MT-116 CALCULUS AND ANALYTICAL GEOMETRY
CREDIT HOURS
Theory = 3
Practical = 0
COURSE LEARNING OUTCOMES (CLOs)
| S. No. | CLOs | PLO | Taxonomy |
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| 2 | To be displayed. | TBD | TBD |
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COURSE CONTENT
- Set and Functions: Define rational, irrational and real numbers; rounding off a numerical value to specified value to specified number of decimal places or significant figures; solving quadratic, and rational inequalities in involving modulus with graphical representation; Definition of set, set operations, Venn diagrams, De Morgan’s laws, Cartesian product, Relation, Function and their types (Absolute value, greatest integer and combining functions). Graph of some well-known functions. Limit of functions and continuous and discontinuous functions with graphical representation.
- Differential Calculus: Differentiation and Successive differentiation and its application: Leibnitz theorem. Taylor and Maclaurin theorems with remainders in Cauchy and Lagrange form, power series. Taylor and Maclaurin series,L Hopitals rule, extreme values of a function of one variable using first and second derivative test, asymptotes of a function, curvature and radius of curvature of a curve, partial differentiation, extreme values of a function of two variables with and without constraints. Solution of non-linear equation, using Newton Raphson method.
- Integral Calculus: Indefinite integrals and their computational techniques, reduction formulae, definite integrals and their convergence. Beta and Gamma functions and their identities, applications of integration relevant to the field.
- Sequence & Series: Sequence, Infinite Series, Application of convergence tests such as comparison, Root, Ratio, Raabe's and Gauss tests on the behavior of series.
- Analytical Geometry: Review of vectors, scalars and vector products, Three-dimensional coordinate system and equation of straight line and plane and sphere, curve tracing of a function of two and three variables, surface revolutions, coordinate transformation.
- Complex Number: Argand diagram, De Moivre formula, root of polynomial equations, curve and regions in the complex plane, standard functions and their inverses (exponential, circular and Hyperbolic functions).
RECOMMENDED BOOKS
Text Book(s)
- Joel Hass, Christopher Heil, Maurice Weir, Przemyslaw Bogacki, ‘Thomas’ Calculus’, 15th ed., Pearson, 2023.
- James Stewart, Daniel Klegg, Saleem Watson, ‘Calculus’, 9th ed., Cengage Learning, 2020.
Reference Book(s)
- Howard Anton, ‘Calculus’, 12th ed., Wiley, 2021.
*For details of Taxonomy Levels CLICK HERE
