- Real numbers, Sequences, Series, Power Series, Limit, Continuity, Differentiability, Mean Value Theorems and applications.
- Linear approximation, Newton and Picard method, Trapezoidal and Simpsonʹs rule, Error bounds.
- Taylorʹs theorem (one variable), Approximation by polynomials, Critical points, Convexity, Curve tracing.
- Riemann integral, Fundamental theorems of integral calculus, Improper integrals.
- Space coordinates, Lines and planes, Polar coordinates, Graphs of Polar equations, Cylinders, Quadric Surfaces, Volume, Area, Length.
- Continuity, Differentiability of vector functions, Arc Length, Curvature, Torsion, Serret‐Frenet formulas.
- Functions of two or more variables, Partial derivatives. Statement (only) of Taylorʹs theorem for a function of two variables. Criteria for maxima/minima/saddle points. Applications of maxima/minima for functions of two variables.
- Multiple integrals: Double, Triple integrals, Fubini’s theorem, Jacobians, Surface integrals, Vector calculus, Green, Gauss and Stokes theorem.
You can download the syllabus below in .pdf format:
Syllabus