Mathematics Notes
A collection of mathematics notes and interactive demonstrations
Topics
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Algebra
Analysis
- Continuity in Euclidean and Metric Spaces
- Sequences in Euclidean and Metric Spaces
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Complex Analysis
- Algebraic Properties
- Regions of the Complex Plane
- Complex Functions
- Limits and Continuity of Complex Functions
- Derivatives of Complex Functions
- Harmonic Functions
- Zeros and Singularities
- Elementary Functions
- Complex Indefinite Integrals
- Contour Integrals
- Indepenence of Path of Contour Integrals
- Cauchy-Goursat Theorem
- Cauchy Integral Formula
- Taylor and Maclaurin Series
- Laurent Series
- Classification of Singularities
Applied
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Differential Equations
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Ordinary Differential Equations
- ODE Credits
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Chapter 01 Basic Concepts
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Chapter 02 Special Types Of First Order Equations
- Meaning of the Differential
- First Order Differential Equation with Homogenous Coefficients
- Differential Equations with Linear Coefficients
- Exact Differential Equations
- Recognizable Exact Differential Equations
- The Linear Differential Equation
- Equations Permitting a Choice of Method
- Summary of First Order Differential Equations
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Chapter 03 Problems Leading To First Order Equations
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Chapter 04 Linear Differential Equations Of Order Greater Than One
- Linear Independence of Functions. The Linear Differential Equation of Order n.
- Solution of the Homogeneous Linear Differential Equation of Order n with Constant Coefficients
- Solution of the Nonhomogeneous Linear Differential Equation of Order n with Constant Coefficients (Method of Undetermined Coefficients)
- Solution of the Nonhomogeneous Linear Differential Equation by the Method of Variation of Parameters
- Solution of the Linear Differential Equation with Nonconstant Coefficients. Reduction of Order Method.
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Chapter 05 Operators And Laplace Transforms
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Chapter 06 Problems Leading To Linear Equations Of Order Two
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Chapter 90 Series Solutions
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Chapter 91 Initial And Boundary Values Problems
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Partial Differential Equations
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Discrete
- Recurrence Relations
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Cellular Automata
Foundations
- Set Theory
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Logic And Proofs