BM-102: Engineering Mathematics -I syllabus for BM 1st Year C20 regulation APSBTET

Engineering Mathematics -I detailed syllabus for Diploma in Bio-Medical Engineering (BM) for C20 regulation curriculum has been taken from the APSBTET official website and presented for the BM students. For course code, course name, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For Diploma in Bio-Medical Engineering 1st Year scheme and its subjects, do visit BM 1st Year C20 regulation scheme. The detailed syllabus of engineering mathematics -i is as follows.

Course Objectives

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Course Outcomes:

1. Identify various functions, resolve partial fractions and solve problems on matrices.
2. Solve problems using the concept of trigonometric functions, their inverses and complex numbers.
3. Find the equations and properties of straight lines, circles and conic sections in coordinate system.
4. Evaluate the limits and derivatives of various functions.
5. Evaluate solutions for engineering problems using differentiation.

Unit I

Algebra

1. Relations and Functions:Define Set, Ordered pairs, Cartesian product, Relations, functions, domain & range of functions. Describe types of functions (in-to, many-to-one, one-one, onto and bijective) and inverse functions – examples.
2. Partial Fractions:Define rational, proper and improper fractions of polynomials. Resolve rational fractions in to their partial fractions covering the types mentioned below.
1. f(x) / (ax + b)(cx + d)
2. f(x) / (ax + b)^2 (cx + d)
3. f(x) / (x^2 + a^2)(bx + c)
4. f(x) / (x^2 + a^2)(x^2 + b^2)
3. Matrices:Definition of a matrix, types of matrices-examples, algebra of matrices-equality of two matrices, sum, scalar multiplication and product of matrices. Transpose of a matrix-Symmetric, skew symmetric matrices-Minor, cofactor of an element-Determinant of a square matrix-Laplace’s expansion, properties of determinants. Singular and non singular matrices-Adjoint and multiplicative inverse of a square matrix- examples-System of linear equations in 3 variables-Solutions by Cramers’s rule and Matrix inversion methodexamples.

Unit II

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Unit III

Coordinate Geometry

1. Straight lines: various forms of straight lines, angle between lines, perpendicular distance from a point, distance between parallel lines-examples.
2. Circle: locus of a point, Circle, definition-Circle equation given (i) centre and radius, (ii) two ends of a diameter (iii) centre and a point on the circumference (iv) three non collinear points – general equation of a circle – finding centre, radius.
3. Definition of a conic section, equation of a conic when focus directrix and eccentricity are given. properties of parabola, ellipse and hyperbola in standard forms.

Unit IV

Differential Calculus

1. Concept of Limit- Definition- Properties of Limits and Standard Limits -Simple Problems-Continuity of a function at a point- Simple Examples only.
2. Concept of derivative- Definition (first principle)- different notations-derivatives of elementary functions- problems. Derivatives of sum, product, quotient, scalar multiplication of functions – problems. Chain rule, derivatives of inverse trigonometric functions, derivative of a function with respect to another function, derivative of parametric functions, derivative of hyperbolic, implicit functions, logarithmic differentiation – problems in each case. Higher

order derivatives – examples – functions of several variables – partial differentiation, Euler’s theorem-simple problems.

Unit V

Applications of Derivatives:

1. Geometrical meaning of the derivative, equations of Tangent and normal to a curve at any point. Lengths of tangent, normal, subtangent and subnormal to the curve at any point – problems.
2. Physical applications of the derivative – velocity, acceleration, derivative as a rate measure -Problems.
3. Applications of the derivative to find the extreme values – Increasing and decreasing functions, finding the maxima and minima of simple functions – problems leading to applications of maxima and minima.
4. Using the concept of derivative of a function of single variable, find the absolute error, relative and percentage errors and approximate values due to errors in measuring.

Text Books:

For the complete syllabus, results, class timetable, and many other features kindly download the iStudy App
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Reference Books:

1. Shanti Narayan, A Textbook of matrices, S.Chand&Co.
2. Robert E. Moyer & Frank Ayers Jr., Schaum‟s Outline of Trigonometry, 4th Edition,Schaum‟s Series
3. M.Vygodsky, Mathematical Handbook, Mir Publishers, Moscow.
4. Frank Ayers & Elliott Mendelson, Schaum‟s Outline of Calculus, Schaum‟s Series

For detailed syllabus of all other subjects of Diploma in Bio-Medical Engineering, C20 regulation curriculum do visit BM 1st Year subject syllabuses for C20 regulation.

For all Diploma in Bio-Medical Engineering exam timetable, visit APSBTET BM all semester exam timetable direct link.