# Calculus (2110014) Old Code : 110014

5
Credit
3 + 2 + 0
Lect + Tuto + Pract
Teaching Scheme
70 + 30 + 0
ESE + PA + ALA
Theory Marks
30 + 0 + 20
ESE + OEP + PA
Practical Marks
###### ESE - End Semester Examination, PA - Progress Assessment, ALA - Active Learning Assignments, OEP -Open Ended Problem

Prerequisite
Student should be able to graph elementary functions and solve both linear equations and inequalities. Students entering in Calculus should have a firm grasp of algebra and trigonometry, trigonometric functions, inverse trigonometric functions and their properties, exponential and logarithmic function. Continuity and Differentiability of functions, Derivatives of Functions in Parametric Forms, Mean Value Theorem, Rate of Change of Quantities, Increasing and Decreasing Functions, Tangent, Normal and Maxima and Minima of single variable function. Integrals, Integration as an Inverse Process of Differentiation, Integrals of some Particular Functions, Integration by Partial Fractions, Integration by Parts, Definite Integral, Fundamental Theorem of Calculus, Evaluation of Definite Integrals by Substitution, Properties of Definite Integrals, Area under Simple Curves and Area between Two Curves by integration.
Rationale

Mathematics is a language of Science and Engineering.

Course Outcome
1.  Add together infinitely many numbers.
2.  Represent a differentiable function f(x) as an infinite sum of powers of x.
3.  Decide on convergence or divergence of a wide class of series.
4.  See concavity of graph and find out points of inflection.
5.  Observe behaviour of function f(x) as x goes to infinity/ negative infinity.
6.  Able to evaluate indeterminate forms using L'Hospital's Rule.
7.  To answer at least about the convergence or divergence of integral when integral is not easily evaluated using techniques known.
8.  Able to evaluate the volume of solids such as pyramid, sphere, etc. by slicing method.
9.  Generate the solid by rotating region about an axis in its plane and hence calculating the volume of solid, by disk method.
10.  If the solid of revolution has a hole in it, then determine the volume by washer method.
11. Evaluate partial derivatives.
12. Apply the knowledge to solve some practical problems, such as constrained optimization problems and other problems involving Partial differentiation
13. Evaluate a double integral in polar coordinates.
14. Reverse the order of integration for a double integral.
15. Evaluate a triple integral to find volume in rectangular coordinates, cylindrical coordinates, and spherical coordinates.

Active Learning

Preparation of power-point slides, which include videos, animations, pictures, graphics for better understanding the applications of Calculus to engineering applications – The faculty will allocate chapters/ parts of chapters to groups of students so that the entire syllabus of Calculus is covered. The power-point slides should be put up on the web-site of the College/ Institute, along with the names of the students of the group, the name of the faculty, Department and College on the first slide. The best three works should be sent to achievements@gtu.edu.in.

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