Department of Mathematics COURSE OUTLINE
Bangladesh University of Engineering and Technology
PART A: General Information
1. Course Number MATH 157
Course Title CalculusI
Credit (Contact) Hours 3.0 (3.0)
2. Level and Term (Section) Level-1, Term-1
Academic Session July 2022
3. Type of Course Core Course
Offered to Department of EEE
4. Pre-requisite Course(s) None
5. Course Website https://---.math.buet.ac.bd
6. Lecture Schedule Saturday (00:00-00:00 am)
Sunday (00:00-00:00 am)
Wednesday (00:00-00:00 am)
7. Important Dates For important dates and examination schedules and latest updates,
please follow the course website.
8. Course Teacher(s)
Name (Initials): Office: Email: Consultation Hour(s)
Md. Saddam Hossain Ga-215(B), Mathematics saddam@math.buet.ac.bd Xday (00:00-00:00 am)
Dr. K M Ariful Kabir Ga-215(G) km_ariful@math.buet.ac.bd Yday (00:00-00:00 am)
PART B: Course Details
9.Course Content (As approved by the Academic Council)
• Differential Calculus: Limits, continuity and differentiability. Successive differentiation of various
types of functions. Leibnitz's theorem. Rolle'stheorem, Meanvalue theorem, Taylor's and Maclaurin’s
theorems in finite and infinite forms. Lagrange's form of remainder. Cauchy's form of remainder.
Expansion of functions. Evaluation of indeterminate forms by L'Hospital's rule. Partial differentiation,
Euler's theorem. Tangent and Normal. Sub tangent and subnormal inCartesian and polar coordinates.
Determination of maximum and minimum values of functions. Curvature. Asymptotes and curve
tracing.
• Integral Calculus: Integration by the method of substitution. Standard integrals. Integration by
successive reduction. Definite integrals, its properties and use in summing series. Walli's formulae.
Improper integrals. Beta function and Gamma function. Area under plane curves and area of a region
enclosed by two curves in Cartesian and polar coordinates. Volume and surface area of solids of
revolution.
10.Course Objectives
• To provide the appropriate tools of calculus to solve applied problems.
• To provide the standard methods of indefinite and definite integrals with theirapplications.
11.Knowledge required
Familiarity with basic properties of set theory and function;fundamental concepts of pre-calculus and
preliminary knowledge to solve algebraic and transcendental equations.
12. Course Outcomes
CO CO Statement Corresponding Domains and Delivery Assessment
No. PO(s)* Taxonomy level(s) Method(s) and Tool(s)
Activity(-ies)
1 Explain the fundamental PO(b) C2 Lectures, Written
concepts of limits, Homework exams,
derivatives, and expansion Assignment
of functions.
2 Demonstratethe idea of PO(a) C3 Lectures, Written
indefinite and definite Homework exams,
integrals to evaluate Assignment
integrals
3 Apply the idea of PO(b) C3 Lectures, Written
accumulation to calculate Homework exams,
area, volume and surface Assignment
area.
*PO (a): Engineering knowledge; PO(b): Problem analysis; PO (c): Design/development of solutions; PO(d):
Investigation; PO(e) Modern tool use; PO(f): The engineer and society; PO(g): Environment andsustainability;
PO(h): Ethics; PO(i): Individual work and teamwork; PO(j): Communication; PO(k): Project managementand
finance; PO(l): Life-long learning.
**The cognitive domain (C) and its Taxonomy Levels (1 to 6) aim to develop the mental skills and the
acquisition of knowledge of the individual. The cognitive domain encompasses of six categories which include:
C1- knowledge/remember; C2-understand/explain/estimate; C3-apply; C4-analysis;
C5-evaluate/judge/verify; C6-synthesis/design/create/construct.
13. Assessment Strategy
• Class Participation: Class participation and attendance will be recorded in every class.
• Continuous Assessment: Continuous assessment for any of the activities such as quizzes, assignment,
presentation etc. The scheme of the continuous assessment for the course will be declared on the first
day of classes.
• Final Examination: A comprehensive term final examination will be held at the end of the term
following the guideline of academic council.
14. Distribution of Marks
Class Participation 10%
Continuous Assessment 20%
Final Examination 70%
Total 100%
15. Textbooks
• Calculus by Howard Anton, IrlBivens and Stephen Davis.
• Differential and Integral Calculus by B.C. Das and B.N. Mukherjee.
• Integral Calculus with applications by A.K. Hazra.
16. Reference Books
• Differential Calculus by P.N. Chatterjee.
• Advanced Engineering Mathematics by Erwin Kreyszig, Herbert Kreyszig and Edward J. Norminton.
• Integral Calculus by Howard Anton.
17. Lecture plan
Weekly schedule: For Differential Calculus
Weekly plan for course content and mapping with Cos
Weeks Topics
Week-1 to 2
Limits, Continuity, and differentiability.
Week-3 to 4 Successive differentiation of various types of functions.
Week-5 to 8 Leibnitz's theorem. Rolle's theorem. Mean value theorem. Taylor's and
Maclaurin’s theorems in finite and infinite forms. Lagrange's form of
remainders. Cauchy's form of remainders.
Week-9 to 10 Expansion of functions. Evaluation of indeterminate forms by
L'Hopitals rule. Partial differentiation. Euler's theorem.
Week-11 to Tangent and Normal. Subtangent and subnormal inCartesian and polar
12 co-ordinates. curvature, Asymptotes.
Week-13 to Determination of Maximum and minimum values of functions with
14 applications.
Weekly schedule: For Integral Calculus
Week Topics
Week-1 Integration by the method of substitution,
Week-2 Standard integrals.
Week-3 Integration by successive reduction.
Week-4 Definite integrals, its properties
Week-5 Use of definite integral in summing series. Walli's formulae.
Week-6 Class test
Week-7 Improper integrals.
Week-8 Beta function and Gamma function.
Week-9 Area under plane curves in Cartesian and polar coordinates
Week-10 Area of a region enclosed by two curves in Cartesian and polar
coordinates
Week-11 Volume of solids of revolution.
Week-12 Area of surface of revolution
Week-13 Class Text
Week-14 Review class
18. Important University Policies
• Rules and regulations for the undergraduate programmes:
https://www.buet.ac.bd/info/Academicinformation/RulesUndergradprogram
Course Outline Prepared by SAC 13/08/2022
Course Outline Reviewed by Dr.NazmaParveen 04/09/2022
