1. Introduction to mathematical logic and set theory - statement, proposition, logical connectives, quantifiers, necessary and sufficient conditions, set operations, number sets, intervals.
2. Real sequences – basic concepts, properties, arithmetic and geometric sequence and their application.
3. Real sequences – limit of a sequence, improper limit of a sequence, definition of Euler's number e.
4. Function of a single real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing).
5. Function of a single real variable – inverse functions, elementary functions, graph of a function and its transformation, points of intersection.
6. Function of a single real variable – continuous function, limit of a function at a point, properties of limits, one-sided limits.
7. Function of a single real variable – improper limit of a function, limit of a funciton at infinity, properties of continuous functions.
8. Function of a single real variable – derivative of a function, slope of a tangent line at a point, equation of a tangent line and normal line to a curve at a point, differentiation techniques, higher order derivatives.
9. Function of a single real variable - differential of a function, Rolle's and Lagrange'S Theorem, l'Hospital's Theorem, Taylor and Maclaurin polynomial.
10. Function of a single real variable - monotonoic function, local and global extrema of a function.
11. Function of a single real variable – convex and concave function, inflexion points, asymptotes - horizontal, vertical, oblique.
12. Linear algebra – matrix, matrix operation, rank of a matrix.
13. Linear algebra – determinant of a matrix, properties of determinant, Sarrus' scheme, Laplace's formula, inverse matrix, matrix equations.
14. Linear algebra – vector, vector operation, linearly independent vectors, vector spaces, inner product of vectors, length of a vector.
2. Real sequences – basic concepts, properties, arithmetic and geometric sequence and their application.
3. Real sequences – limit of a sequence, improper limit of a sequence, definition of Euler's number e.
4. Function of a single real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing).
5. Function of a single real variable – inverse functions, elementary functions, graph of a function and its transformation, points of intersection.
6. Function of a single real variable – continuous function, limit of a function at a point, properties of limits, one-sided limits.
7. Function of a single real variable – improper limit of a function, limit of a funciton at infinity, properties of continuous functions.
8. Function of a single real variable – derivative of a function, slope of a tangent line at a point, equation of a tangent line and normal line to a curve at a point, differentiation techniques, higher order derivatives.
9. Function of a single real variable - differential of a function, Rolle's and Lagrange'S Theorem, l'Hospital's Theorem, Taylor and Maclaurin polynomial.
10. Function of a single real variable - monotonoic function, local and global extrema of a function.
11. Function of a single real variable – convex and concave function, inflexion points, asymptotes - horizontal, vertical, oblique.
12. Linear algebra – matrix, matrix operation, rank of a matrix.
13. Linear algebra – determinant of a matrix, properties of determinant, Sarrus' scheme, Laplace's formula, inverse matrix, matrix equations.
14. Linear algebra – vector, vector operation, linearly independent vectors, vector spaces, inner product of vectors, length of a vector.