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Differential Calculus [1]

Paper Code: 
25CMAT111
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
1. Acquaint the students with fundamental concepts of single variable calculus.
2. Explore the solution of problems from a mathematical perspective and prepare students to succeed
in upper level math, science, engineering and other courses that require calculus.
3. Determine whether an infinite series is convergent or divergent.
Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

25CMAT 111

 

 

Differential Calculus (Theory)

 

 

 

 

 

 

CO1: Compare the consequences of mean value theorems for differentiable functions and be able to compute the expression for the derivative of a curve and the pedal equation for cartesian and polar curves.

CO2: Compute the convergence of infinite non-negative series and alternative series using various convergence tests.

CO3: Evaluate the expression for the derivative of a composite function using the chain rule of differentiation. Analyze the extremas of a function of two or more variables and classify them as minima, maxima, or saddles.

CO4: Determine the radius, center, and chord of curvature, envelopes and asymptotes for polar and cartesian curves.

CO5: Compute the critical points and be able to trace cartesian and polar curves.

CO6: Contribute effectively in course-specific interaction.

 

Approach in teaching:

Interactive Lectures, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, Solving tasks

 

 

 

Quiz, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
Mean Value Theorem and Derivative of an Arc
12.00

Taylor’s and Maclaurins theorems with different remainders, Expansion of sin(x), cos(x), ex, log(1+x), (1+x)m, Derivative of an arc, Pedal equation (Cartesian and Polar Curves).

 

 

Unit II: 
Series Convergence
12.00

Infinite series of non-negative terms, Convergences (definition), Test for Convergence (Without Proof): Comparison test, Cauchy’s nth root test, D’Alembert’s ratio test, Raabe’s test, De Morgan's test, Cauchy’s condensation test, Logarithm ratio test, Gauss test. Alternating Series – Leibnitz Test, Absolute and conditional convergence.

 

Unit III: 
Partial Differentiation and Extreme points
12.00

Partial differentiation, Total derivative, Euler’s theorem for homogeneous functions, Maxima and minima of functions of two independent variables: necessary and sufficient conditions (without proof), Lagrange’s undetermined multipliers (without proof) and related problems.

 

Unit IV: 
Curvature, Envelope and Asymptote
12.00

Radius, Center and chord of curvature, Envelopes for the family of cartesian curves having one and two parameters, Asymptotes (cartesian and polar curves).

 

Unit V: 
Curve Tracing
12.00

Multiple points, Classification of double points: Node, Cusp, Point of inflexion, Tracing of Cartesian and polar curves.

 

Essential Readings: 
  • Shanti Narayan, Differential Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 2008.
  • M. Ray and G.C. Sharma, Differential Calculus, Shivalal Agarwal & Co. Agra, 2010.
  • Gorakh Prasad, Text Book on Differential Calculus, Pothishala Pvt. Ltd, Allahabad, 2000.
  • H.S. Dhami, Differential Calculus, New Age International (P) Ltd., New Delhi, 2012.
  • Chaurasia, Goyal, Agarwal, Jain, Differential Calculus, RBD, Jaipur, 2020.

 

References: 
  • Schaum’s, Theory and Problems of Advanced Calculus, Schaum’s outline series New York, 2011.  
  • Ahsan Akhtar and Sabiha Ahsan, A Text Book of Differential Calculus, PHI Ltd. New Delhi, 2009.
  • G.N. Berman, A Problem Book in Mathematical Analysis, Mir Publishers, Moscow, 2016.
  • G.C. Sharma and Madhu Jain, Calculus, Galgotia Publication, Dariyaganj, New Delhi, 2003.
  • Ulrich L. Rohde, G.C. Jain, Ajay K. Poddar and A.K.Ghosh Introduction to Differential Calculus, Wiley Publications USA, 2012.

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Academic Year: 
2025-2026 [9]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/differential-calculus-14

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/differential-calculus-14
[2] https://ocw.mit.edu/courses/18-014-calculus-with-theory-fall-2010/pages/course-notes/
[3] https://nptel.ac.in/courses/111104144
[4] https://www.onlinemathlearning.com/asymptote.html
[5] https://nptel.ac.in/courses/111105121
[6] https://www.hindawi.com/journals/ijmms/contents/year/2022/
[7] http://jami.or.kr/?ckattempt=1
[8] https://www.worldscientific.com/worldscinet/ijm
[9] https://maths.iisuniv.ac.in/academic-year/2025-2026