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course contents - ug - National Institute of Technology Karnataka

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NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA, SURATHAKAL<br />

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Department <strong>of</strong> Mathematical and Computational Sciences<br />

MA100 ENGINEERING MATHEMATICS - I (3-1-0) 4<br />

Infinite series, Convergence and Divergence. Power Series, Fourier series, Half range expansions,<br />

Successive Differentiation, Polar curves, Angle between radius vector and tangent. Curvature. Mean<br />

value theorems. Functions <strong>of</strong> several variables, Partial differentiation. Taylor's theorem for a function <strong>of</strong><br />

two variables. Extreme values. Errors and Approximations. Reduction formulas for integration, Curve<br />

tracing. Applications.<br />

Shanti Narayan: Differntial Calculus, 1990 Edn, Shyam Lal Charitable Trust, Delhi<br />

Shanti Narayan: Integral Calculus, 1989 Edn, S. Chand & Co., Delhi<br />

C.B. Thomas and Finney: Calculus and Analytical Geometry, 8 th Edn, Narosa Pub.<br />

R. Courant and F. John: Introduction to Calculus, Vols. I & II, Springer Verlag (Indian Edn).<br />

MA101 ENGINEERING MATHEMATICS - II (3-1-0) 4 PREREQ: MA100<br />

Vector Calculus, Vector differentiation and vector integration, Line, Surface and Volume integrals.<br />

Green's, Gauss Divergence and Stoke's Theorems. Multiple integrals. Jacobians. Beta and Gamma<br />

Functions, Ordinary differential equations. Partial differential equations. One dimensional heat<br />

conduction equation and wave equation. Derivation and solution.<br />

Murray R. Spiegel : Vector Analysis , 1959 Edn, Schaum Pub.<br />

Erwin Kreyszig: Advanced Engg. Mathematics, 8 th Edn., Wiley Eastern.<br />

E. D. Rainville and P. E. Bedient : A short <strong>course</strong> in differential equations,6 th Edn, McMillan Pub.<br />

Shanti Narayan : Integral Calculus, 1989. Edn. Sultan Chand& Co., Delhi<br />

R. Courant and F.John: Introduction to Calculus, Vols. I & II, Springe Verlag (Indian Edn).<br />

MA201 CONCRETE MATHEMATICS (3-0-0) 3 PREREQ: MA101/ MA151<br />

Sums and Recurrences, General methods. Finite and infinite calculus. Floors and ceilings.<br />

Applications. Number Theory, Congruences, Chinese Remainder Theorem. Generating functions.<br />

Solving recurrences. Special generating functions, Convolutions and Exponential generating functions.<br />

Graham, Knuth, and Patashnik, Concrete Mathematics: A foundation for Computer Science, Pearson ,<br />

2000.<br />

MA202 ISCRETE MATHEMATICAL STRUCTURES (3-0-0) 3 PREREQ: MA101/ MA151<br />

Propositional and Predicate Calculus, Normal forms, Applications to Artificial Intelligence, Lattice<br />

Theory and Boolean Algebra, Introduction to Graph Theory � Trees, Planarity, Connectivity,<br />

Traversability, Shortest Path and Spanning Tree Algorithms. Groups: Cosets, Normal Subgroups,<br />

Permutation groups, Burnside�s Theorem and simple applications.<br />

J.P.Tremblay & R. Manohar, Discrete Math. Structures with app. to Comp.Sc., McGraw Hill.<br />

C.L.Liu, Elements <strong>of</strong> Discrete Mathematics, McGraw Hill.<br />

Kenneth Rosen, Discrete Mathematics and its applications, TMH<br />

MA203 GRAPH THEORY (3-0-0) 3 PREREQ: MA101/ MA151<br />

Graphs: Introduction to Graphs, Digraphs, Bigraphs, Connectivity, Trees, Traversability, Coverings and<br />

Independence, Planarity, Coloring, Representation <strong>of</strong> Graphs, Enumeration <strong>of</strong> graphs.<br />

F. Harary, Graph Theory, Narosa Pub.<br />

Narsingh Deo, Graph Theory with app. to Engg. & Comp.Sc., PHI<br />

D.B.West, Introduction to Graph Theory, PHI.<br />

MA204 LINEAR ALGEBRA AND MATRICES (3-0-0) 3 PREREQ: MA101/ MA151<br />

Linear dependence, Basis, vector spaces and subspaces. Expansion by Co-factors, Inverse by<br />

Partitioning, Linear Transformations, Rank and echelon matrices. Homogeneous linear equations, Basic<br />

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NITK-Course Contents(UG)2010 Page 127 <strong>of</strong> 134

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