Structure and Matrices in Julia Programming - Lecture 3
Explore matrices, sparse structures, and SVD for image compression and computational thinking in Julia, with practical applications in machine learning and linear algebra.
Tricks and Tips in Numerical Computing - Keynote
Explore advanced numerical computing techniques, from complex differentiation to low-precision arithmetic, with insights on error analysis, matrix operations, and IEEE standards for improved computational accuracy and efficiency.
Get Ready for Polynomials in Algebra 2
Comprehensive guide to mastering polynomials in Algebra 2, covering factoring, simplification, graphing, and solving using the quadratic formula. Essential preparation for advanced algebraic concepts.
Excel Array Formulas & Functions - 50 Examples of How to Become an Array Expert
Master Excel array formulas with 50 practical examples, covering fundamental concepts, advanced functions, and real-world applications for data analysis and reporting.
Review of Complex Numbers
Comprehensive overview of complex numbers, covering imaginary unit i, operations, simplification, graphing, and absolute value. Ideal for students seeking a thorough understanding of complex number concepts.
3D on Apple II
Explore 3D graphics on Apple II+ using AppleSoft BASIC. Learn matrix math, rotation techniques, and cube rendering in this nostalgic coding challenge.
Systems of Differential Equations - Diagonalization and Jordan Canonical Form
Explore diagonalization and Jordan Canonical Form for systems of differential equations, covering eigenvectors, complex conjugates, repeated eigenvalues, and general matrix applications.
Non-Normal Linear Systems and Transient Energy Growth - Bypass Transition to Turbulence
Explore non-normal linear systems and their role in turbulence, including examples, code demonstrations, and applications in fluid dynamics and bypass transition.
Drawing Phase Portraits for Nonlinear Systems
Learn to analyze nonlinear systems by drawing phase portraits, identifying fixed points, linearizing, and inferring global dynamics. Gain practical skills in stability analysis using eigenvalues and eigenvectors.
Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points
Explore imaginary eigenvalues and center fixed points in 2D ODE systems. Learn to compute eigenvectors, write solutions, and understand geometric intuition behind rotational dynamics.
Systems of ODEs - Saddle Points and Instability
Explore unstable saddle points in 2D linear ODEs, their applications in energy-efficient transport, and analysis using eigenvalues, eigenvectors, and phase portraits.
Eigenvalues and Eigenvectors
Explore eigenvalues and eigenvectors, key concepts in linear algebra. Learn to compute them for any matrix, understand their significance in transformations, and apply them to solve complex linear systems.
More Examples of Second Order Differential Equations
Explore advanced examples of second-order ODEs, including characteristic polynomials, initial conditions, and matrix systems. Learn to solve, plot, and interpret results using MATLAB.
Engineering Math Pre-Req - Quick and Dirty Introduction to Python
High-level introduction to essential Python commands for engineering math, covering arithmetic, loops, arrays, plotting, and solving equations and differential equations.
Engineering Math Pre-Req - Quick and Dirty Introduction to Matlab
High-level introduction to essential Matlab commands for engineering math, covering arithmetic, loops, matrices, plotting, and solving equations and differential equations.
Gentle Introduction to Modeling with Matrices and Vectors - A Probabilistic Weather Model
Explore probabilistic weather modeling using matrices and vectors, with practical examples in Python and MATLAB. Learn to represent and update weather states mathematically.
Learn NumPy in 30 Minutes
Master essential NumPy functions for efficient array operations, data manipulation, and numerical computing in Python. Covers basics to advanced topics like multidimensional arrays, broadcasting, and linear algebra.
Equations of Lines Practice Test Full Solutions
Comprehensive step-by-step solutions for linear equations practice test, covering slope-intercept, point-slope, and standard forms. Ideal for mastering various methods of line representation and manipulation.
Parallel and Perpendicular Lines Practice Test - Full Solutions
Step-by-step solutions for determining parallel and perpendicular lines, including examples and practice problems to reinforce understanding of slope relationships and line equations.
Determine if Three Points are Collinear - Distance Formula Method Practice Test Full Solutions
Step-by-step solutions for determining collinearity using the distance formula method, covering five practice problems. Includes explanations of alternative, more efficient approaches.
Matrix Transpose Isn't Just Swapping Rows and Columns
Explore a unique visualization of matrix transpose, focusing on changing perspective rather than swapping rows and columns. Gain insights into covectors, metric tensors, and adjoints in various fields.