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Lecture Notes
Below are the lecture notes from my course on multivariable calculus, as well as some
handouts I give to students for some of the experiments in the introductory physics
lab courses. Note that I update my notes each term, but this website may not link to
the latest editions.
Notes on MTH3015: Calculus III
Visualizing 3D Curves with WolframAlpha
Week 1: Introduction to 2D and 3D co-ordinate spaces; introduction to vector, vector spaces, vector operations
Week 2: Parametrization
Week 3: Vector-valued Functions; Curves
Week 4: Functions of Several Variables; Limits and Continuity
Week 5: Partial Derivatives; The Chain Rule
Week 7: Directional Derivative and Gradient
Week 8: Taylor Series and Extrema
Week 9: Double Integrals; Polar Integrals
Week 10: Triple Integrals; Cylindrical and Spherical Co-ordinates
Week 11: The Transformation Theorem
Notes on IPL/CPS Physics Labs
Lab Report Grading Structure
Experiment 9: Maxwell's Wheel
Experiment 12: The Simple Pendulum
Experiment 13: Simple Harmonic Motion
$\newcommand{\vect}[1]{{\mathbf{#1}} }$
$\renewcommand{\vec}[1]{{\overrightarrow{#1}} }$
$\newcommand{\norm}[1]{{\left|\left|#1\right|\right|} }$
$\newcommand{\D}{{{\mathcal D}} }$
$\newcommand{\C}{{{\mathcal C}} }$
$\newcommand{\E}{{{\mathcal E}} }$
$\newcommand{\R}{{\mathbb{R}} }$
$\newcommand{\Rtwo}{{\mathbb{R}^2} }$
$\newcommand{\Rthree}{{\mathbb{R}^3} }$
$\newcommand{\V}{{\mathbb{V}} }$
$\newcommand{\T}{{\mathbb{T}} }$
$\newcommand{\nhat}{{\vect{\hat{n}}} }$
$\newcommand{\vi}{{\vect{i}} }$
$\newcommand{\vj}{{\vect{j}} }$
$\newcommand{\vk}{{\vect{k}} }$
$\newcommand{\f}{{\vect{f}} }$
$\newcommand{\g}{{\vect{g}} }$
$\newcommand{\vz}{{\vect{0}} }$
$\newcommand{\Du}{{D_{\vect{u}}} }$
$\DeclareMathOperator{\sgn}{sgn}$
$\DeclareMathOperator{\dist}{dist}$
$\DeclareMathOperator{\area}{Area}$
$\DeclareMathOperator{\vol}{Volume}$
$\newcommand{\xcm}{{x_\mathrm{CM}} }$
$\newcommand{\ycm}{{y_\mathrm{CM}} }$
$\DeclareMathOperator{\grad}{\bf grad}$
$\DeclareMathOperator{\ave}{ave}$
$\DeclareMathOperator{\std}{std}$
Notes on Experiment 13: Simple Harmonic Motion
Sujeet Akula
SHM without Extra Weights
Damped Harmonic Motion
Experiment 14: Standing Waves
Experiment 16: Electric Field and Electric Potential