Mathematics-I
Created by Pavl_G
Outline:
This repository houses re-usable equations and formulas for the following:
- Calculus
- Functions.
- Transcendental functions.
- Differential calculus.
- The Chain Rule.
- Fundamental theorem of calculus.
- Integration by parts (anti-derivation of the chain rule).
- First-order differential equations.
- Second-order differential equations.
- Vectors.
- Basic operations on vectors.
- Dot product and projection vectors.
- Cross product.
- Triple product.
- Polar coordinates.
- Polar-to-rectangular coordinates.
- Vectorial analysis using the fundamental theorem.
- Appendices: Proofs
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- Appendix-A: Derivation of the first-order differential equations for the transcendental functions.
- Appendix-B: Derivation of the trigonometric identities.
- Appendix-C: Derivation of the fundamental theorem part-01 & part-02.
- Appendix-D: Derivation of the vector normalization formula.
- Appendix-E: Derivation of the dot product and the projection vectors.
- Appendix-F: Derivation of the cross product.
- Appendix-G: Derivation of the triple product.
- Appendix-H: Derivation of the vectorial polar coordinates from the rectangular coordinates.
- Appendix-I: Mathematical analysis models (univariable & multivariable), and continuum to Mathematics-II.
- =============================
- Discrete Mathematics
- Sets & Relations.
- Types of relations: Paths. Operations. Undetermined relations.
- Finite-State-Automaton.
- Mapping FSA using Sets and Relations.
- Manipulating relations in computerized data structures.
- Mapping FSA using vectors and matrices data structures.
- Algorithms on FSA.
- Asymptotic analysis on FSA.
- The fundamental theorem of calculus in FSA-based algorithms.
- Appendices
- =============================
- Appendix-A: Symbolic Designation of mathematical analysis
- Appendix-B: Algorithm Analysis
- Appendix-C: Analysis by example
- Appendix-D: FSA Analysis.
- Appendix-F: Time-warp states and FSA.
- Appendix-E: Implementation using Automata4j.
- =============================
- Linear algebra
- Elimination methods.
- Gaussian’s Elimination.
- Vectorial matrices.
- Linear dependance and independence.
- Linear Interpolation.
- Linear Extrapolation.
- Eigenvalues.
- Appendices
- =============================
WIP
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pepogerges33@gmail.com
Tel
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Egypt, Cairo