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 10 week duration
MM3CRT01: CALCULUS
5 hours/week (Total Hours: 90)
4 credits
Syllabus
Text Books:
1. Shanti Narayan, P.K.Mittal: Differential Calculus , SChand and Company
2. George B Thomas Jr: Thomas’ Calculus (12thEdition), Pearson.
Module I: Differential Calculus (27 hrs)
Expansion of functions using Maclaurin’s theorem and Taylor’s theorem, Concavity and points of
inflexion. Curvature and Evolutes. Length of arc as a function derivatives of arc, radius of curvature –
Cartesian equations only. (Parametric, Polar, Pedal equation and Newtonian Method are excluded)
Centre of curvature, Evolutes and Involutes, properties of evolutes. Asymptotes and Envelopes.
Text 1: Chapter 6, Chapter 13, Chapter 14 , Chapter 15 ( Section 15.1 to 15.4 only), Chapter 18
(Section 18.1 to 18.8 only).
Module II: Partial Differentiation (18 hrs)
Partial derivatives, The Chain rule, Extreme values and saddle points, Lagrange multipliers.
Text 2 Chapter 14 (Sections 14.3, 14.4, 14.7 and 14.8 only) All other sections are excluded
Module III: Integral Calculus (20 hrs)
Volumes using Crosssections, Volumes using cylindrical shells, Arc lengths, Areas of surfaces of
Revolution.
Text 2: Chapter 6 (Section 6.1 to 6.4 only (Pappus Theorem excluded)
Module IV: Multiple Integrals (25 hrs)
Double and iterated integrals over rectangles, Double integrals over general regions, Area by double
integration, Triple integrals in rectangular coordinates, Triple integrals in cylindrical and spherical
coordinates, Substitutions in multiple integrals.
Text 2: Chapter 15 (Sections 15.4 and 15.6 are excluded)
References
1. T.M Apostol Calculus Volume I & II(Wiley India)
2. WidderAdvanced Calculus, 2nd edition
3. K.C. Maity& R.K Ghosh Differential Calculus( New Central Books Agency)
4. K.C. Maity& R.K Ghosh Integral Calculus( New Central Books Agency)
5. Shanti Narayan, P.K. Mittal Integral Calculus (S. Chand & Co.)
Learning Objectives:
 The students get an idea for mathematical reasoning through analyzing, proving and explaining concepts
 Problemsolving techniques are applied to diverse situations in physics, engineering and other mathematical contexts
Learning Outcomes :
After completing this course the learner should be able to
 Find the higher order derivative s, concavity, points of inflexion , curvature, Evolute, Length of the arc, radius of curvature, and centre of curvature of curves& c.
 Expand a function using Taylor’s and Maclaurin’s series.
 Understand the concept of asymptotes and their equations.
 Learn about partial derivatives and its applications.
 Find the area under a given curve, length of an arc of a curve when the equations are given in parametric and polar form.
 Find the area and volume by applying the using different methods. They become aware of the Multiple integrals.

Module I: Differential Calculus (27 hrs)
Expansion of functions using Maclaurin's theorem and Taylor's theorem, Concavity and points of inflexion. Curvature and Evolutes. Length of arc as a function derivatives of arc, radius of curvature  Cartesian equations only. (Parametric, Polar, Pedal equation and Newtonian Method are excluded) Centre of curvature, Evolutes and Involutes, properties of evolutes. Asymptotes and Envelopes.

Module II: Partial Differentiation (18 hrs)
Partial derivatives, The Chain rule, Extreme values and saddle points, Lagrange multipliers. Text 2 Chapter 14 (Sections 14.3, 14.4, 14.7 and 14.8 only) All other sections are excluded

Module III: Integral Calculus
Volumes using Crosssections, Volumes using cylindrical shells, Arc lengths, Areas of surfaces of Revolution.

Module IV: Multiple Integrals (25 hrs)
Double and iterated integrals over rectangles, Double integrals over general regions, Area by double integration, Triple integrals in rectangular coordinates, Triple integrals in cylindrical and spherical coordinates, Substitutions in multiple integrals.
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