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Learning UNIVERSITY CALCULUS Made Easy

Course offered by : Nazir

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Course Id: 185


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Details


https://www.youtube.com/watch?v=MUIje0PsUXo

Simplified version of University Calculus that will help each and every students to learn and achieve a better score.

Topics covered / Highlights


This is a list of calculus topics.

Contents

  • Limits
  • Differential calculus
  • Integral calculus
  • Special functions and numbers
  • Numerical integration
  • Lists and tables
  • Multivariable
  • Series
  • History
  • Nonstandard calculus

Limits

  • 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
  • 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
  • Rolle's theorem

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
  • Shell integration

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

Multivariable

  • Partial derivative
  • Disk 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

Who can attend this ?


University Students , University Teachers

Pre requisites


Basic Knowledge of secondary Mathematics

What am I going to get from this Class ?


The sky is the Limit for learning.

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Trainer Profile


Nazir

Master of Mathematics

10 Years Teaching Experience , Successful & Satisfied students , High Quality teaching knowledge


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