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Basic Calculus [1]

Paper Code: 
25GMAT401
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

  1. Students will be expected to actively do mathematics, such as analyzing data, constructing hypotheses and solving problems.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

COURSE Code

COURSE Title

25GMAT

401

 

 

 

 

 

 

Basic Calculus

(Theory)

 

 

 

 

 

 

CO1: Analyze functions, calculate limits and derivatives and apply these concepts to solve problems in various fields.

CO2: Evaluate the differentiation techniques for various types of functional polynomials, trigonometric, logarithmic and exponential functions.

CO3: Develop calculus ideas for real-world circumstances by solving optimization problems, identifying crucial points and analyzing rates of change.

CO4: Explain the integration methods, including integration by parts, partial fractions and substitution.

CO5: Explain the fundamental theorem of calculus, the basic properties of definite integrals and techniques for evaluating definite integrals.

CO6: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, Assigned tasks

 

 

 

 

Quiz,

Individual and group tasks,

Open Book Test, Semester End Examination

 

Unit I: 
Limits, Continuity and differentiability
12.00
 Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Continuity and differentiability
 
Unit II: 
Differentiation of functions
12.00
 Polynomial, Trigonometric, Logarithmic and Exponential functions, Derivative of composite functions, Chain rule, Derivative of functions expressed in parametric forms, Second order derivatives.
 
Unit III: 
Applications of derivatives
12.00
 Rate of change of bodies, Increasing/decreasing functions, Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool), Simple problems (that illustrate basic principles and understanding of the subject as well as in real life situations).
 
Unit IV: 
Integration of functions
12.00
 Integration as an inverse process of differentiation, Integration of a variety of functions by substitution, By partial fractions and by parts, Evaluation of some elementary integral problems based on them.
 
Unit V: 
Applications of Integration
12.00
Fundamental theorem of calculus (without proof), Basic properties of definite integrals and evaluation of definite integrals.
 
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.
  • H.S. Dhami, Differential Calculus, New Age International (P) Ltd., New Delhi, 2012.
References: 
  • Ahsan Akhtar and Sabiha Ahsan, A Text Book of Differential Calculus, PHI Ltd. New Delhi, 2009.
  • G.C. Sharma and Madhu Jain, Calculus, Galgotia Publication, Dariyaganj, New Delhi, 2003.
  • Schaum’s, Theory and Problems of Advanced Calculus, Schaum’s outline series New York

 

 

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Academic Year: 
2025-2026 [4]

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Source URL: https://maths.iisuniv.ac.in/node/1438

Links:
[1] https://maths.iisuniv.ac.in/node/1438
[2] https://people.math.wisc.edu/~angenent/Free-Lecture-Notes/free221.pdf
[3] https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/2011.  
[4] https://maths.iisuniv.ac.in/academic-year/2025-2026