Existence and uniqueness of solution for first-order differential equations, general second-order linear ODEs, homogeneous equations, nonhomogeneous equations, variable coefficients, variation of parameters, Systems of ODEs, Fourier series, Laplace transform, interpretation of problems in mathematical terms, single-step numerical methods for ODEs. Introduction to Partial Differential Equations.
Partial differentiation, grad, div, curl, multiple integrals, line integrals, surface integrals, differential equations, first order differential equations, homogeneous linear differential equations, boundary conditions. Formulation of various problems relevant to materials and mining engineering - the concepts above are used.
This course provides the foundations of analysis and rigorous calculus for students who will take subsequent courses where these mathematical concepts are central of applications, but who have only taken courses with limited proofs. Topics include topology of Rn, implicit and inverse function theorems and rigorous integration theory.
Construction of Real Numbers. Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.
Function spaces; Arzela-Ascoli theorem, Weierstrass approximation theorem, Fourier series. Introduction to Banach and Hilbert spaces; contraction mapping principle, fundamental existence and uniqueness theorem for ordinary differential equations. Lebesgue integral; convergence theorems, comparison with Riemann integral, L^p spaces. Applications to probability.
Course examines the following: analytic functions, Cauchy-Reimann equations, contour integration, Cauchy's theorem, Taylor and Laurent series, singularities, residue calculus, conformal mapping, harmonic functions, Dirichlet and Neumann problems and Poisson integral formulas. Course includes studies of linear differential equations in the complex plane, including Bessel and Legendre functions.
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.
This is a seminar series that will preview the core fields in Mechanical and Industrial Engineering. Each seminar will be given by a professional in one of the major areas in MIE. The format will vary and may include application examples, challenges, case studies, career opportunities, etc. The purpose of the seminar series is to provide first year students with some understanding of the various options within the Department to enable them to make educated choices for second year. This course will be offered on a credit/no credit basis. Students who receive no credit for this course must re-take it in their 2S session. Students who have not received credit for this course at the end of their 2S session will not be permitted to register in session 3F.
Humanities and Social Science elective
This course explores the relationship between changing technologies and cultural representations and teaches a methodology that bridges the world of the artist and the world of the engineer. It enables engineers to explore how the analysis of art has been used in the discussion of the social impacts of technological innovation and to use these methods as they develop new skills in essayistic argument and increase critical vocabulary.
This is a basic course in engineering thermodynamics. Topics covered include: properties and behaviour of pure substances; equation of states for ideal and real gases; compressibility factor; first and second laws of thermodynamics; control mass and control volume analyses; applications of first and second laws of thermodynamics to closed systems, open systems and simple thermal cycles.
Production Fundamentals: Metal casting; metal forming - rolling, forging, extrusion and drawing, and sheet-metal forming; plastic/ceramic/glass forming; metal removal - turning, drilling/ boring/reaming, milling, and grinding; non-traditional machining - ECM, EDM and laser cutting; welding; surface treatment; metrology. Environmental issues in manufacturing processes, recycling of materials. Automation Fundamentals: Automation in material processing and handling - NC, robotics and automatically-guided vehicles; flexible manufacturing - group technology, cellular manufacturing and FMS; and computer-aided design - geometric modelling, computer graphics, concurrent engineering and rapid prototyping.
Instruction and assessment of communication centered around course deliverables that will form part of an ongoing design portfolio.
Design of mechanical joints. Elasto-plastic torsion of circular sections. Elasto-plastic bending of beams. Residual stresses. Shearing stresses in beams. Analysis of plane stress and plane strain problems. Pressure vessels. Design of members using strength criteria. Deflection of beams. Statistically indeterminate structures.
Introduction to the methods of Data Science. Exploratory data analysis and visualization; tools for reproducible analysis. Principles and tools for data collection; awareness of bias in collection methods. Data cleaning. Descriptive statistics and feature analysis. Assessment of data with respect to scientific theories. Data interpretation fallacies. Geographical data representation and manipulation. Text processing, the natural language processing pipeline, and sentiment analysis. Fundamentals of social network analysis and centrality measures. Cloud-based data processing.
Introduction to complex analysis. Multivariate integration with application to calculation of volumes, centroids and moments. Vector calculus. Divergence, curl and gradient operators. Green's theorem. Gauss' theorem. Stokes' theorem. Integral transforms. Laplace transforms and Fourier series, integral and transform.
Use of data in engineering decision processes. Elements of probability theory. Discrete and continuous random variables. Standard distributions: binomial, Poisson, hypergeometric, exponential, normal etc. Expectation and variance. Random sampling and parameter estimation. Confidence intervals. Hypothesis testing. Goodness-of-fit tests. Regression and correlation. Statistical Process Control and quality assurance. Engineering applications in manufacturing, instrumentation and process control.
Introduction to probability (the role of probability and data in engineering; concepts of population vs. sample). Sample space and events. Definitions of probability. Conditional probability and Bayes' rule. Concept of random variables. Discrete, continuous, and joint distributions. Statistical independence. Expectation, variance, covariance, and correlation. Important discrete and continuous distributions that explain engineering-related phenomena. Brief introduction to the homogeneous Poisson process and related distributions. How to derive distributions. Transformation of random variables. Fundamental sampling distributions, Chi-square, t, and F distributions. Central limit theorem, laws of large numbers. One sample estimation (methods of maximum likelihood, bootstrapping, and jackknife) and hypothesis testing.
