COURSE: B Sc (ELECTRONICS)
SEMESTER: I
SUBJECT: MATHEMATICS-I
SUBJECT CODE: BSCE-12
BLOCK I - ALGEBRA
Unit -1: Determinants
Introduction to Determinants, Minors and Cofactors, Properties of determinants,
Laplace's Expansion of determinant, Solutions of Simultaneous linear Equations by
determinants (Cramers Rule)
Unit-2: Matrices
Definition, Types of Matrices, Matrix Addition, Subtraction and Multiplication. Ad
joint and Inverse of a matrix, Characteristic roots or Eigen values, Cayley - Hamilton
theorem. Characteristic vectors or Eigen vectors, Properties of Eigen Vectors.
Unit-3: Vector Algebra
Introduction to vectors, Addition and Subtraction of vectors, Properties of Addition of
vectors, Position vector of a point, Ratio formula product of two vectors, Scalar or
Dot product of two vectors, Work done as a scalar product, Vector product or Cross
product, Moment of a force. Scalar triple product, Vector triple product.
BLOCK II - DIFFERENTIAL CALCULUS
Unit-1: Trigonometry
Introduction, Measurement of Angles, Trigonometric ratios. Trigonometric functions.
Trigonometric functions of sum and difference of two angles. Transformation
formulae. Trigonometric functions of multiple and sub-multiple angles. Properties and
solution of triangles. Inverse Trigonometric functions.
Unit-2: Limits and Continuity
Definition of variables, Definition of functions. Kinds of functions. Evaluation of
simple limits, some important limits. Left hand and Right hand limits, continuity of a
function. Differentiability of a function.
Unit-3: Differentiation
Definition of differentiation, Differentiation of a function from first principle.
Differentiation of sum, product and quotient of function. Derivatives of a functionChain Rule, Implicit function, Parametric function, Logarithmic differentiation.
Successive differentiation, calculus of
Unit-4: Application of differentiation
Tangents and Normal's. Increasing and decreasing functions, Maxima and Minima.
Unit-5: Partial differentiation
Partial derivatives of first order, second order, Total derivative, chain Rule,
Homogenous function, Euler's theorem on differentiation of Implicit function
BLOCK III - INTEGRAL CALCULUS
UNIT-1: Integration
Introduction, Definition, Hyperbolic functions Standard results, Indefinite Integrals
Integration by the method of Substitution. Standard formula. Integration by parts.
Integration by partial fraction method, Integration of Irrational functions. Integration
of Trigonometric functions
Unit-2: Definite Integrals
Introduction, Theorems on definite integrals-problems
UNIT-3: Application of Integration
Find Area, Volume and RMS value of a function. Problems.
UNIT-4: Vector Calculus
Differentiation of a vector, Scalar and vector paint functions, Directional derivatives,
Gradient, Divergence.
********************************************