Vectors and Basic Mathematics
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Everything a batch would cover. Scan the 16 parts, then read into the one that’s yours.
Elementary Algebra
- common formulae
- polynomial linear and quadratic equations
- binomial theorem and expansion
Elementary Trigonometry
- angles and systems of measurement
- four quadrants and sign conventions
- limits of trigonometric ratios
- graphs of sine and cosine
- important trigonometric formulae
- reduction formulae for general angles
- inverse trigonometric functions
- sine and cosine rules for triangles
Basic Coordinate Geometry
- origin and axes
- position of a point
- distance formula
- slope of a line
- straight line equations
- dependent and independent variables
- plotting velocity–time relations
Parabola and Quadratic Equations
- shape of the parabola and physics applications
Differentiation
- limit of a function
- derivative of a function
- graphical representation of derivative
- defining instantaneous velocity and acceleration
- properties of derivatives
- derivatives of power sine and cosine
- product rule
- quotient rule
- chain rule
- double differentiation
- applications of derivative in physics
- maximum and minimum values
Elementary Integration
- integration as inverse of differentiation
- standard formulae for integration
- definite integral
- algebraic method to evaluate definite integral
- properties of definite integral
- substitution method
- geometrical significance
Applications of Integration
- deriving equations of motion by calculus
- graphical interpretation of integration
Vectors and Scalars
- definitions and distinction
Representation of Vectors
- notation and geometric representation
Addition of Vectors
- triangle law
- parallelogram law
- polygon law
- subtraction of vectors
- properties of vector addition
Analytical Method of Vector Addition
- magnitude and direction of the resultant
Unit Vectors
- i j k notation and use
Components of a Vector
- rectangular x and y components
- writing a vector from its components
- rectangular components in three dimensions
- addition of vectors by means of components
- direction cosines
Position and Displacement Vectors
- definitions and applications
Scalar (Dot) Product
- definition and properties
- dot product of unit vectors
Vector (Cross) Product
- definition and properties
- cross product of unit vectors and physical applications
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- 59 subtopics
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A teacher who doesn’t fully own a chapter teaches it half-convincingly, and you absorb the hesitation.
Learn it from someone who owns it, and you absorb their certainty instead.Usually taken before this one
- Class 10 mathematics