Course Title: Mathematics II (3 Cr.)
Course Code: CAMA154
Class Load: 5 Hrs. / Week (Theory: 3 Hrs, Tutorial: I Hr., Practical: 1 Hrs)
Unit I Limits and Continuity
Limit of a function, Indeterminate forms. Algebraic 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. (Methematica)
Unit 2 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)
Unit 3 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)
Unit 4 Integration and Its Applications
Rieman's Integral; Fundamental theorem (Without Pint): Technique of Integration; Evaluation sand Approximation of Definite Integrals; Improper Integrals; Applications of Definite Integrals; Quadrate, Rectification; Volume and Surface Integral. Trapezoidal and Simpson's Rules of Numerical Integration.(Mathematica)
Unit 5 Differential Equations
Differential Equation and its Order and Degree. Differential Equations of First Order and First Degree; Differential Equations with Separable Variables, Homogeneous and Exact Differential Equations.
Unit 6 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)
Course Code: CAMA154
Class Load: 5 Hrs. / Week (Theory: 3 Hrs, Tutorial: I Hr., Practical: 1 Hrs)
Unit I Limits and Continuity
Limit of a function, Indeterminate forms. Algebraic 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. (Methematica)
Unit 2 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)
Unit 3 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)
Unit 4 Integration and Its Applications
Rieman's Integral; Fundamental theorem (Without Pint): Technique of Integration; Evaluation sand Approximation of Definite Integrals; Improper Integrals; Applications of Definite Integrals; Quadrate, Rectification; Volume and Surface Integral. Trapezoidal and Simpson's Rules of Numerical Integration.(Mathematica)
Unit 5 Differential Equations
Differential Equation and its Order and Degree. Differential Equations of First Order and First Degree; Differential Equations with Separable Variables, Homogeneous and Exact Differential Equations.
Unit 6 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)
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