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• Applications of integrals: Area between curves
• Average values & Volumes
• Techniques of integration: Integrals of elementary functions
• Integrals of hyperbolic and trigonometric functions
• Integrals of Logarithmic and Exponential functions
• Integration by parts
• Integrals using substitution and Integrals of partial fractions
• Improper integrals.
• Mid Term Exams
• Arc length and Area of a surface of revolution.
• Sequences and series, Convergence and Absolute convergence, Tests for convergence
• Integral test, P series test, Comparison test, Limit comparison test, Alternating Series test, Ratio test, Root test
• Power series, Convergence of power series, Representation of functions as power series
• Differentiation and Integration of power series, Taylor and McLauran series
• Conic section and Parameterized curves and polar coordinates
• Curves defined by parametric equations, Calculus with parametric curves, Tangents, Areas, Arc length
• Polar coordinates, Polar curves, Tangents to polar curves, Areas and arc length in polar coordinates.
• Final Term Exam