# Unit -I Unit -II Unit III Unit- IV Unit -V

## Transcription

Unit -I Unit -II Unit III Unit- IV Unit -V

AHL-003-A L T P Cr. 3 1 0 4 MATHEMATICS βI (Common for all Branches of Integrated B. Tech) SECTION -A Unit -I Trigonometric Functions: Addition and subtraction formulae, product formulae and their application in engineering problems. Transformation from product to sum or difference of two angles or vice versa, multiple and submultiple angles, Conditional identities, Graphs of trigonometric functions πππ π, πππ π ππ§π πππ π. Unit -II Function, Limit and Continuity: Definition of function, domain, co-domain and range of a function, real valued function, domain and range of these functions, types of functions and graph of these functions. Intuitive idea of limit, Limit of polynomials and rational functions, trigonometric, exponential and logarithmic functions. Continuity of a function at a given point. Unit III Differentiability: Differentiability, derivate of sum, difference, product and quotient of function, derivative of polynomials and trigonometric functions, derivative of composite functions, chain rule. Derivative of exponential and logarithmic functions. SECTION- B Unit- IV Integrals: Integration as reverse process of differentiation, Integration by substitution, by partial fraction, by parts, simple integrals of the following types: ππ₯ π₯ 2 ±π 2 , ππ₯ π₯ 2 ±π 2 π₯ 2 β π2 ππ₯, , ππ₯ π 2 βπ₯ 2 , ππ₯ ππ₯ 2 +ππ₯ +π , ππ₯ ππ₯ 2 +ππ₯ +π , ππ₯ +π ππ₯ 2 +ππ₯ +π ππ₯ , ππ₯ +π ππ₯ 2 +ππ₯ +π ππ₯ , π2 ± π₯ 2 ππ₯, ππ₯ 2 + ππ₯ + π ππ₯ , (ππ₯ + π) ππ₯ 2 + ππ₯ + π ππ₯ . Unit -V Vectors: Vectors and scalars, magnitude and direction of a vector, Direction cosines and direction ratios of a vector. Types of vectors( equal, zero, unit, parallel and collinear vectors), position vector of a point, negative of a vector, components of vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio, scalar(dot) product of vectors, projection of a vector on a line, vector(cross) product of vectors, scalar triple product of vectors. Unit- VI Higher Order Derivatives: Higher order derivatives, Leibnitz theorem. Applications: Finding Tangents, Normal, Points of Maxima/Minima, Increasing/Decreasing functions NOTE: The syllabus is divided into 2 sections comprising three units each. Total seven questions would be set. One question would be compulsory that would comprise all the units. Remaining six questions will be set from both the sections taking three questions from each section. Students need to attempt at least two questions from each section. A student has to attempt five questions in all. RECOMMENDED BOOKS 1. Applied Mathematics Vol. I by SS Sabharwal and Others by Eagle Prakashan,Jalandhar 2. Engineering Mathematics Vol. I by Ishan Publishing House 3. Applied Mathematics Vol. I by RD Sharma 4.Engineering Mathematics by Dass Gupta 5. Higher Engineering Mathematics by BS Grewal; Khanna Publishers, Delhi AHL-004-A L T P Cr. 3 1 0 4 MATHEMATICS-II (Common for all Branches of Integrated B. Tech) SECTION -A Unit -I Matrices and Determinant: Definition of matrix, addition, subtraction and multiplication of matrices (up to third order). Determinant of a square matrix upto 3rd order, properties of determinant, minors, cofactors, Adjoint and inverse of a matrix, Solving system of linear equations in two or three variables(having unique solution) using inverse of a matrix. Unit- II Series: AP and GP; Sum, nth term, Permutations and Combinations, Binomial theorem for positive, negative and fractional index (Without proof). Applications of Binomial theorem. Unit- III Complex Numbers: Definition, Real and Imaginary parts of a complex number, polar and Cartesian representation of a complex number and conversion from one form to the other, conjugate of a complex number, modulus and argument of a complex number, addition, subtraction, multiplication and division of a complex number. Problems on Demoivreβs theorem SECTION-B Unit - IV Differential Equations: Formation of differential equation ,Solution of first order and first degree differential equation by Variable separation, Homogeneous differential equation and reducible homogeneous differential equations , Linear differential equations. Unit -V Co-ordinate Geometry: Area of a triangle, Centroid and incentre of a triangle (given the vertices of a triangle), Simple problems on locus, Equation of straight line in various standard forms (without proof) with their transformation from one form to another, Angle between two lines and finding perpendicular distance from a given point to a given line. Unit -VI Conic Sections: Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of parabola, ellipse and hyperbola, Standard equation of circle. NOTE: The syllabus is divided into 2 sections comprising three units each. Total seven questions would be set. One question would be compulsory that would comprise all the units. Remaining six questions will be set from both the sections taking three questions from each section. Students need to attempt at least two questions from each section. A student has to attempt five questions in all. RECOMMENDED BOOKS 1. Engineering Mathematics by Ishan Publication 2. Applied Mathematics Vol. II by SS Sabharwal and Others; Eagle Parkashan, Jalandhar 3. Applied Mathematics Vol. II by Dr RD Sharma 4. Higher Engineering Mathematics by BS Grewal; Khanna Publishers, Delhi