Syllabus (MATHEMATICS)

Course Type: MAJ-5

Semester: 4

Course Code: BMTMMAJ05T

Course Title: Analytical Geometry (3D), Vector Calculus & Partial Differential Equations

(L-P-Tu): 5-0-1

Credit: 6

Practical/Theory: Theory

Course Objective: TO BE DONE

Learning Outcome: The whole course will have the following outcomes: Upon successful completion of this course the students will be able to CO1: understand the three dimensional geometry of planes, straight lines, spheres, cones and cylinders. CO2: acquire knowledge of cyl

Syllabus:

Unit -1: Analytical Geometry (3D) [Credit: 2, 30L]

• Plane; Straight lines.
• Sphere: General Equation, Circle, Sphere through circle, Tangent, Normal.
• Cone: General homogeneous second degree equation, Enveloping cone, Section of cone by a plane, Tangent and normal, Condition for three perpendicular generators, Reciprocal cone, Right circular cone, Cylinder, Enveloping cylinder, Right circular Cylinder.
• Conicoids: Ellipsoid, Hyperboloid, Paraboloid: Canonical equations only. Plane sections of it.
• Transformation of coordinates, Reduction of general second degree equations.

Unit -2: Vector Calculus [Credit: 2, 30L]

• Product of three or more vectors.
• Vector Calculus: Continuity and differentiability of vector-valued function of one variable, Space curve, Arc length, Tangent, Normal. Serret-Frenet’s formulae. Integration of vector-valued function of one variable.
• Vector-valued functions of two and three variables, Gradient of scalar function, Gradient vector as normal to a surface, Divergence and Curl, their properties.
• Evaluation of line, surface and volume integrals.
• Green’s theorem in the plane. Gauss and Stokes’ theorems (Proof not required) and problems based on these.

Unit -3: Partial Differential Equation [Credit: 2, 30L]

• Partial Differential Equations – Basic concepts and Definitions. Mathematical Problems. First- Order Equations: Classification, Construction and Geometrical Interpretation. Method of Characteristics for obtaining General Solution of Quasi Linear Equations. Canonical Forms of First- order Linear Equations. Method of Separation of Variables for solving first order partial differential equations. Solution by Lagrange’s and Charpit’s method.

Reading References:

1. S.L. Loney; The Elements of Coordinate Geometry; Arihant.
2. Shantinarayan; Analytical Solid Geometry; S. Chand.
3. J.G. Chakraborty & P.R. Ghosh, Advanced Analytical Geometry, U.N. Dhur & Sons Pvt. Ltd.
4. R.M. Khan, Analytical Geometry of two and three dimensions and vector analysis, New central book agency (P) Ltd., Kolkata.
5. Arup Mukherjee and Naba Kumar Bej, Analytical Geometry of Two and Three dimensions (Advanced level), Books & Allied Pvt. Ltd.
6. Shantinarayan and P K Mittal, A Text Book of Vector Analysis, S. Chand.
7. J.G. Chakraborty & P.R. Ghosh, Vector Analysis, U.N. Dhur & Sons Pvt. Ltd.
8. Robert J.T. Bell, An Elementary Treatise on Coordinate Geometry of Three Dimensions, McMilan & Co. Ltd., London.
9. S. Lipschutz, D. Spellman, M.R. Speigel, Vector Analysis, Schaum’s outline series.
10. J. Marsden and Tromba, Vector Calculus, McGraw Hill.
11. Ghosh & Maity, Vector Analysis, New Central Book Agency (P) Ltd.
12. Dipak Kumar Ghosh; Introduction to Partial Differential Equation and Laplace Transform; NCBA.
13. I.N. Sneddon, Elements of Partial Differential Equations, McGraw Hill, New York
14. F.H. Miller, Partial Differential Equations, John Wiley and Sons.