Calculus-ii
(MATH-112)
Introduction
Dr. Hina Dutt
hina.dutt@seecs.edu.pk
SEECS-NUST
Semester Planner
Course Logistics
Calculus-II
Course Code:
MATH-112
Semester:
Second
Credit Hours:
3+0
None
Instructor:
Dr. Hina M. Dutt
Prerequisite
Codes:
Class:
Office:
A-306 Faculty Block
Telephone:
051-90852378
Lecture Days:
Tuesday, Wednesday,
Friday
E-mail:
hina.dutt@seecs.edu.pk
Class Room:
CR-11
Consulting
Hours:
Tuesday: 1500-1700 hours
Friday: 1500-1700 hours
Lab Engineer:
N/A
Lab Engineer
N/A
Email:
Updates on LMS: After every lecture
Knowledge
Group:
BSCS-12C 2k22
Course Description
This is the second course of Calculus. As continuation of
Calculus I, it focuses on techniques of integration and
applications of integrals. The course also aims at
introducing the students to infinite series, parametric
curves and polar coordinates.
Course Objectives
Upon completion of the course, the student will be able to:
➢ integrate various types of functions using the various integration methods:
substitution rule, integration by part, trigonometric substitution, partial fractions,
rational substitution.
➢ apply integration to find areas, volumes, arc length, and surface areas, evaluate
improper integrals,
➢ find the limit of sequences, use various convergence tests (geometric series test,
divergence test, integral test, comparison tests, alternating series tests, ratio test,
and root test) to determine convergence or divergence of series, estimate sum of
some series,
➢ find the interval and radius of convergence of power series,
➢ represent some functions as power series.
Course Learning Outcomes (CLOs)
At the end of the course the students will be able to:
CLO-1. Understand the basic concepts of integration and its
application to compute area and arc length.
CLO-2. Evaluate and carryout the convergence analysis of
sequences and series.
CLO-3. Understand basic 3-D geometry.
* BT= Bloom’s Taxonomy, C=Cognitive domain, P=Psychomotor
domain, A= Affective domain
PLO BT Level*
2
C-3
3
C-5
2
C-2
Programme Learning Outcomes (CLOs)
PLOs/CLOs
CLO1
PLO 1 (Academic Education)
PLO 2 (Knowledge for Solving Computing Problems)
√
PLO 3 (Problem Analysis)
PLO 4 (Design/Development of Solutions)
PLO 5 (Modern Tool Usage)
PLO 6 (Individual and Team Work)
PLO 7 (Communication)
PLO 8 (Computing Professionalism and Society)
PLO 9 (Ethics)
PLO 10 (Lifelong Learning)
CLO2
CLO3
√
√
Bloom’s Taxonomy
Course Sections
Techniques of Integration
Polar Coordinates and Polar Curves
Sequences and Series
3-D Geometry
Lecture breakdown
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Topics
Integrals of elementary, hyperbolic, trigonometric, logarithmic and exponential functions.
Integration by parts, Partial fractions, Trigonometric integrals and substitution
Approximate integration.
Improper integrals.
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
Sequences and series.
Mid Semester Exam
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 Maclaurin series. Approximations by Taylor polynomials
Coordinate system. Rectangular, cylindrical and spherical coordinates. The dot product, the cross
product.
Equations of lines and planes.
Quadric surfaces
Class Presentations
End Semester Exam
Marks Distribution
Marks Distribution
10
10
50
30
Quizzes
Assignments & Class Presentations
MSE
ESE
Text Books
➢Calculus and Analytic Geometry (9th Edition)
➢Thomas’ Calculus (14th Edition)
➢Advanced Engineering Mathematics (9th Edition)
Reference Books
➢Stewart, James. Single Variable Calculus: Early Transcendentals 6th edition.
Pacific Grove, Ca:Brooks/Cole, Thompson Learning, 2008.
➢H. Anton, I. Bevens, S. Davis, Calculus, 8th Edition, John Wiley & Sons, Inc. 2005
➢Hughes-Hallett, Gleason, McCallum, et al, Calculus Single and Multivariable, 3rd
Edition. John Wiley & Sons, Inc. 2002.
➢Frank A. Jr, Elliott Mendelson, Calculus, Schaum’s outlines series, 4th Edition,
1999
➢C.H. Edward and E.D Penney, Calculus and Analytics Geometry, Prentice Hall, Inc.
1988
➢E. W. Swokowski, Calculus and Analytic Geometry, PWS Publishers, Boston,
Massachosetts,
What is
Calculus
Calculus
The word Calculus comes from
Latin meaning "small stone".
Because it is like understanding
something by looking at small
pieces.
Calculus is a branch of mathematics that deals with
rates of change.
Branches of Calculus
Differential Calculus cuts something into small pieces
to find how it changes.
Integral Calculus joins (integrates) the small pieces
together to find how much there is.
Differential Calculus and Integral Calculus are like
inverses of each other, just like multiplication and
division are inverses.
Calculus in
Computer
Science
Calculus in Computer Science
Calculus is used in an array of computer science areas, including
creating graphs or visuals, simulations, problem-solving applications,
coding in applications, creating statistic solvers, and the design and
analysis of algorithms.
Calculus in Computer Science
Computer algebra systems compute integrals and derivatives directly,
either symbolically or numerically. In addition, any software that
simulates a physical system that is based on continuous differential
equations necessarily involves computing derivatives and integrals.