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.