Insight of the subject:

The WBUT Instrumentation Engineering 1st Sem Mathematics-1(M101) basically deals with the study of various mathematical operations and mathematical relationships. The subject deals with the methods of solving problems, and that too with a different approach all together. There are plenty of topics in this subject that helps the candidates in solving out bigger problems of their respective trades.

Examination:

The WBUT Instrumentation Engineering 1st Sem Mathematics-1(M101) question paper has all together 12 questions in the subjective part and 12 MCQs. The questions are asked from almost every aspect of the syllabus.

Paper pattern:

All together there are 12 MCQs out of which the candidates are required to answer only 10. The paper is divided basically in to three sections. Section one has MCQs; section B has short questions of 5 marks each. All together there are 6 questions out of which the candidates are required to answer any three. The last section is section C which has long type questions of 15 marks each. There are 5 to 6 questions in this section, and the candidates are required to answer any 3.

Recommended Books:

1. B.S. Grewal “Engineering Mathematics”, S. Chand & Co., New Delhi.

2. Integral Calculus, Das & Mukherjee

3. Engineering mathematics, Das and pal

Syllabus:

Infinite Series:

Sequence, Convergence and Divergence of Infinite series – and typical examples of convergent and divergent series.

Comparison test (statement only) and related problems

Ratio test (statement only) and related problems

Cauchy’s root test (statement only) and related problems

Alternating series, Leibnitz’s theorem (without proof), absolute convergence and related problems.

Calculus of Functions of One Variable:

Review of limit and continuity and differentiability.

Successive differentiation, Leibnitz’s theorem (without proof but with problems of the type of recurrence relations in derivatives of different orders and also to find (yn)0 ):

Rolle’s Theorem (statement only); Mean Value Theorems—Lagrange & Cauchy (statement only), Taylor’s theorem (without proof and problems in respect of direct use and applications of the theorem only), Expansions of functions by Taylor and Maclaurin series. Maclaurin’s expansion in infinite series of the functions: log (1+x), ex, sinx, cosx, (a+x)n , n being a negative integer or a fraction L’Hospital’s Rule (statement only) and related problems.

Integration of m, n is positive integers.

Application:

Rectification

Three Dimensional Geometry (Cartesian):

Direction Cosine, Direction Ratio; Equation of a Plane (general form, normal form and intercept form); Equation of a Straight Line passing through one point and two points; Pair of intersecting planes representing a straight line.

Elementary ideas of surfaces like sphere, Right Circular Cone and Right Circular Cylinder (through Geometrical configuration) and equations in standard forms.

Calculus of Functions of Several Variables:

Introduction of Function of several variables and examples.

Knowledge of limit and continuity.

Partial derivative & related problems. Homogeneous Functions and Euler’s Theorem (statement only) & Problems up to 3 variables.

Chain rules and related problems.

Differentiation of implicit functions & related problems.

Total differentials and related problems.

Maxima, minima and saddle points – definition, condition of extrema & problems for two variables. Lagrange’s multiplier method – problems related to two variables only.

Line Integral, Double Integrals, Triple Integral – Discussion w.r.t. different types of limits and problems; Moment of Inertia, Centre of Gravity.

Jacobian – Definition and related problems for two variables. Applications to areas and volumes, surface area of revolution.

Vector Calculus:

Scalar and Vector fields – Definition and Terminologies; Products: dot, cross, box, vector triple product.

Gradient, directional derivative, divergence, curl. (with problems).

Tangent planes and normals and related problems.

Statements of Green’s theorem, Divergence theorem, Stokes’ theorem with applications.

Download WBUT Instrumentation Engineering 1st Sem Mathematics-1 (M101) Papers