrams and stress-strain relationships for materials are discussed. Stress and deformation in axially loaded members and flexural members (beams) are also covered.

**Exclusion:**CIV100H1

**Total AUs:**51.20

APS161H1 - Dynamics

**Credit Value:**0.50

This course on Newtonian mechanics considers the interactions which influence 2-D, curvilinear motion. These interactions are described in terms of the concepts of force, work, momentum and energy. Initially the focus is on the kinematics and kinetics of particles. Then, the kinematics and kinetics of systems of particles and solid bodies are examined. Finally, simple harmonic motion is discussed. The occurrence of dynamic motion in natural systems, such as planetary motion, is emphasized. Applications to engineered systems are also introduced.

**Exclusion:**MIE100H1

**Total AUs:**51.20