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Applied Calculus-I & II: Course Outline

Objective: Teach the concepts of calculus and analytic geometry and the applications of these concepts to the solution of engineering problems.

Calculus-I

  • Complex Numbers
  • DeMoivre’s Theorem and its Applications
  • Simple Cartesian Curves
  • Functions and Graphs
  • Symmetrical Properties
  • Curve Tracing
  • Limit and Continuity
  • Differentiation of Functions
  • Derivative as Slope of Tangent to a Curve and as Rate of Change
  • Application to Tangent and Normal
  • Linearization
  • ​ Maxima/Minima and Point of Inflexion
  • Taylor and Maclaurin Expansions and their convergence
  • Integral as Anti-derivative
  • Indefinite Integration of Simple Functions

Methods of Integration:

  • Integration by Substitution
  • Integration by Parts
  • Integration by Partial Fractions
  • Definite Integral as Limit of a Sum
  • Application to Area
  • Arc Length
  • Volume and Surface of Revolution
  • Complex Numbers
  • DeMoivre’s Theorem and its Applications
  • Simple Cartesian Curves
  • Functions and Graphs
  • Symmetrical Properties
  • Curve Tracing
  • Limit and Continuity
  • Differentiation of Functions
  • Derivative as Slope of Tangent to a Curve and as Rate of Change
  • Application to Tangent and Normal
  • Linearization
  • ​Maxima/Minima and Point of Inflexion
  • ​Taylor and Maclaurin Expansions and their convergence
  • Integral as Anti-derivative
  • Indefinite Integration of Simple Functions.

Methods of Integration:

  • Integration by Substitution
  • Integration by Parts
  • Integration by Partial Fractions
  • Definite Integral as Limit of a Sum
  • Application to Area
  • Arc Length
  • Volume and Surface of Revolution

Calculus-II

 

  • Functions of Several Variables
  • Partial Differentiation
  • Multiple Integrals
  • Line Integrals
  • Surface Integrals
  • Green’s and Stoke’s Theorem
  • Fourier series
  • Periodic functions
  • Functions of any period P = 2L
  • Even functions
  • Odd functions
  • Half Range expansions
  • Fourier Transform
  • Laplace Transform
  • Z-Transform

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