Karnataka Open University BTECH Syllabus

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Here is the syllabus
MATHEMATICS -I

1 : LIMITS AND CONTINUITY OF A FUNCTION.

2 : DIFFERENTIATION.
Definition, Derivative by first principle, Differentiation of implicit functions, Differentiation of trigonometric functions, Differentiation of inverse trigonometric functions, Transformation, Differentiation of exponential and Logarithmic Functions, Hyperbolic functions, Derivatives of the inverse hyperbolic functions, Differentiation with respect to a function, Differentiation of Parametric Equations.

3 : SUCCESSIVE DIFFERENTIATION
Calculation of nth derivative, Leibnitz’s theorem.

4 : GENERAL THEOREMS, EXPANSION OF FUNCTIONS.
Rolle’s Theorem, Mean value theorem (Lagrange’s form), Increasing and Decreasing functions, Mean value theorem (Cauchy’s form).
Expansion of functions;
Taylor’s expansion theorem, Maclaurin’s theorem, Taylor’s and Maclaurin’s infinite series.

5 : INDETERMINATE FORM
L’ Hospital’s rule, Evaluation of % form, Evaluation of form, Evaluation of form, Evaluation of 00, 1, 0 form.

6 : CURVATURE
Radius of curvature, Special formula for parametric equations, Radius of curvature at the origin.

7 : MAXIMA AND MINIMA
Maximum and Minimum values of a function.

8 : ELEMENTARY INTEGRATION
Table of elementary integrals, Simple examples.

9 : INTEGRATION BY SUBSTITUTION
Introduction, Change of independent variable in , Working rule to evaluate by the substitution, Four important integrals, standard forms, Integrals of tan x, cot x, sec x, cosec x.

10 : INTEGRATION BY PARTS
, , Important integrals.




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