This page contains Syllabus of Mathematics II of BCA.

Title | Mathematics II |

Short Name | |

Course code | CACS154 |

Nature of course | Theory + Practical |

Second Semester | |

Full marks | 60 + 20 + 20 |

Pass marks | 24 + 8 + 8 |

Credit Hrs | 3 |

Elective/Compulsary | Compulsary |

### Course Description

**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 and Unit Content

- 1. Limits and Continuity
- teaching hours: 6 hrs
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)

- 2. Differentiation
- teaching hours: 6 hrs
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)

- 3. Application of Differentiation
- teaching hours: 8 hrs
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)

- 4. Integration and Its Applications
- teaching hours: 8 hrs
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)

- 5. Differential Equations
- teaching hours: 7 hrs
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.

- 6. Computational Method
- teaching hours: 10 hrs
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 and Practical works

**Laboratory- Works **

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