# Mathematics I (Calculus) Syllabus

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