CTEVT 1st Sem Math I Online Class

• Cardinality of set, Power set, Properties of set algebra, De Morgan’s laws
• Real number systems, intervals and absolute value
• Relations and Functions, idea of domain and range
• Types of functions, exponential and logarithmic functions with their graphs

2.1 Revision: Basic trigonometric formulae, Identities, conditional identities, Height and distance

2.2 Trigonometric Equations and Inverse Circular Functions

• General solutions of the equations of type Sin x = k, Cos x = k, and Tan x = k
• Formulae involving inverse circular functions
• Simple identities and equations involving circular functions

2.3 Properties of Triangles

• The Sine, Cosine, and projection laws (with proofs)
• The half angle formulae, Tangent laws, and area of a triangle (without proofs)
• Simple cases on solution of triangles

3.1 Limit and Continuity

• Limit of functions, Indeterminate forms (only 0/0, ∞/∞, and ∞−∞)
• Algebraic properties of limits (without proof)
• Theorems on limits (without proof)
• Continuity and discontinuity of function, types of discontinuity

3.2 Derivatives

• Definition, geometrical and physical meanings of derivative
• Derivatives from definition of simple functions like x^n, (ax+b)^n, sin(ax + b), e^(ax), a^x, log x
• Rules of derivatives (sum, difference, product, quotient, and chain rules)
• Derivatives of trigonometric, parametric, and implicit functions
• Higher order derivatives

3.3 Integration

• Definition and notation, Basic rules of integration
• Fundamental integrals and Integration by substitution
• Integration by parts and Definite integrals

4.1 Progressions

• Arithmetic, Geometric, and Harmonic Progressions
• Sum of infinite geometric series, Sum of First natural numbers
• Sum of squares and cubes of First n natural numbers (without proof)

4.2 Permutations and Combinations

• Principle of counting, Types of Permutation
• Combination and its properties (without proof)

4.3 The Binomial Theorem

• Binomial theorem (without proof)
• Expansion of binomial expressions, general terms, middle terms, and terms free from variables
• Expansion of binomial expression for any index
• Expansion of exponential and logarithmic functions (without proof)

5.1 Straight Lines

• Three standard forms of a line, general form: ax + by + c = 0
• The line through the intersection of two lines, concurrency of lines, area of triangle
• Angle between two lines, bisector of angle between two lines, length of perpendicular from a point on a line

5.2 Pair of Lines

• Homogeneous equation of second degree
• General equation of second degree representing two lines
• Angle between a pair of lines and bisectors of the angles for a line pair (without proof)
• Condition for general equation of second degree to represent a line pair (without proof)
• Lines joining the origin to the points of intersection of a curve and a line

5.3 The Circle

• Standard and central forms
• General and Diameter forms (without proof)
• Tangent and normal to the circle
• Condition of tangency of a straight line to a circle (without proof)

• Thapa et al., Engineering Mathematics (Volume I, Three Years Diploma), Sukunda Pustak Bhawan
• Bajracharya et al., Basic Mathematics (Grade XI/XII), Sukunda Pustak Bhawan
• Nath et al., Engineering Mathematics I, Vidhyarthi Publisher and distributors
• Other references selected by the related lecturer(s) that meet the content of this subject.