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Engineering Mathematics

lastmod 2018-08-27created 2015-02-129 edits

Learning Course

  1. EngineeringMathematics:Course:Basic: Engineering mathematics basics
  2. EngineeringMathematics:Course:LinearEquation: Linear equations
  3. EngineeringMathematics:Course:PythagoreanTheorem: Pythagorean theorem
  4. EngineeringMathematics:Course:Circle: Equation of a circle
  5. EngineeringMathematics:Course:LogarithmicFunction: Logarithmic functions

Table of content

Engineering mathematics STUDY INDEX.

  1. Basics: EM_turtle-01_Basics.7z
    1. Pythagorean Theorem
    2. Square Root of 2 is an Irrational Number
    3. Trigonometric Function
    4. Sum and Difference Identities of trigonometric functions
    5. Equation of a Circle
    6. Equation of a Parabola
    7. A beautiful number, Euler's Number
    8. Origin of the logarithmic function (Logarithmic Function)
    9. Decibel and Logarithmic Function
    10. Complex Number
    11. Homogeneous Function
  2. Calculus: EM_turtle-02_Calculus.7z
    1. Meaning of differentiation (Differentiation)
    2. Meaning of the limit (Limit)
    3. Why did Cauchy agonize over limits?
    4. Squeeze Theorem
    5. Mean Value Theorem
    6. Intermediate Value Theorem
    7. Fixed Point Theorem
    8. Extreme Value Theorem
    9. Meaning of integration (Integration)
    10. Mean value theorem in integral form (Mean Value Theorem for Integraiton)
    11. Exact Differential
    12. L'Hopital's Rule
  3. Analysis: EM_turtle-03_Analysis.7z
    1. Monotone Convergence Theorem
    2. Infinite Series
    3. Taylor Series
    4. Harmonic Series and Euler-Mascheroni Constant
    5. Infinite Product
    6. Dirac's Delta Function
  4. Differential Equation: EM_turtle-04_Differential_Equation.7z
    1. Meaning of differential equations (Differential Equation)
    2. Linear Ordinary Differential Equation
    3. Solution of ODE Based on Power Series
      1. Application of Frobenius Method
    4. Solution of the First Order Linear Ordinary Differential Equation
    5. Sturm-Liouville Theory
      1. Completeness of Eigenfunctions
    6. Bessel's Differential Equation
    7. Spherical Bessel's Differential Equation
    8. Legendre's Differential Equation
  5. Linear Algebra: EM_turtle-05_Linear_Algebra.7z
    1. Matrix
    2. Determinant
    3. Geometric Meaning of Determinant
  6. Vector and Tensor: EM_turtle-06_Vector_and_Tensor.7z
    1. Quarternion
    2. Coordinate-system-based vectors (Vector)
    3. Meaning of the gradient (Gradient)
    4. Meaning of divergence (Divergence)
    5. Meaning of curl (Curl)
    6. Vector Identity
    7. Helmholtz' Theorem
    8. Green's Identity
    9. Tensor
    10. Tensor and Coordinate Transformation
    11. Tensor Calculus
    12. Tensor Calculus for Orthogonal Coordinate Systems
      1. Circular Cylindrical Coordinate System
      2. Spherical Coordinate System
  7. Complex Analysis: EM_turtle-07_Complex_Analysis.7z
    1. An easy understanding of complex analysis (Introduction to Complex Analysis)
    2. Laurent Series
    3. Multi-Valuedness of Complex Function
  8. Fourier Series and Integral Transform: EM_turtle-08_Fourier_Series_and_Integral_Transform.7z
    1. The beginning of Fourier series (Fourier Series)
    2. Riemann-Lebesgue Lemma
    3. The younger brother who surpasses the elder: Fourier Transform
    4. Hankel Transform
  9. Probability and Statistics: EM_turtle-09_Probability_and_Statistics.7z
    1. Probability
    2. Permutation and Combination
    3. Binomial Theorem
    4. Statistics
  10. Special Functions: EM_turtle-10_Special_Functions.7z
    1. Gamma Function
    2. Incomplete Gamma Function
    3. Digamma Function
    4. Beta Function
    5. Bessel Function
      1. Asymptote of Bessel Function
    6. Exponential Integral
    7. Sine Integral
    8. Cosine Integral

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