# Mathematics II Syllabus - BCA (TU)

Mathematics II Syllabus

• Short Name M-II
• Course code CACS154
• Semester Second Semester
• Full Marks 60 + 20 + 20
• Pass Marks 24 + 8 + 8
• Credit Hrs 3
• Elective/Compulsary Compulsary

### Mathematics II

Chapter wise complete Notes.

### 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.

### Unit Contents

#### 1. Limits and Continuity : 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 : 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 : 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 : 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 : 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 : 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)

### Laboratory- Works

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

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