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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