CalculusI, II, III: Calculus II
Course Outline
Techniques of integration: Integrals of elementary, hyperbolic, trigonometric, logarithmic and exponential functions.
Integration by parts, substitution and partial fractions. Approximate integration. Improper integrals. Gamma functions.
Applications of integrals: Area between curves, average value. Volumes. Arc length.
Area of a surface of revolution. Applications to Economics, Physics, Engineering and Biology.
Infinite series: Sequences and series. Convergence and absolute convergence.
Tests for convergence: divergence test, 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 McLaurin series. Approximations by Taylor polynomials.
Conic section, 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.
Text Books
Related books
E Books

PietroLuciano Buono
Publisher: De Gruyter
Date of Publication: 2016 
W. W. Sawyer
Publisher: Mathematical Association of America
Date of Publication: 1961 
C.B. Gupta, A.K. Malik, and V. Kumar
Publisher: New Age International Pvt. Ltd., Publishers
Date of Publication: 2009 
Carla C. Morris and Robert M. Stark
Publisher: Carla C. Morris and Robert M. Stark
Date of Publication: 2015 
David Perkins
Publisher: Mathematical Association of America
Date of Publication: 2012 
J. David Logan
Publisher: John Wiley & Sons, Incorporated
Date of Publication: 2013 
N. S. Narasimha Sastry, Mohan Delampady, and B. Rajeev
Publisher: World Scientific Publishing Co Pte Ltd
Date of publication: 2009