Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Bachelors Level/First Year/First Semester/Science csit/first semester/mathematics i/syllabus

B.Sc Computer Science and Information Technology

Institute of Science and Technology, TU

Nature of the course: (Theory)

F.M: 60+40 P.M: 24+16

Credit Hrs: 3Hrs

Mathematics I [MTH117]
Course Objective
i.
The objective of this course is to make students able to understand and formulate real world problems into mathematical statements.
ii.
develop solutions to mathematical problems at the level appropriate to the course.
iii.
describe or demonstrate mathematical solutions either numerically or graphically.
Course Description

The course covers the concepts of functions, limits, continuity, differentiation, integration of function of one variable; logarithmic, exponential, applications of derivative and antiderivatives, differential equations, vectors and applications, partial derivatives and Multiple Integrals.

S1:Function of One Variable[5]
1
Four ways of representing a function, Linear mathematical model, Polynomial, Rational, Trigonometric, Exponential and Logarithmic functions, Combination of functions, Range and domain of functions and their Graphs
S2:Limits and Continuity[4]
1
Precise definition of Limit, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and Slant asymptotes
S3:Derivatives[4]
1
Tangents and velocity, Rate of change, Review of derivative, Differentiability of a function, Mean value theorem, Indeterminate forms and L’Hospital rule
S4:Applications of Derivatives[4]
1
Curve sketching, Review of maxima and minima of one variable, Optimization problems, Newton’s method
S5:Antiderivatives[5]
1
Review of antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite integral, The Fundamental theorem of calculus, Improper integrals
S6:Applications of Antiderivatives[5]
1
Areas between the curves, Volumes of cylindrical cells, Approximate Integrations, Arc length, Area of surface of revolution
S7:Ordinary Differential Equations[6]
1
Introduction, Introduction to first order equations Separable equations, Linear equations, Second order linear differential equations, Non homogeneous linear equations, Method of undetermined coefficients
S8:Infinite Sequence and Series[5]
1
Infinite sequence and series, Convergence tests and power series, Taylor’s and Maclaurin’s series
S9:Plane and Space Vectors[4]
1
Introduction, Applications, Dot product and cross Product, Equations of lines and Planes, Derivative and integrals of vector functions, Arc length and curvature, Normal and binormal vectors, Motion in space
S10:Partial Derivatives and Multiple Integrals[3]
1
Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values, Multiple integrals
References
1.
Calculus Early Transcendentals, James Stewart, 7E, CENGAGE Learning
2.
Calculus Early Transcendentals, Thomas, 12th Editions, Addision Wesley
Labrotary Work