Mathematics for Architecture II

Syllabus

1. Vector Algebra and Calculus (10 hours)
   1. Two and three dimensional vectors
   2. Scalar products and vector products of three and four vectors
   3. Reciprocal system of vectors
   4. Vector differentiation and integration: velocity and acceleration
   5. Directional derivative and gradient
   6. Divergence and curl
2. Matrices and their Applications (10 hours)
   1. Algebra of matrices
   2. Rank of matrices and its application in system of linear equations
   3. Vector space, linear dependence and independence
   4. Linear transformations
   5. Eigen value, Eigen vectors and Cayley-Hamilton theorem with applications
3. Statistics (10 hours)
   1. Measure of central tendency: mean, median and mode
   2. Measure of partition: range, inter quartile range, quartiles, deciles and percentiles
   3. Measures of dispersion: mean deviation, standard deviation
   4. Correlation and regression
   5. Measures of skewness and kurtosis
4. Probability (10 hours)
   1. Review of basic probability
   2. Conditional probability, Bayes' theorem
   3. Random variable and probability distribution
   4. Binomial and Poisson's distribution
5. Mensuration (5 hours)
   1. Area of regular polygon, area of irregular rectilinear figures, field book
   2. Estimation of area using trapezoidal rule and Simpson's rule