MA101 CALCULUS NEW MODIFIED SYLLABUS FOR S1 , S2 KTU STUDENTS


CALCULUS MODIFIED NEW S1 S2 SYLLABUS FOR KTU STUDENTS

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MODULE 1 {15%}

Single Variable Calculus and Infinite series
(Book I –sec 9.3,9.5,9.6,9.8)

Basic ideas of infinite series and convergence -.Geometric series- Harmonic series-Convergence tests-comparison, ratio, root tests (without proof). 

Alternating series- Leibnitz Test- Absolute convergence, Maclaurins series-Taylor series - radius of convergence.

(For practice and submission as assignment only: Sketching, plotting and interpretation of hyperbolic functions using suitable software.
Demonstration of convergence of series by software packages)

MODULE 2 {15%}

Partial derivatives and its applications
(Book I –sec. 13.3 to 13.5 and 13.8)

Partial derivatives–Partial derivatives of functions of more than two variables - higher order partial derivatives - differentiability, differentials and local linearity - The chain rule – Maxima and Minima of functions of two variables - extreme value theorem (without proof)-relative extrema .

MODULE 3 {15%}

Calculus of vector valued functions
(Book I - 12.1,12.2,12.4&12.6,13.6 &13.7)

Introduction to vector valued functions- parametric curves in 3-space Limits and continuity – derivatives - tangent lines – derivative of dot and cross product- definite integrals of vector valued functions- unit tangent-normal- velocity-acceleration and speed–Normal and tangential components of acceleration.

Directional derivatives and gradients-tangent planes and normal vectors (For practice and submission as assignment only:

Graphing parametric curves and surfaces using software packages )

MODULE 4 {15%}

Multiple integrals
(Book I-sec. 14.1, 14.2, 14.3, 14.5)

Double integrals- Evaluation of double integrals – Double integrals in non-rectangular coordinates- reversing the order of integration- Area calculated as a double integral-
Triple integrals(Cartesian co ordinates only)- volume calculated as a triple integral- (applications of results only)

MODULE 5 {20%}

Topics in vector calculus
(Book I-15.1, 15.2, 15.3)


Vector and scalar fields- Gradient fields – conservative fields and potential functions – divergence and curl - the operator - the Laplacian.

Line integrals - work as a line integral-
independence of path-conservative vector field –
(For practice and submission as assignment only:
graphical representation of vector fields using
software packages)

MODULE 6 {20%}

Topics in vector calculus (continued)
(Book I sec., 15.4, 15.5, 15.7, 15.8)

Green’s Theorem (without proof- only for simply connected region in plane), 

Surface integrals – Divergence Theorem (without proof for
evaluating surface integrals) , Stokes’ Theorem (without proof for evaluating line integrals)

(All the above theorems are to be taught in regions in the rectangular co ordinate system only)

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