plpconsult
plpconsult

Calculus thru differential equations

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20.00 USD /single lesson (60 min.)
Science / Math

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General information

nick plpconsult
country Switzerland
languages English
contact

Education

2 years calculus thru differential equations with a course gpa of 3.7

2 years of graduate school including multivariable calculus energy methods, finite element analysis, matrix mathematics, hydrodynamics and structural dynamics and advanced structural design.

plus 38 years in design and engineering analysis thru contruction.

Experience: 4 years

About me

Before calculus (precalculus)
  • Graph of a function
  • Linear function
  • Secant line
  • Slope
  • Tangent
  • Concave function
  • Finite difference
  • Radian
  • Factorial
  • Binomial theorem
  • Free variables and bound variables
Limits[edit]
  • Limit (mathematics)
  • Limit of a function
    • One-sided limit
  • Limit of a sequence
  • Indeterminate form
  • Orders of approximation
  • (ε, δ)-definition of limit
Differential calculus
  • Derivative
  • Notation
    • Newton's notation for differentiation
    • Leibniz's notation for differentiation
  • Simplest rules
    • Derivative of a constant
    • Sum rule in differentiation
    • Constant factor rule in differentiation
    • Linearity of differentiation
    • Power rule
  • Derivative (examples)
  • Chain rule
  • local linearization
  • Product rule
  • Quotient rule
  • Inverse functions and differentiation
  • Implicit differentiation
  • Stationary point
    • Maxima and minima
    • First derivative test
    • Second derivative test
    • Extreme value theorem
  • Differential equation
  • Differential operator
  • Newton's method
  • Taylor's theorem
  • L'Hôpital's rule
  • General Leibniz rule
  • Mean value theorem
  • Logarithmic derivative
  • Differential (calculus)
  • Related rates
  • Regiomontanus' angle maximization problem
Integral calculus
  • Antiderivative/Indefinite integral
  • Simplest rules
    • Sum rule in integration
    • Constant factor rule in integration
    • Linearity of integration
  • Arbitrary constant of integration
  • Fundamental theorem of calculus
  • Integration by parts
  • Inverse chain rule method
  • Integration by substitution
    • Tangent half-angle substitution
  • Differentiation under the integral sign
  • Trigonometric substitution
  • Partial fractions in integration
    • Quadratic integral
  • Proof that 22/7 exceeds π
  • Trapezium rule
  • Integral of the secant function
  • Integral of secant cubed
  • Arclength
Special functions and numbers
  • Natural logarithm
  • e (mathematical constant)
  • Exponential function
  • Hyperbolic angle
  • Hyperbolic function
  • Stirling's approximation
  • Bernoulli numbers
Numerical integration
  • Rectangle method
  • Trapezium rule
  • Simpson's rule
  • Newton–Cotes formulas
  • Gaussian quadrature
Lists and tables
  • Table of common limits
  • Table of derivatives
  • Table of integrals
  • Table of mathematical symbols
  • List of integrals
  • List of integrals of rational functions
  • List of integrals of irrational functions
  • List of integrals of trigonometric functions
  • List of integrals of inverse trigonometric functions
  • List of integrals of hyperbolic functions
  • List of integrals of exponential functions
  • List of integrals of logarithmic functions
  • List of integrals of area functions
Multivariable
  • Partial derivative
  • Disk integration
  • Shell integration
  • Gabriel's horn
  • Jacobian matrix
  • Hessian matrix
  • Curvature
  • Green's theorem
  • Divergence theorem
  • Stokes' theorem
Series
  • Infinite series
  • Maclaurin series, Taylor series
  • Fourier series
  • Euler–Maclaurin formula