# Mathematics I (Calculus) Syllabus

 Title Mathematics I (Calculus) Short Name Course code MTH112 Nature of course Theory and Practice Semester first-semester Full marks 100 Pass marks 40 Credit Hrs 3 Elective/Compulsary Compulsary

### 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