Engineering Mathematics-II syllabus

SPPU First Year Engineering, 2024 pattern, Semester II. Course code BSC-151-BES. Five units, 40 hours of theory, with the marks scheme, outcomes and books taken from the official syllabus book.

4 credits (3 theory + 1 tutorial)CCE 30 + End-Sem 70Term work 255 units x 8 hours
40hours of theory
05.units
04.credits

Unit-wise syllabus

UNIT I

Integral Calculus

8 hours
Reduction FormulaeBeta and Gamma functionsDifferentiation Under Integral SignError functions
UNIT II

Curve Tracing and Solid Geometry

8 hours
Tracing of Curves: Cartesian, Polar and ParametricRectification of curvesCartesian, Spherical polar and Cylindrical coordinate systemsSphere, Cone and Cylinder
UNIT III

Multiple Integrals and Applications

8 hours
Double and Triple integrationsChange of order of integrationApplications: Area, Volume, MassCentre of Gravity and Moment of Inertia
UNIT IV

First Order Ordinary Differential Equation

8 hours
Exact differential equationsEquations reducible to exact formLinear differential equationsEquations reducible to linear form and Bernoulli’s equation
UNIT V

Applications of Differential Equations

8 hours
Orthogonal TrajectoriesNewton’s Law of CoolingKirchhoff’s Law of Electrical CircuitsRectilinear Motion and Simple Harmonic MotionOne dimensional Conduction of Heat

Marks and credits

HeadMarksCredit
Theory: CCE303
Theory: End-Semester70
Tutorial / term work251

The prerequisites listed in the syllabus are integration, differential equations and three-dimensional coordinate systems. The course covers advanced integration, curve tracing, solid geometry, multiple integrals and their applications, and mathematical modelling of physical systems with differential equations. Term work is based on assignments on the units, with performance and continuous internal assessment.

Course outcomes

  1. CO1Apply reduction formulae, Beta and Gamma functions, differentiation under the integral sign and error functions to evaluate integrals.
    Covers Unit I
  2. CO2Trace curves, measure arc length, and apply solid geometry to the sphere, cone and cylinder.
    Covers Unit II
  3. CO3Evaluate multiple integrals and use them for area, volume, centre of gravity and moment of inertia.
    Covers Unit III
  4. CO4Solve first order ordinary differential equations: exact, reducible to exact, linear and reducible to linear.
    Covers Unit IV
  5. CO5Model physical systems with ordinary differential equations: Newton’s law of cooling, electrical circuits, rectilinear motion, mass-spring systems and heat transfer.
    Covers Unit V

Books

Text books

Reference books

Video lectures

The syllabus lists one playlist for this course, the same one it lists for Engineering Mathematics-I: NPTEL / YouTube playlist.

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FAQ

How many credits is Engineering Mathematics-II in the SPPU 2024 pattern?

BSC-151-BES carries 4 credits: 3 for theory (3 hours a week) and 1 for the tutorial (1 hour a week).

How are the marks split?

Theory is graded out of 100: CCE (continuous internal evaluation) 30 and End-Semester 70. Term work is a separate 25 marks tied to the tutorial credit.

How many units are there?

Five units of 8 hours each, 40 hours in total: integral calculus, curve tracing and solid geometry, multiple integrals, first order ordinary differential equations, and applications of differential equations.

How is term work assessed?

Through assignments on the units, based on performance and continuous internal assessment. The syllabus sets tutorial batches of at most 22 students.

Which books does the syllabus list?

Text books: B. V. Ramana and B. S. Grewal, both titled Higher Engineering Mathematics. Six reference books are listed too, including Kreyszig, Thomas’ Calculus and S. L. Ross on differential equations.