### KTU Revised Syllabus for First Year B.Tech Calculus

**COURSE NO. COURSE NAME CREDITS YEAR OF INTRODUCTION**

**MA 101 CALCULUS 4 2016**

**MODULE I**

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 TestAbsolute 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 bysoftware packages)

**MODULE II**

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 III**

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 IV**

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 V**

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 2 , 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 VI**

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)