SBTE Syllabus for Engineering Mathematics II:
The Course Content and Curriculum of Engineering Mathematics II comprises of the following Chapters and topics:
(b)Vector Algebra and Statistics
Here is the detailed information about all the topics that are included in the above from a to d
-Functions: constants, variables, functions, graphical representations, of functions, odd & even functions, explicit & implicit functions & other types of Functions.
-Limits: definitions, fundamental theorem, important hand limit. Definition fundamental theorem, important formulas and its important deduction, simple problems.
-Continuity of a Function: left hand limit and right hand limit. Definition of a continuous function, simple problems to test the continuity of a function.
-Differentiation of a function: increment, differential co efficient, derivatives of an algebraic, trigonometric, exponential, logarithmic, and inverse functions from first principle, differentiation of sum, difference, product quotient of two functions, fundamental theorems of differentiation of implicit function and parametric functions.
-Geometric Meaning: Significance of derivative and its sign, geometric interpretation of dy/dx equation of tangents and normals to a curve. Angle between two curves.
-Application of dy/dx: approximate calculations and small errors interpretations of dy/dx as a rate measure, practical problems, maximum & minimum functions of single variable.
-Successive Differentiation: definition and notations, the nth derivatives of some special functions, leibnithz theorem.
-Partial Differentiation: idea of partial differentiation , partial derivatives, successive partial derivatives, euler theorem on homogeneous functions, partial differentiation of implicit functions, total differential.
-Integration: integration as inverse process of differentiation, introduction, integration by transformation, integration by substitution and integration by parts.
-The definite Integral: Properties of the definite integral problem of area by integration method.
(b)Vectors and Statics:
-Introduction to Vectors: definition of scalars and vectors with example, representation of a vector, types of vectors, (unit vector, zero vector, negative vector, and equality of vectors) addition and subtraction of vectors, multiplication by a scalar.
-Position vector: position vector of a point resolution of vectors (coplanar vectors and space vectors) point of division, centroid of triangle.
-Product of two vectors: scalar or dot vector, vector or cross product, geometrical interpretation and their properties.
-Product of three vectors: scalar product of three vectors, vectors product of three vectors and its geometrical meaning.
-Physical application: test of collinearity, coplanarity and linear dependence of vectos, work done as a scalar product.
-Statics via vectors: resultant of two forces acting as a point, parallel forces , moments
-Introduction: definition of a differential equation, formation of a differential equation, ordinary and partial differential equation, order and degree of a differential equations.
-Equation of first order and first degree: solution of different types of equations variable equation, homogeneous equation, equation reducible to homogeneous form, linear equation exact differential equation.
-Linear differential equation: with constant coefficients of orders two, definition, complete solutions rules for finding the complementary function. Rules for finding the particular integral simple problems.
(d)Dynamics via Calculus:
-Introduction: Definition of important terms, used in dynamics, uniformity velocity, uniform acceleration, motion under gravity, simple problems.
-Projectile: terminology, motion of a projectile velocity at any point, greatest height, time of flight and horizontal range, two directions of projectile, minimum speed for range, motion of a given height