LasthrimProjection

A mathematics undergraduate summarization book with JULIA and Python codes

Coverage:

1. Calculus
2. Basic Elementary Linear Algebra
3. Basic Discrete Mathematics
4. Basic Probability and Statistics
5. Basic Dynamical System and Bifurcation Theory
6. Differential Equations
7. Partial Differential Equation
8. Introduction to Real Analysis

Lasthrim Projection Book

The current book can be seen here (in pdf format):

Lasthrim Projection book (July 18th, 2024)

Lasthrim Projection' Galleries for JULIA-Calculus

Chapter 0: Preliminaries	Chapter 1: Limits
ch0-7-plotsincoswithpi.jl	ch1-1-plotlimitfunctions.jl

Chapter 2: The Derivative	Chapter 3: Applications of the Derivative
ch2-2-thederivative-leibniznotation.jl	ch3-5-applicationsofthederivative-example1-f(x).jl

Chapter 4: The Definite Integral	Chapter 5: Applications of the Integral
ch4-6-trapezoidalruleplot	ch5-2-solidofrevolution

Lasthrim Projection' Galleries for JULIA-Elementary Linear Algebra

Chapter 1: Systems of Linear Equations and Matrices	Gaussian Elimination
ElementaryLinearAlgebra.ipynb

Chapter 1: Row Reduction with Variables	Chapter 2: Cramer's Rule

Chapter 3: Euclidean Vector Spaces	Chapter 3: Norm of a Vector in 3-D

Chapter 10: Fractals-Sierpinski Triangle	Coming soon
ch10-13-fractals-sierpinskitriangle1.jl

Lasthrim Projection' Galleries for JULIA-Discrete Mathematics

Chapter 1: Logic and Proofs	Chapter 2: Sets, Functions, Sequences, and Sums
ch1-tautology.jl	ch2-venndiagram.jl

Lasthrim Projection' Galleries for JULIA-Differential Equations

Chapter 1.1: Direction Fields	Chapter 1.2: Solutions of Some Differential Equations
ElementaryDifferentialEquations.ipynb

Chapter 2.2: Direction Field and Integral Curves	Chapter 2:
ElementaryDifferentialEquations.ipynb

MyLeo Pendulum	Wait for it
pendulumplot1.jl

Lasthrim' Galleries for JULIA-Real Analysis

Chapter 1: Logic and Proofs	Chapter 2: Quantifiers
RealAnalysis.ipynb

Chapter 3: Rational Numbers	Chapter 4: Trigonometric Functions
RealAnalysis.ipynb

Chapter 5: Complex Numbers	Chapter 6: Sequences
RealAnalysis.ipynb

Lasthrim Projection' Galleries for Python-Calculus

Cycloid Animation	Cycloid Around Cycloid
Click	Click

3D Prism	3D Half Cylinder
Click	Click

3D Cylinder Plot	Solid of Revolution Around x and y
Click	Click

Lasthrim Projection' Galleries for Python-Differential Equations

Vector Field	Vector Field Changing Color
Click	Click

Vector Field 3D	Electromagnetic Field Plot
Click	Click

Heat Equation 3D Plot	Heat Equation 2D Plot
Click	Click

Finite Difference 3D Cube	Finite Difference 3D Solution to Heat Equation
Click	Click

Inverse Laplace Transform Plot	Laplace Transform 3D Plot
Click	Click

Laplace Transform Plot	Laplace Transform Computation
Click	Click

Fourier Transform Plot	Fourier Series Animation
Click	Click

Fourier Series: Time to Frequency Spectrum	Fourier Series 3 Sine Waves
Click	Click

Fourier Series 3D Synthesis DFT	Fourier Series Real Form
Click	Click

Fourier Series Computing	Fourier Series DFT
Click	Click

Lasthrim Projection' Galleries for Python-Partial Differential Equations

Heat Equation 1 dimension	Fourier Series Computation and Plot
Click	Click

Lasthrim Projection' Galleries for Python-Recursive

Maze Solver	Sliding Tile Solver
Click	Click

Barnsley Fern	Sierpinski Carpet
Click	Click

Koch Snowflake	Hilbert Curve
Click	Click

Droste Maker	Flood Fill
Click	Click

Source

1. Purcell, Edwin J., Varberg Dale, Rigdon, Steven E. Calculus 9th Edition
2. https://stackoverflow.com/
3. Rorres, Chris, Anton, Howard. Elementary Linear Algebra with Supplemental Applications 10th Edition
4. Boyce, William E., DiPrima, Richard C. Elementary Differential Equations and Boundary Value Problems 9th Edition
5. Simmons, George F., Differential Equations With Applications and Historical Notes 3rd Edition
6. Julia Discourse (https://discourse.julialang.org)