MT1008 - MULTIVARIABLE CALCULUS
NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES, FAST-NU
Course Title
Multivariable Calculus
Course Code
MT1008
Department
Fast School of Computing (FSC)
Campus
Lahore
HEC Knowledge Area
Natural Sciences
Credit Hrs.
3
Pre-requisite(s)
Calculus & Analytical Geometry
Grading Scheme
Relative
Applicable From
Spring 2024
Course Objective
Develop a thorough understanding of advanced topics of multivariable calculus and their
applications. Understand the concept of Laplace Transform, Fourier Series, Fourier
Transform
No.
Assigned Program Learning Outcome (PLO)
An ability to identify, formulate, research literature, and analyze complex engineering problems reaching
2
substantiated conclusions using first principles of mathematics, natural sciences and engineering science.
I = Introduction, R = Reinforcement
E = Evaluation, A = Assignment, Q = Quiz, M = Midterm, F=Final, L = Lab, P = Project, W = Written Report.
No.
1
2
3
Course Learning Outcome (CLO) Statements
Defining Functions of Several Variables, Computing Partial Derivatives,
Directional and Gradient Vectors.
Evaluation of Multiple Integrals in Different Coordinate Systems and
Their Applications to Work, Circulation, Flux, Green's Theorem, and
Stokes' Theorem.
Some Integral Transforms, Orthogonal Functions, and Their Applications
in Expanding Functions into Series, Including Laplace and Fourier
Transforms, and Concepts of Sequences and Series.
FSC, Lahore.
Page 1 of 3
Assessment Tools
Q1, M1, A1, F
S1, S2, A1, A2, A3, Q2,
Q3, F
Q4, A4, F
MT1008 - MULTIVARIABLE CALCULUS
NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES, FAST-NU
Title
Author
Publisher
Text Books
Title
Author
Publisher
Reference Books
Week
1
2
3
4
5
6
6A
7
8
9
10
11
12
12A
13
14
15
16
Thomas Calculus (Thirteenth Edition).
George B. Thomas, Jr.
PEARSON.
Differential Equations with Boundary-Value
Problems (Ninth Edition)
Dennis G. Zill.
Cengage Learning.
Advanced Modern Engineering Mathematics, 4th edition, by Glyn James.
Calculus (Sixth Edition) By Swokowski.
Course Contents/Topics
Functions of several variables, Limit and continuity of Higher
dimensions.
Partial derivatives, Chain Rule, Directional Derivative and Gradient
Vectors.
Double and Iterated Integrals over Rectangles, Double Integrals over
General Regions, Area by Double Integration.
Quiz#1
Double integrals in polar form, Triple Integrals in Rectangular
Coordinates.
Triple integral in cylindrical and spherical coordinates, Line Integral
Quiz#2
Vector Fields and line Integrals: Work Circulation and Flux. Path
Independence
Sessional Exam -I
Conservative Fields and Potential Functions, Greens Theorem in the
Plane, Surfaces and Area.
Surface Integrals, Stocks Theorem.
Quiz#3
The Divergence Theorem and a Unified theory, Definition of the
Laplace Transform.
Inverse Transforms and Transforms of Derivatives.
Operational Properties I, Translation on the S-Axis, Translation on the tAxis, Orthogonal Functions.
Sessional Exam -II
Fourier Series, Fourier Cosine and Sine Series.
Definition of the Fourier Transform and Example.
Sequence and Infinite series, Integral Test
Quiz#4
Absolute convergence, ratio and root test
Final Exam
FSC, Lahore.
Page 2 of 3
Chapter*
CLO*
14.1, 14.2
1
14.3, 14.4, 14.5
1
15.1, 15.2, 15.3
2
15.4, 15.5
2
15.7, 16.1
16.2-3
2
16.4, 16.5
2
16.6, 16.7
2
16.8, 7.1
2, 3
7.2
2
7.3, 11.1
2
11.2, 11.3
2.3
2
2
10.1-3
2
10.4,5
2
MT1008 - MULTIVARIABLE CALCULUS
NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES, FAST-NU
Weightage distribution is given below.
Assessment Tools
Assignments (4)
Quizzes (4)
Home work
Sessional I
Sessional II
Final Exam
Weightage
7%
8%
5%
15%
15%
50%
Important Instructions for Students
1. Grading Scheme: The Grading is Relative.
2. Combined Grading: Grading for all sections taught by the same teacher within the department
will be combined.
3. Attendance Policy: Attendance will be taken 5 minutes after the lecture begins. Students not
present in class at that time will be marked absent.
4. Classroom Discipline: Disrupting the lecture or annoying the teacher may result in disciplinary
action (DC punishment).
5. Homework Marks: The homework marking scheme will be shared by the course instructor.
6. Office Hours: Students are encouraged to discuss subject-related queries during the designated
office hours.
7. Study Advice: Pay equal attention to examples as to the questions in the exercise.
FSC, Lahore.
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