This page contains a collection of my notes and formula sheets from courses I've taken at the University of Alberta. Feel free to use, share, and modify at your leisure. Please keep in mind that these notes were designed to provide a quick reference during examinations, so please be aware of things that your course may include that I haven't included in my notes. All pdfs were typeset using LaTeX unless XeLaTeX was specified in the preamble of the .tex file.
Mathematics
| Class | Description | TeX | |
|---|---|---|---|
| Calculus II (MATH 101) | 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. | series_strategy.pdf | series_strategy.tex |
| Differential Equations (MATH 201) | First-order equations; second-order linear equations: reduction of order, variation of parameters; Laplace transform; linear systems; power series; solution by series; separation of variables for PDEs. | pde_strategy.pdf | pde_strategy.tex |
| Theory of Functions of a Complex Variable (MATH 311) | Complex numbers. Complex series. Functions of a complex variable. Cauchy's theorem and contour integration. Residue Theorem and its applications. Inverse Laplace transform. |
Electrical Engineering
| Class | Description | TeX | |
|---|---|---|---|
| Electrical Circuits II (ECE 203) | The main objective of the course is to introduce students to standard methods for analyzing and solving different types of RLC circuits. Steady-state and dynamic behaviour of first and second order circuits will be studied using conventional time-domain and frequency-domain tools. The concept of complex frequency and generalized phasors will be introduced as a means to facilitate steady-state AC analysis. The complete circuit response will be investigated by examining both the natural and forced responses. Laplace transforms, transfer functions and bode plots will be used as circuit analysis tools. Basic non-linear circuit elements such as the diode and operational amplifier will also be studied in the course. The analysis of large circuits with passive elements will be explored by utilizing two-port network models. | ece203.pdf | ece203.tex |
| Introduction to Digital Logic Design (ECE 210) | Boolean algebra, truth tables, Karnaugh maps. Switching devices and their symbology with an introduction to NAND and NOR logic. Number systems, codes, minimization procedures, synthesis of combinational networks. Synchronous sequential circuits, flip-flops, counters. Arithmetic circuits. Introduction to computer-aided design and simulation tools for digital design and implementation. | ece210.pdf | ece210.tex |
| Continuous Time Signals and Systems (ECE 240) | Introduction to linear systems and signal classification. Delta function and convolution. Fourier series expansion. Fourier transform and its properties. Laplace transform. Analysis of linear time invariant (LTI) systems using the Laplace transform. | ece240.pdf | ece240.tex |
Physics
| Class | Description | TeX | |
|---|---|---|---|
| Wave Motion, Optics and Sound (PHYS 130) | This is a course about the physics of oscillating systems, an example of which is a the simple pendulum, and the incredibly important phenomenon which arises from systems of connected oscillators: waves. Once we have understood the physical properties of mechanical waves, such as sound waves, which rely on a physical medium to propagate we shall consider electromagnetic waves. The different properties of EM waves, which being a fundamental field require no medium to propagate, meant that the wave nature of light was unknown for centuries and we shall discuss basic geometric optics, where light is treated as rays, before moving on to show the wave nature of light through various interference phenomena. | ||
| Classical Mechanics (PHYS 244) | Newton's laws of motion; projectiles and charged particles; momentum and angular momentum; conservative forces and energy; oscillations, coupled oscillators and normal modes; calculus of variations; Lagrangian mechanics; two-body central force problems; Hamiltonian mechanics. | phys244.pdf | phys244.tex |
| Introduction to Modern Physics (PHYS 271) | Experimental evidence for limitations of classical physics; review of special relativity: quantization of charge, light, and energy; blackbody radiation, photoelectric effect, Compton effect; models of the atom; wavelike properties of particles; the uncertainty principle, the Schrödinger equation, the infinite and finite square well, the harmonic oscillator, tunneling; the hydrogen atom, orbital angular momentum and electron spin; spin and statistics; selected topics. | phys271.pdf | phys271.tex |
| Electricity and Magnetism (PHYS 281) | Electric fields; Gauss' law; electric potential; capacitance and dielectrics; electric current and resistance; DC circuits; magnetic fields; Ampere's Law; Faraday's Law; inductance; magnetic properties of matter, AC circuits; Maxwell's equations; electromagnetic waves. | phys281.pdf | phys281.tex |
| Experimental Physics for Engineers (PHYS 292) | This course aims to teach general methods for measurement and general principles of data analysis utilizing classical experiments with emphasis on developing transferable skills. Experiments in mechanics, electromagnetism and atomic physics. | phys292.pdf | phys292.tex |
Engineering (Miscellaneous)
| Class | Description | TeX | |
|---|---|---|---|
| Introduction to Tangible Computing I and II (CMPUT 274/275) | CMPUT 274/275 is an experimental 2-course pilot introduction to computer science. It integrates the introductory computing courses (CMPUT 174/175) with the second-year introductory algorithms course (CMPUT 204) and the second-year introductory systems course (CMPUT 201). The course uses a problem-based approach to motivate the concepts and illustrate their application. It will be using the Arduino concrete-computing platform so that students will both become familiar with the typical screen-keyboard-mouse style of computing, but also the kind of embedded computing that is behind the scenes in the many devices that surround us. Delivery is hands-on, with the classes taking place in the lab environment. | ||
| Introduction to Reinforcement Learning (CMPUT 365) | This course provides an introduction to reinforcement learning, which focuses on the study and design of learning agents that interact with a complex, uncertain world to achieve a goal. The course will cover multi-armed bandits, Markov decision processes, reinforcement learning, planning, and function approximation (online supervised learning). The course will take an information-processing approach to the study of intelligence and briefly touch on perspectives from psychology, neuroscience, and philosophy. | ||
| Engineering Mechanics (ENGG 130) | Equilibrium of planar systems. Analysis of statically determinate trusses and frames. Friction. Centroids and centres of gravity. Forces and moments in beams. Second moments of area. Note: Students in all sections of this course will write a common final examination. | engg130.pdf | engg130.tex |
| Mechanics (EN PH 131) | Kinematics and dynamics of particles; gravitation; work and energy; linear momentum; angular momentum; systems of particles; introduction to dynamics of rigid bodies. | enph131.pdf | enph131.tex |
| Materials Science I (MAT E 201) | An introduction to the science of materials from the standpoint of the relationships between atomic, molecular and crystal structure to material properties. Atomic bonding, crystal structure and crystal imperfections. Structures of metallic, non-metallic and composite materials. Diffusion, electrochemical and corrosion properties; strengthening mechanisms, mechanical properties and failure; electrical conductors, semiconductors, and dielectrics; thermal, magnetic, and optical properties. | mate201.pdf | mate201.tex |
| Introductory Statistics for Engineering (STAT 235) | Descriptive data analysis. Calculus of probability. Binomial, multinomial, Poisson, normal, beta, exponential, gamma, hypergeometric, and Weibull distributions. Sampling distributions. Estimation, testing hypotheses, goodness-of-fit tests, and one-way analysis of variance. Linear correlation and regression. Sampling. Quality control. Use of a microcomputer software package for statistical analyses in engineering applications. | stat235.pdf | stat235.tex |