Applied Calculus-I & II: Course Outline

• 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

• 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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