1

Students entering in Calculus should have a firm grasp of algebra and trigonometry. They
should be able to graph elementary functions and solve both linear equations and inequalities.
The objective of Calculus is for students to learn the basics of the Calculus. They will study
Convergence of series, Curve tracing, Expansion of function and error estimation, an
introduction to the Fundamental Theorem of Calculus, Partial differentiation and its
applications, Multiple integrals and its applications.
More generally, the students will improve their ability to think critically, to analyze a real
problem and solve it using a wide array of mathematical tools. These skills will be invaluable
to them in whatever path they choose to follow, be it as a mathematics major or in pursuit of
a career in one of the other sciences.
They will also able to apply these ideas to a wide range of problems that include the
equations of motion, related rates, curve sketching and optimization. The students should be
able to interpret the concepts of Calculus algebraically, graphically and verbally.
After the successful completion of the course, students will be able to
• Determine the convergence of infinite series
• Calculate the derivatives of functions of several variables
• Graphing and optimization of the functions
• Compute the basic multiple integrals
The course is designed in such a way that it can be covered comprehensively in period of
semester.



2

Convergence of Sequences and Series, Power Series and radius of
convergence.



3

Monotonic function, Concavity and Convexity of a curve, Points of
inflection, Curve tracing: Cartesian and Polar curves.



4

Monotonic function, Concavity and Convexity of a curve, Points of
inflection, Curve tracing: Cartesian and Polar curves.



5

Taylor’s series, Maclaurin’s series, Convergence of Taylor’s series and
error estimation, Indeterminate forms,



6

Fundamental theorem of calculus, Leibnitz,s Rule, Reduction
formulae.



7

Improper Integrals and its convergence, Application of definite
integrals: volume by slicing, by rotation about an axis and by cylindrical
shells.



8

Limit, Continuity of functions of several variables, Partial derivatives,
Chain rules, Euler’s theorem



9

Application of partial derivatives: Tangent planes and normal,
Linearization and error approximation, extreme values and saddle
points, Lagrange multipliers, partial derivatives with constrained
variables, Taylor’s expansion.



10

Double and Triple integrals, Change of order of integration, Change of
variables, Jacobian. Applications: Area, Volume.


