Basic Engineering Mathematics(SC-102) Diploma in Computer Engineering

 Unit I - Algebra

1. Logarithms:

• Define the properties of logarithms and differentiate between natural and common logarithms.
• What is the meaning of e and how does it relate to the exponential function?
• Represent logarithm as a function and explain its graphical representation.
• Solve questions involving changing between logarithmic and exponential forms, simplification using properties, and finding unknowns in logarithmic equations.

2. Partial Fractions:

• Differentiate between rational, proper, and improper fractions of polynomials.
• Resolve rational fractions into partial fractions based on different types of denominators:
  • Distinct linear factors.
  • Repeated linear factors.
  • Quadratic factors.
  • Combinations of linear and quadratic factors.
• Solve problems related to finding partial fractions and integrating rational functions using partial fractions.

Unit II - Matrices and Determinants

• Define a matrix and differentiate between various types (e.g., square, diagonal, symmetric, etc.).
• Perform basic operations on matrices, including addition, subtraction, scalar multiplication, and product.
• Calculate the transpose of a matrix and identify symmetric and skew-symmetric matrices.
• Understand the concepts of minors, cofactors, and determinants.
• Determine the determinant of a square matrix up to 3rd order using Laplace's expansion.
• Apply properties of determinants to solve problems.
• Define singular and non-singular matrices and calculate the adjoint and multiplicative inverse of a square matrix.
• Solve problems involving inverse matrices and simultaneous linear equations.

Unit III - Trigonometry

• Derive and apply formulas for sine, cosine, tangent, and cotangent of compound angles (A ± B).
• Solve problems involving trigonometric ratios of multiple and sub-multiple angles.
• Prove trigonometric identities related to sum, difference, multiple, and sub-multiple angles.
• Solve simple problems using the derived formulas.

Unit IV - Properties of Triangles and Complex Numbers

• State and apply the sine rule, cosine rule, tangent rule, and projection rule to solve triangles.
• Define hyperbolic functions and their identities.
• Express inverse hyperbolic functions in terms of logarithms.
• Define complex numbers, modulus, conjugate, and perform arithmetic operations on them.
• Convert complex numbers between modulus-amplitude (polar) and exponential (Euler) forms.

Unit V - Transformations and Inverse Trigonometric Functions

• Transform products into sums and vice versa using trigonometric identities.
• Solve problems involving these transformations.
• Define inverse trigonometric functions and their domains and ranges.
• Express an angle A in terms of other inverse trigonometric functions when given A=sin-1 x.
• Apply properties of inverse trigonometric functions and identities to solve problems.

Unit VI - Solutions of Simultaneous Equations and Triangles

• Solve systems of linear equations in 3 variables using Cramer's rule, matrix inversion method, and elementary row operations.
• Apply Gauss-Jordan method to solve a system of equations in 3 unknown variables.
• Solve a triangle when given:
  • Three sides (SSS)
  • Two sides and an included angle (SAS)
  • One side and two angles (SAA)