Introduction to Functions: Mathematical and physical meaning of functions, graphs of various functions. Hyperbolic functions.
Introduction to Limits: Theorems of limits and their applications to functions. Some useful limits, right hand and left hand limits. Continuous functions and their applications.
Derivatives: Introduction to derivatives. Geometrical and physical meaning of derivatives. Partial derivatives and their geometrical
significance. Application problems. (Rate of change, marginal analysis).
Higher Derivatives: Leibnitz theorem, Rolles theorem, Mean value theorem. Taylors and Maclaurins series.
Evaluation of Limits Using L‟Hospital‟s Rule: Indeterminate forms.
Applications of Derivatives: Asymptotes, tangents and normals, curvature and radius of curvature, maxima and minima of a function of single variable (Applied problems), differentials with application. Euler‟s theorem, total differentials, maxima and minima of two variables.
Integral Calculus: Methods of Integration by substitutions and by parts. Integration of rational and irrational algebraic functions. Definite integrals, improper integrals, Gamma and Beta functions, reduction formulae. Cost function from marginal cost, rocket flights, area under curve, etc. Vector Algebra: Introduction to vectors. Scalar and vector product of three and four vectors. Volume of parallel oppiped and tetrahedron.
To give the idea of calculus and its applications in the engineering field.
After completion of this course the student should be able to:
i) Know the derivative as a rate measurer, slope of a straight line etc
and integration as the area under curve.
ii) Solve the application problems related to their field
iii) Know the vector algebra and vector calculus.