Indian Institute of Management Rohtak

Course Outline

Course Title : Differential Calculus-I

Credits : 1 (20 Sessions)
Type : Compulsory
Session Duration : 75minutes
Term : I
Year : 2024
Faculty : Dr. Lalit Kumar
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Introduction

The objective of this course is to gain proficiency in differential calculus. Differential calculus
develops the concepts of limit, continuity and derivative; and is fundamental for many concepts in
business and economics.

Course Objectives

The specific objectives of the course are:

1) To understand fundamental concept of calculus including limits, continuity and
differentiability.
2) To learn about applications of derivatives for relative extrema and sketching of curves.
3) To understand the quantitative change in the behaviors of the variables and apply them on the
problems related to business and economics.
Pedagogy

The pedagogy would be a mix of Lecture, Discussion, Group exercises, Assignments, Quizzes and
Project Work.

Evaluation Scheme
Assessment/Quizzes/CP 10 %
Project work/Presentation 20%
Mid Term Exam 35.%
Final Exam 35 %

Brief Outline

Differentiation: Functions, Monotone functions, Limits and continuity, intermediate value theorem,
derivative, concavity, point of inflexion, relative extrema using first and second derivative tests;
Asymptotes, sketching and tracing of curves, inverse functions, exponential and logarithmic
functions; hyperbolic functions.

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Mean Value Theorems: Rolle’s theorem, Lagrange’s mean value theorem. Applications. Derivatives
of functions of several variables: Functions of several variables; Limits and continuity; Partial
differentiation; Directional derivatives; Extrema of functions of two variables.

Learning Outcomes:

Upon completion of course, the participants can obtain thorough knowledge of Limits and Continuity:
Understand the concept of limits and evaluate them for various functions. Differentiate between one-
sided, two-sided, and infinite limits. Discuss continuity at a point and continuity over an interval.
Interpret & Derivatives: Find derivatives of various function types using differentiation rules. Interpret
the derivative of a function at a point. Apply the chain rule, implicit differentiation, and derivatives
of inverse functions. Calculate. Applications of Derivatives: Solve related rates problems. Use linear
approximation and differentials. Identify extrema and critical points of a function. Apply the mean
value theorem. Evaluate graphs using the first and second derivative test. Solve optimization
problems. Understand. Integration: Calculate indefinite integrals using basic integration techniques.
Interpret definite integrals and apply the Fundamental Theorem of Calculus. Use substitution for both
indefinite and definite integrals., Integrate functions involving exponential, logarithmic, and inverse
trigonometric functions. Approximate integrals when the antiderivative is challenging to find.
Geometric and Physical Applications: Calculate areas of curved regions using integration. Find
volumes of solids of revolution. Determine arc length and surface area. Apply integration to real-
world concepts like mass, density, work, and force

Text Book: [1]. Stewart J. (2012), Calculus Early Transcendentals (7thedition) , Brooks/Cole
Cengage Learning.

Other Readings (To be arranged by students):

[2]. Strauss, M.J., Bradley, G. L. and Smith, K. J. (2007). Calculus (3rd edition), Pearson Education.
[3]. Deborah,H.-H., Gleason, A. H., et al. (2014), Applied Calculus (5th edition), John Wiley.
[4]. Narayan, S., (1961), Differential Calculus, S Chand & Copany.

Other Materials (To be provided in course pack)

a) Assignments with multiple choice questions.
b) Some standard functions together their fundamental properties.
Some results and examples from reference [4].

Special Instructions:

Read and prepare well in advance for case presentation &discussion in the class. Chapter for each
session is indicated in the Session Plan. The sessions will be of 75 minutes’ duration. R indicates
additional readings. C indicates cases.

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 Session Plan

Session Topic and Sub-topics Reference(Book Case / Exercise / Assignment

No. chapter / Page
numbers from the
book/Additional
readings)

1 Sequences, Functions Chapter 11.1, and Exercise from chapter 11, chapter
and Models Chapter 1 1/Additional assignment and problems given
by faculty

2 Limits, Continuity Chapter 2 Exercise Chapter 2/ Additional assignment

and problems given by faculty

3 Derivatives, Rate of Chapter 2 Exercise Chapter 2/ Additional assignment

Change and problems given by faculty

4 Rules of Differentiation Chapter 3 Exercise Chapter 3/ Additional assignment

and problems given by faculty

5 Normal and Tangents Chapter 3 Exercise Chapter 3/ Additional assignment

and problems given by faculty

6 Linear Approximation Chapter 3 Exercise Chapter 3/ Additional assignment

and problems given by faculty

7 Intermediate Value Chapter 4 Exercise Chapter 4/ Additional assignment

Theorems and problems given by faculty

8 Curve Sketching Chapter 4 Exercise Chapter 4/ Additional assignment

and problems given by faculty

9 Curve Sketching Chapter 4 Exercise Chapter 4/ Additional assignment

and problems given by faculty

10 Optimization Problems Chapter 4 Exercise Chapter 4/ Additional assignment

(With business and and problems given by faculty/Quiz
economics examples)

11 Functions of several Chapter 14 Exercise Chapter 14/ Additional assignment

variables, Limit and problems given by faculty

12 Continuity of functions Chapter 14 Exercise Chapter 14/ Additional assignment

of several variables and problems given by faculty

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13 Partial Derivatives Chapter 14 Exercise Chapter 14/ Additional assignment
and problems given by faculty

14 Differentiability and Chapter 14 Exercise Chapter 14/ Additional assignment

Directional Derivatives and problems given by faculty

15 Chain Rule Chapter 14 Exercise Chapter 14/ Additional assignment

and problems given by faculty

16 Vectors, Dot Product, Chapter 12, 16 Exercise Chapter 12, 16/ Additional
Cross Product, Gradient, assignment and problems given by faculty
Curl, Divergence

17 Infinite Series Chapter 11 Exercise Chapter 11/ Additional assignment

and problems given by faculty

18 Taylor’s Theorem and Chapter 14 Exercise Chapter 14/ Additional assignment

Linear Approximation and problems given by faculty

19 Optimization of multi- Chapter 14 Exercise Chapter 14/ Additional assignment

variable problems (With and problems given by faculty
business and economics
examples)

20 Lagrange Multipliers, Chapter 14, Exercise Chapter 14/ Additional assignment

Project Work, Group Project and problems given by faculty/Group
Presentation Project/Quiz

Important Note: The Course will not tolerate plagiarism, copying or active or passive collaboration
in this type of dishonest behavior in papers written by our students. This penalty for plagiarism will
be immediate failure of the course. Furthermore, the Institute will initiate proceedings against the
student that could lead to his/her expulsion from the programme.