Dr. A P J Abdul Kalam Technological University / Kerala Technological university KTU First year (S1 S2) B.tech Syllabus for Calculus ( MA101)

Module 1 - Single Variable Calculus and Infinite series

Introduction. Exponential and Logarithmic functions. Graphs and Applications involving exponential and Logarithmic functions. Hyperbolic functions and inverses-derivatives and integrals. Indeterminate forms. Basic ideas of infinite series and convergence. Convergence tests-comparison, ratio, root and integral tests (without proof). Geometric series and p-series. Alternating series, conditional and absolute convergence, Leibnitz test. Maclaurins series-Taylor series - radius of convergence. (Sketching, plotting and interpretation of Exponential, Logarithmic and Hyperbolic functions using suitable software. Demonstration of convergence of series by mathematical software) (Book I –sec.6.1, 6.4, 6.5, 6.8, 9.3 to 9.9)

Module 2 - Three dimensional space

Rectangular coordinates in three space-graphs in three space, cylindrical surfaces – Quadric surfaces, Traces of surfaces – the quadric surfaces –Technique for graphing quadric surfaces-Translation – reflection –technique for identifying quadric surfaces, cylindrical and spherical coordinates-constant surfaces- converting coordinates-equations of surfaces in cylindrical and spherical coordinates

Module 3 - Functions of more than one variable

Introduction- Functions of two or more variables – graphs of functions of two variables- level curves and surfaces –graphing functions of two variables using technology, Limits and continuity - 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. (Sketching, plotting and interpretation of functions of two variables, level curves and surfaces using mathematical software) (Book I –sec. 13.1 to 13.5 and 13.8)

Module 4 - Calculus of vector valued functions

Introduction to vector valued functions- parametric curves in 3-D space- parametric curves generated with technology –Parametricequations for intersection of surfaces -limits and continuity – derivatives - tangent lines – derivative of dot and cross product-definite integrals of vector valued functions- change of parameter-arclength-unit tangent-normal-binormal-curvature-motion along a curve –velocity-acceleration and speed – Normal and tangential components of acceleration. Directional derivatives and gradients-tangent planesand normal vectors-Lagrange multiplier method – extremum problem with constraint (vector approach). (Book I-12.1-12.6, 13.6,13.7, 14.9)

Calculus Syllabus   Continues next page >>

Related