Mathematics For B.Sc. Students Semester IV: MJ-6, 7 & 8 | Complex Analysis-1, Mechanics, & Linear Programming - NEP 2020 Jharkhand

• Master Complex Analysis: Explore the elegance of the complex plane, analytic functions, and conformal mappings. Delve into power series, Taylor and Laurent expansions, and the transformative power of bilinear transformations.
• Understand Mechanics: Navigate the principles of statics, the centre of gravity, and the fascinating dynamics of motion. Analyse real-world phenomena like simple harmonic motion, central force fields, and the geometry of cycloidal motion.
• Optimize with Linear Programming: Learn to formulate and solve optimization problems using the simplex method, duality concepts, and transportation and assignment algorithms.

I. COMPLEX ANALYSIS-I

Unit I: Complex Plane and Functions 

1. Algebra and Representation of Complex Numbers
2. Complex Plane, Stereographic Projection and Riemann Sphere
3. Limits and Continuity of Complex Functions

Unit II: Analytic Functions and Cauchy Riemann Equations

4. Differentiation of Complex Functions
5. Branch Cut and Branch of Multi-Valued Functionsma

Unit III: Power Series

6. Representation of a Function by Power Series

Unit IV: Conformal Representation

7. Transformation and Jacobian 

II. MECHANICS

Unit I: Statics

1. Equilibrium of a System of Particles

Unit II: Centre of Gravity and Common Catenary

2. Centre of Gravity and Catenary

Unit III: Rectilinear Motion

3. Rectilinear Motion

Unit IV: Kinematics and Kinetics of The Motion

4. Motion in a Plane

III. LINEAR PROGRAMMING

1. Linear Programming: Applications and Model Formulation
2. Linear Programming: The Graphical Method
3. Linear Programming: The Simplex Method
4. Duality in Linear Programming
5. Transportation Problem
6. Assignment Problem
7. Theory of Simplex Method
8. Revised Simplex Method
9. Dual-Simplex Method
10. Bounded Variables LP Problem
11. Pre-Study for Operations Research