This page contains Syllabus of Mathematics I (Calculus) of CSIT.
Title | Mathematics I (Calculus) |
Short Name | |
Course code | MTH112 |
Nature of course | Theory and Practice |
First Semester | |
Full marks | 100 |
Pass marks | 40 |
Credit Hrs | 3 |
Elective/Compulsary | Compulsary |
Course Description
Units and Unit Content
- 1. Function of One Variable
- teaching hours: 5 hrs
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
- 2. Limits and Continuity
- teaching hours: 4 hrs
Precise definition of Limit, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and
Slant asymptotes
- 3. Derivatives
- teaching hours: 4 hrs
Tangents and velocity, Rate of change, Review of derivative, Differentiability of a function,
Mean value theorem, Indeterminate forms and L’Hospital rule
- 4. Applications of Derivatives
- teaching hours: 4 hrs
Curve sketching, Review of maxima and minima of one variable, Optimization problems,
Newton’s method
- 5. Antiderivatives
- teaching hours: 5 hrs
Review of antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite
integral, The Fundamental theorem of calculus, Improper integrals
- 6. Applications of Antiderivatives
- teaching hours: 5 hrs
Areas between the curves, Volumes of cylindrical cells, Approximate Integrations, Arc length,
Area of surface of revolution
- 7. Ordinary Differential Equations
- teaching hours: 6 hrs
Introduction, Introduction to first order equations Separable equations, Linear equations, Second
order linear differential equations, Non homogeneous linear equations, Method of undetermined
coefficients
- 8. Infinite Sequence and Series
- teaching hours: 5 hrs
Infinite sequence and series, Convergence tests and power series, Taylor’s and Maclaurin’s
series
- 9. Plane and Space Vectors
- teaching hours: 4 hrs
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
- 10. Partial Derivatives and Multiple Integrals
- teaching hours: 3 hrs
Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values,
Multiple integrals
- 11. Old Syllabus
- teaching hours: 0 hrs
Lab and Practical works