Course Title: 
Differential and Integral Calculus
Course Code: 
Year Taught: 
Undergraduate (UG)
School of Engineering

'Differential and Integral Calculus' is a course offered in the second semester of  B. Tech. programs at the School of Engineering, Amrita Vishwa Vidyapeetham.

Course Outcomes

CO Code Course Outcome Statement
CO1 S e lect suitable parameterization of curves and to find their arc lengths
CO2 Find partial derivatives of multivariable functions and to use the Jacobian in practical problems.
CO3 Understand the finite differences and apply to numerical differentiations.
CO4 Understand the concept of integration and numerical integration.
CO5 Apply Fundamental Theorem of Line Integrals and multiple integrals to solve problems in fluid mechanics, thermodynamics and other problems.

CO-PO Mapping

CO Code PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO 10 PO   11 PO   12 PSO 1 PSO2 PSO3
CO1 2 3 3 3                     2
CO2 2 3 3 3                     2
CO3 2 3 3 3                     2
CO4 2 3 3 3                     2
CO5 2 3 3 3                     2

Unit – 1

Functions – Functions and their graphs, Shifting and scaling of graphs; Limits and Continuity of a function- one- sided and two-sided limit; Differentiation – Tangents and derivative, derivative as function, differentiability, continuity of a function; vertical tangent; horizontal and vertical asymptotes, Slope, Tangent, Normal, Curvature, Binormal, Minima and Maxima of a function; Application of derivatives – Concavity and Curve Sketching; Filling and draining of tanks; Derivative of a function - Chain Rule, Implicit Differentiation, Mean Value Theorem, Partial and Total Derivative

Unit – 2

Finite differences - Difference Approximations – Forward, Backward and Central Differences; Numerical Differentiation.

Integral as Anti-derivative, Area under Curve, Limit of Sums: Riemann Integral; Integration Formulae - Techniques of Integration; Definite Integrals - Lengths, Areas, Volume, Work, Pressures, Forces; Numerical Integration: Trapezoidal and Simpson’s Rules.

Unit – 3

Double and Triple Integrals: An Introduction; Application Problems: Thermodynamics (Heat, Work), Fluid Mechanics (without introducing vector calculus), Mass Transfer (NTU in packed beds), Chemical Reaction Engineering (RTD)

Course Evaluation Pattern:

Test-1 -15 marks (two hour test)

CA - 20 marks (Quizzes / assignments / lab practice) Test – 2- 15 marks (two-hour test)

End semester- 50 marks.

Total - 100 marks.

Supplementary exam for this course will be conducted as a three-hour test for 50 marks.

Text Books

  1. James Stewart, Calculus: Early Transcendentals, 7th Edition, Cengage Learning, 2012
  2. Maurice Weir and Joel Hass, Thomas’ Calculus, 12th Edition, Pearson Education India Pvt. Ltd., 2016

References Books

  1. Bruce Finlayson, Introduction to Chemical Engineering Computing, John Wiley & Sons, 2006