INSTITUTE OF BUSINESS ADMINISTRATION
BS III PROGRAM
(MORNING)
COURSE OUTLINES
Course Title: Calculus II
Semester:
Fall 2009
Number:
MTS111
Credit Hrs:
3
Teacher:
Muhammad Imtiaz
Note: Class meets twice a week each time for a 75 minute session
TEXT BOOK:
 Calculus by Howard Anton, IRL Bivens, Stephen, 5th Edition, John Wiley and Sons.
 Differential Equations and Boundary Value Problems by Denis G. Zill and Michael R. Cullen, 3rd Edition, PWS
Publishing Company.
REFERENCE BOOKS:
 Calculus by Swokowski, 5th Edition, PWS Publishing Company.
 Calculus by M.N.M.Talpur, Sindh Text Book Board, Jamshoro, Sindh.
Course Plan:
Assessment Scheme:
Two Tests each of 20 marks during semester
Quizzes & Assignment (around 5 marks each)
Terminal Examination
Total
Grading Scheme:
= 40 marks
= 20 marks
= 40 marks
= 100 marks
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Topics covered
Introduction to conic sections, Definition of Parabola, Ellipse and
Hyperbola, Translation of coordinate axes, Geometrical properties of
parabola, ellipse and hyperbola,
Standard equations of parabola, ellipse and hyperbola, Generalized
Quadratic equation in x and y. Rotation of axes, Elimination of cross
product term.
Rotation of axes, Elimination of cross product term, The Discriminant,
Sketchs of conic sections from general quadratic equations.
Rectangular coordinate system in space, Distance, Midpoint and Sphere,
generalized and standard equations of sphere, cylindrical surfaces.
Vectors in geometrically and in coordinate system, Rules for vector
arithmetic, Dot and Cross product, Orthogonal vectors.
Direction cosines, direction ratios, properties of dot and cross product,
Triple scalar product.
Parametric equations of lines, vector equations of lines, line segment.
Shortest distance between two lines, angle between two lines.
Coordinate planes, Planes parallel to the coordinate planes.
Equations of plane in 3-Dimension (cont.)
Distance between point and a plane, angle between two planes, Some
quadratic surfaces.
The Gradient, Properties of the gradient, gradient as normal to the level
curve,
Divergence, curl and their properties.
Gauss’s theorem
Green’s theorem
Double and Triple Integrals in Cartesian
Cylindrical and Spherical Coordinates System
Applications of Double and Triple Integrals
Definition of Sequence, Graphs of sequences, Limit of a Sequence
Monotone sequences, Testing for monotonicity
Eventually monotone sequences, Convergence of monotone sequence.
Sums of infinite series, convergence of infinite series
Geometric series, Harmonic series, Convergence Test, Divergence Test
Algebraic properties of infinite series, Integral test, p-series,
Comparison test, Ratio test, Root test, Limit comparison test.
Orthogonal functions, Orthogonal set,
Norm, Square norm, Generalized Fourier series,
Fourier series, Even and Odd functions,
Cosine and Sine series, Half-range series.