# Mathematics I (Calculus) - Syllabus

Embark on a profound academic exploration as you delve into the Mathematics I (Calculus) course () within the distinguished Tribhuvan university's CSIT department. Aligned with the 2074 Syllabus, this course (MTH112) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 100 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.

#### Units

Function of One Variable

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

Limits and Continuity

Precise definition of Limit, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and

Slant asymptotes

Derivatives

Tangents and velocity, Rate of change, Review of derivative, Differentiability of a function,

Mean value theorem, Indeterminate forms and L’Hospital rule

Applications of Derivatives

Curve sketching, Review of maxima and minima of one variable, Optimization problems,

Newton’s method

Antiderivatives

Review of antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite

integral, The Fundamental theorem of calculus, Improper integrals

Applications of Antiderivatives

Areas between the curves, Volumes of cylindrical cells, Approximate Integrations, Arc length,

Area of surface of revolution

Ordinary Differential Equations

Introduction, Introduction to first order equations Separable equations, Linear equations, Second

order linear differential equations, Non homogeneous linear equations, Method of undetermined

coefficients

Infinite Sequence and Series

Infinite sequence and series, Convergence tests and power series, Taylor’s and Maclaurin’s

series

Plane and Space Vectors

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

Partial Derivatives and Multiple Integrals

Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values,

Multiple integrals

Old Syllabus