# Mathematics II - Syllabus

Embark on a profound academic exploration as you delve into the Mathematics II course () within the distinguished Tribhuvan university's BCA department. Aligned with the BCA Curriculum, this course (CACS154) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 60 + 20 + 20 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.

**Course Description **

This course includes the topics from calculus and computational methods such as limits and continuity, differentiation & its applications, integration and its applications, differential equation and different computational techniques which are essential as mathematical foundation for computing.

**Course Objectives**

This coarse makes students able to cognize the concept Calculus, Computational methods and their applications in the area of Social Science and Computer Application.

#### Units

Limit of a function, Indeterminate forms, Algebric properties of limit (without proof), Theorems on Limits of Algebraic and Transcendental Function, Continuity of a function, types of discontinuity. Exercises on evaluation of limits and test of continuity.(Mathematica)

Differentiation

Ordered Pairs, Cartesian Product, Relation, Domain and Range of a Relation, Inverse of a Relation; Types of Relations: Reflective, Symmetric, Transitive, and Equivalence Relations. Definition of Function, Domain and Range of a Function, Inverse Function, Special Functions(Identity, Constant), Algebraic(Linear, Quadratic, Cubic), Trigonometric and Their Graphs. Definition of Exponential and Logarithmic functions, Composite Function.(Mathematica)

Application of Differentiation

The derivatives and slope of the curve; Increasing and decreasing function; convexity of curves; maximization and minimization of a function; Differentiation and marginal analysis;price and output; Competitive equilibrium of firm, Illustrations. Drawing graphs of algebraic function by using first and second order derivatives.(Mathematica)

Integration and Its Applications

Riemann Integral; Fundamental Theorem (Without Proof); Technique of Integration; Evaluation and Approximation of Definite Integrals; Improper Integrals; Application of Definite Integrals; Quadrate, Rectification; Volume and Surface Integral. Trapezoidal and Simpson's Rules of Numerical Integration.(Mathematica)

Differential Equations

Differential Equation and its Order and Degree, Differential Equations of First Order and First Degree; Differential Equations with Separable Variables, Homogenous and Exact Differential Equations.

Computational Method

Linear Programming Problem(LPP), Graphical Solution of LPP in two Variables, Solution of LPP by Simplex Method(up to 3 variables), Solution of System of Linear Equations by Gauss Elimination method, Gauss Seidel Method and Matrix Inversion Method, Bisection method, Newton-Raphson Method for Solving Non-Linear Equations.(Excel/Matlab)

#### Lab works

**Laboratory- Works **

Mathematica and/ or Matlab should he used for above mentioned topics.