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B.Stat-105: Calculus
Course Code : B.Stat-105
Course Title : Calculus
Course Type : Related
Level/Term and Section : B.Sc. Honours Part – I
Academic Session : 2019 – 2020
Course Instructor : ×
Pre-requisite (If any) : ×
Credit Value : 4
Total Marks : 100 (Examination 80, Tutorial/Terminal 15, and Attendance 5)

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COURSE DESCRIPTION:
Calculus is the mathematical study of continuous change. This course gives the general idea of real number theory is designed to provide concepts of differentiation and integration of the function of one variable. Students are required to select and apply the general rules correctly in real-life contexts to solve the problems by using mathematical concepts.
COURSE OBJECTIVES (CO):
1)
 Students will know and demonstrate understanding of the concepts from the five branches of mathematics (number, algebra, geometry and trigonometry, statistics and probability, and discrete mathematics).
2)
 Students will use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations including those in real-life contexts.
3)
 Students will select and apply general rules correctly to solve problems including those in real-life contexts.
COURSE LEARNING OUTCOME (CLO):
Upon successful completion of this course, a student will be able to
1)
 Recognize properties of functions and sketch their graphs.
2)
 Apply the procedures of differentiation accurately, including implicit and logarithmic differentiation.
3)
 Perform accurately definite and indefinite integration, using parts, substitution, and inverse substitution; and hence apply the procedures for integrating rational functions.
COURSE PLAN / SCHEDULE:
CLO
Topics to be covered
Teaching-Learning Strategies 
Assessment Techniques 
No. of Lectures
1
Numbers and Functions: Introduction, Numbers, Real line, Absolute value of real numbers and their properties, Function and Relation, Graph of functions, Limits and Continuity.
 Lecturing with Multimedia Projector, Interactive Board and Q/A session Assignment, Class Tests, Presentation, Final Exam.
22
2
Differentiation: Differentiation, Successive differentiation and Leibnitz theorem, Maxima and minima, Indeterminate form and L’Hospitals rule, Rolle’s Theorem, Mean Value Theorem, Taylor’s and Maclaurin’s Formulae.
12
3
Partial Differentiation: Partial derivatives, Homogeneous functions, Euler’s theorem, Tangents and Normal, Asymptotes, Jacobians and its properties.
10
4
Indefinite Integrals: Method of substitution, Integration by parts, Integration by reduction, Special trigonometric functions, Rational fractions.
8
5
Definite Integrals: Fundamental theorem, General Properties, Evaluations of definite integrals and reduction formulae, Ideas of double integral, Triple integral, Rectification, Areas of plane curves, Volumes and solids of revolution.
8
Assessment Strategy Evaluation Policy (Grading System) and make-up procedures: According to the ordinance.

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Main Books Recommended:
1)  Anton, H (2000): Calculus with Analytic Geometry, Wiley, N.Y. [Strang]
2)  Stewart, J. (2003): Calculus: Early Transcendentals (7th Ed.) Brooks, N.Y. [Trench]

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Reference:
3)  Ayres, F. (1982): Calculus, McGraw Hill, N. Y.
4)  Binmore, K.G. (1983): Calculus, Concepts and Methods, CUP, London.
5)  Buck, R. C. (1977): Advanced Calculus, 3rd ed. McGraw – Hill, N.Y.
6)  Edwards, J, (1994): Differential Calculus, Macmillan, London
7)  Lang, S. (1988): First Course in Calculus, 7th ed., Springer-Verlag, N.Y.
8)  Maxwell, A.E. (1957): An Analytical Calculus, Part I & II, C.U.P., London.