Data gathering motivation and methods (observational vs. experimental). Modeling for inference vs. prediction. Data visualizations. Two sample estimation and hypothesis testing. Choice of sample size. Fitting distributions to data. Goodness of fit tests. Simple linear regression and correlation. Multiple linear regression. Model building and model assessment. Design and analysis of single and multi-factor experiments. Analysis of variance. Fixed and random effects models. Multiple comparisons.
Introduction to principles, methods, and tools for the analysis, design, and evaluation of human-centred systems. Consideration of impacts of human physical, physiological, perceptual, and cognitive factors on the design and use of engineered systems. Basic concepts of anthropometrics, work-related hazards, shiftwork, workload, human error and reliability, system complexity, and human factors standards. The human-centred systems design process, including task analysis, user requirements generation, prototyping, and usability evaluation. Design of work/rest schedules, procedures, displays and controls, and information and training systems; design for error prevention and human-computer interaction; design for accessibility and aging populations.
Introduction to neuroanatomy and processes that are core to perception, memory, executive functions, language, decision making, and action. Introduction to stress and emotions, regulation of thought and behaviour, and reward processing. Case studies in Addiction, Depression, Dementia, ADHD, and Dyslexia. Role of neuroimaging and brain lesions in demonstrating the functioning of different pathways and regions of interest within the brain. Use of experiments to test hypotheses concerning brain activities and computations. Conducting a literature review and reporting experimental research, use of elementary statistics, and satisfaction of research ethics requirements.
Introduction to basic mechanical parts and mechanisms: gears, cams, bearings, linkages, actuators and motors, chain and belt drives, brakes and clutches, hydraulics and pneumatics. Tutorials on engineering drawing, sketching, and CAD/CAM in SolidWorks: views and drawing types, 2D sketching, 3D modeling and engineering drawing generation, modeling of assembly and motion analysis/animation. Conceptual design examples and mechanical engineering design process, including selection and applications of mechanisms. Dissection and reverse engineering of selected mechanical devices, mechanisms, and subsystems. Competitive group design project including technical report and 3D printing.
Instruction and assessment of communication centered around course deliverables that will form part of an ongoing design portfolio.
Introduction to algorithms (principles involved in designing, analyzing, and implementing algorithms). Basic data structures (lists, sets, maps, stacks, queues). Graphs and graph search. Decision algorithms (greedy methods and approximation algorithms). Sorting, divide-and-conquer, and recursive algorithms. Trees, heaps, and priority queues. Hashing and hash tables. Algorithmic analysis: big-O complexity. Numerical methods as examples of algorithms and big-O analysis (matrix inversion, matrix decomposition, solving linear system of equations).
Introduction to object-oriented programming using the Java programming language with heavy emphasis on practical application; variable types; console and file input/output; arithmetic; logical expressions; control structures; arrays; modularity; functions; classes and objects; access modifiers; inheritance; polymorphism; common data structures; regular expressions; GitHub; Java Swing; unit testing; introduction to complexity analysis; introduction to parallel computing; design and implementation of programs relevant to industrial engineering needs according to strict specifications.
Introduction to deterministic operations research. Formulations of mathematical models to improve decision making; linear and integer programming; the simplex method; the revised simplex method; branch-and-bound methods; sensitivity analysis; duality; network models; network simplex method; Dijkstra's algorithm; Prim’s and Kruskal’s algorithms; deterministic dynamic programming; applications of deterministic OR in machine learning; common metaheuristics.
Modeling and analysis of systems subject to uncertainty using probabilistic methods. Derivation and application of Bernoulli and Poisson processes, Markov chains, Markov decision processes, Monte Carlo simulation, and queuing models. Applications to engineering, health care, finance, and management.
Corrosion and degradation of materials; Phase transformation and strengthening mechanisms; Mechanical failure, fatigue, creep, impact; Electrical, thermal, magnetic, optical properties of materials; Composite materials.
Classifications of mechanisms, velocity, acceleration and force analysis, graphical and computer-oriented methods, gears, geartrains, cams, flywheels, mechanism dynamics.
Instruction and assessment of engineering communication that will form part of an ongoing design portfolio.
Engineering applications of thermodynamics in the analysis and design of heat engines and other thermal energy conversion processes within an environmental framework; Steam power plants, gas cycles in internal combustion engines, gas turbines and jet engines. Fossil fuel combustion, Alternative fuel combustions, fusion processes and introduction to advanced systems of fuel cells.
Introduction to quality engineering. Quality standards and certification. TQM. Modeling processes with simulation. Making inferences about product quality from real or simulation output data. Introduction to statistical process control. Control charts for variables and attributes. Process capability analysis. Lot Acceptance Sampling.
Engineering applications of thermodynamics in the analysis and design of heat engines and other thermal energy conversion processes within an environmental framework. Steam power plants, gas cycles in internal combustion engines, gas turbines and jet engines. Refrigeration, psychrometry and air conditioning. Fossil fuel combustion and advanced systems includes fuel cells.
Fluid statics, pressure measurement, forces on surfaces. Kinematics of flow, velocity field, streamlines. Conservation of mass. Fluid dynamics, momentum analysis, Euler and Bernoulli equations. Energy and head lines. Laminar flow. Flow at high Reynolds numbers, turbulence, the Moody diagram. External flows. Boundary layers. Lift and drag. Flow separation.