Home Syllabus Mathematics – II

# Mathematics – II

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## Course Objectives:

1. It provides the basic mathematical idea to develop various computer information systems.
2. It gives various mathematical tools for the computer system.

## Course Content:

### Unit I: Fundamental integrals ———————————————— 12 hours

1. Introduction
2. Indefinite integrals
3. Techniques of Integration
4. Integration by substitution
5. Integration by parts
6. Integration by partial fractions
7. Definite Integrals
8. Improper integrals
9. Beta & Gamma function
10. Double integral (Concept only)

### Unit II: Application of integration ——————————————– 7 hours

1. Introduction
2. Rectification
4. Area under a curve
5. Area between the curves
6. Numerical
7. Integration
8. Rectangular rule
9. Trapezoidal rule
10. Simpson’s rule
11. Volume
12. Surface Area. B.
13. Consumer’s surplus & Producer’s surplus

### Unit III: Vector Space ———————————————————– 5 hours

1. Introduction
2. Vector space and subspaces with examples
3. Linear combination of vectors
4. Linear
5. Dependence and independence of vectors
6. Basis and dimension of vector space

### Unit IV: Function of complex variables ————————————– 8 hours

1. Introduction
2. Complex variable
3. Function of complex variables
4. Analytic function
5. Necessary & sufficient conditions for f (z) to be analytic (without proof)
6. Harmonic function,
7. Conformal mappings

### Unit V: Fourier series and Integrals —————————————– 11 hours

1. Introduction
2. Periodic function and trigonometric series
3. Fourier series
4. Fourier sine and cosine series
5. Fourier series in complex form
6. Fourier integral
7. Fourier Sine and Cosine integrals
8. Fourier Sine and Cosine transforms.

### Unit VI: Taylor series ———————————————————— 5 hours

1. Introduction
2. Geometric series
3. Convergence of the geometric series
4. Taylor series
5. Taylor series of a function of one or two variables

## Text Books:

1. Advance Engineering Mathematics , By Erwin Kreyszig, 8th edition .
2. Calculus and Analytical Geometry, By Thomas and Finney

## Reference Books:

1. Applied Mathematics, By R . K. Thukurathi and Dr. K.K Shrestha
2. Engineering Mathematics IV, By Toya Narayan Paudel, Sukunda Pustak Bhawan, Kathmandu Nepal.
3. Differential Equation: By Agnew R.P.; New York, MC GRaw Hill Book Company 1960
4. Introduction to Mathematical Physics: By Charlie Happer; prentice Hall of India Pvt. Ltd.
5. Text Book on Algebra & Theory of Equations: By chandrika Prasad; Pothishala Pvt. Ltd.