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# Course Details ### Learning UNIVERSITY CALCULUS Made Easy

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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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## Nazir

Master of Mathematics

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

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