B.E. (Chemical Engineering) Applied Mathematics II Syllabus - Mumbai University 2026

Module 1: Differential Equations of First Order and First Degree printed in the syllabus as Module Detailed Contents

• 1.1 Exact differential Equations, Equations reducible to exact form by using integrating factors. 1.2 Linear differential equations (Review), equation reducible to linear form, Bernoulli’s equation. # Self learning topics: Simple application of differential equation of first order and first degree to electrical and Mechanical Engineering problem

Module 2: Linear Differential Equations With Constant Coefficients of printed in the syllabus as Module Detailed Contents

Module 3: Beta and Gamma Function, Differentiation under Integral sign printed in the syllabus as Module Detailed Contents

• 3.1 Beta and Gamma functions and its properties. 3.2 Differentiation under integral sign with constant limits of integration. # Self learning topics: Rectification of curves.(Cartesian, Polar and Parametric)

Module 4: Multiple Integration- I printed in the syllabus as Module Detailed Contents

• Pre-requisite: Tracing of curves 4.1 Double integration‐ definition, Evaluation of Double Integrals.(Cartesian & Polar) 4.2 Change the order of integration.(No Evaluation) 4.3 Evaluation of double integrals by changing to polar coordinates

Module 5: Multiple Integration- II printed in the syllabus as Module Detailed Contents

• 5.1 Triple integration definition and evaluation (Cartesian, cylindrical and spherical polar coordinates). 5.2 Application of double integrals to compute Area, Mass. # Self learning topics: Application of triple integrals to compute Volume.

Module 6: Numerical solution of ordinary differential equations of first printed in the syllabus as Module Detailed Contents

• order and first degree, and , Numerical Integration 6.1 Numerical solution of ordinary differential equation using (a) Euler’s method (b) Modified Euler method, (c) Runge‐ Kutta fourth order method 6.2 Numerical integration‐ by (a) Trapezoidal (b) Simpson’s 1/3rd (c) Simpson’s 3/8th rule (all without proof)

References

• 1 Higher Engineering Mathematics, Dr.B.S.Grewal, Khanna Publication
• 2 Advanced Engineering Mathematics, Erwin Kreyszig, Wiley EasternLimited, 9thEd.
• 3 Engineering Mathematics by Srimanta Pal and SubodhBhunia, Oxford University Press
• 4 Applied Numerical Methods with MATLAB for Engineers and Scientists by Steven Chapra, McGraw Hill
• 5 Elementary Linear Algebra with Application by Howard Anton and Christ Rorres. 6th edition. John Wiley & Sons,INC.